How do you find the integral of #(x^3)(lnx) dx#?

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TheTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts.To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formulaTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. ThisTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integrationTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involvesTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts isTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosingTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing oneTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one partTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u ,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of theTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dvTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv =To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrandTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv -To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand asTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \intTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( uTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int vTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u )To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v ,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) andTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , duTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and theTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ),To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the otherTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), whereTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part asTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where (To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( uTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dvTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u )To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ).To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) andTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). InTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and (To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In thisTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dvTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this caseTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv )To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, youTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) areTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you wouldTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would letTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functionsTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of (To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( uTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( xTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u =To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \lnTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

ForTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(xTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For thisTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x)To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integralTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) )To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, letTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) andTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let (To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( uTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dvTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u =To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = xTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \lnTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(xTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 ,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x)To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dxTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) )To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ).To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and (To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). ThenTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dvTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv =To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, youTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = xTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiateTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( uTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dxTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) toTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to findTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). ThenTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, findTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du )To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( duTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) andTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrateTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du )To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) andTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( vTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) toTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to findTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

(To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find (To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( duTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( vTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \fracTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ).To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). AfterwardsTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, youTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{xTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can useTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x}To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integrationTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration byTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} ,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by partsTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dxTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

(To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \intTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v =To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int uTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \fracTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u ,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dvTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv =To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uvTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv -To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \intTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v ,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

NowTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , duTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now,To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du \To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, applyTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply theTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

AfterTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integrationTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applyingTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration byTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying thisTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by partsTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formulaTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formulaTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula,To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, youTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

(To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you canTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you can evaluateTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \intTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you can evaluate theTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \int xTo find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you can evaluate the integralTo find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \int x^To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you can evaluate the integral.To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \int x^3To find the integral of ( x^3 \ln(x) ) with respect to ( x ), you can use integration by parts. This method involves choosing one part of the integrand as ( u ) and the other part as ( dv ). In this case, you would let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, you differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Afterwards, you can use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

After applying this formula, you can evaluate the integral.To find the integral of ( x^3 \ln(x) , dx ), you can use integration by parts. The formula for integration by parts is ( \int u , dv = uv - \int v , du ), where ( u ) and ( dv ) are differentiable functions of ( x ).

For this integral, let ( u = \ln(x) ) and ( dv = x^3 , dx ). Then, find ( du ) and ( v ):

( du = \frac{1}{x} , dx )

( v = \frac{1}{4}x^4 )

Now, apply the integration by parts formula:

( \int x^3 \ln(x) , dx = \frac{1}{4}x^4 \ln(x) - \int \frac{1}{4}x^4 \cdot \frac{1}{x} , dx )

Simplify the integral:

( \int \frac{1}{4}x^4 \cdot \frac{1}{x} , dx = \frac{1}{4} \int x^3 , dx )

This integral is straightforward:

( \frac{1}{4} \int x^3 , dx = \frac{1}{4} \cdot \frac{1}{4} x^4 + C )

Combine the terms:

( \frac{1}{4}x^4 \ln(x) - \frac{1}{16}x^4 + C )

So, the integral of ( x^3 \ln(x) , dx ) is ( \frac{1}{4}x^4 \ln(x) - \frac{1}{16}x^4 + C ), where ( C ) is the constant of integration.