How do you find the antiderivative of #((2x)e^(3x))#?

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Integration byTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. TheTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by partsTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formulaTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts isTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integrationTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a techniqueTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by partsTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique basedTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts isTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on theTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the productTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\intTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule forTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int uTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiationTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. TheTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formulaTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula forTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integrationTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv -To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration byTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by partsTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int vTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts isTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du\To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int uTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du).To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). InTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In thisTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this caseTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, youTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv -To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you canTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \intTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( uTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \int v \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \int v ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \int v , duTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

[ \int u , dv = uv - \int v , du \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

InTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In thisTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) andTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this caseTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, letTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = eTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( uTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x}To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dxTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) andTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ).To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). ThenTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = eTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiateTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( uTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) toTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to findTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dxTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( duTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ).To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). ThenTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) andTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, weTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrateTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiateTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) toTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) toTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to findTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to findTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( vTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( duTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). AfterTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), andTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After findingTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrateTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( duTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dvTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) andTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv )To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to findTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( vTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( vTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), youTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can useTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use theTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integrationTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ duTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration byTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du =To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by partsTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula toTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 ,To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find theTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivativeTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ vTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \fracTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)eTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)e^{To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3}To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)e^{3xTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3} eTo find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)e^{3x}To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3} e^{To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)e^{3x} \To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3} e^{3To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. The formula for integration by parts is (\int u , dv = uv - \int v , du). In this case, you can let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). After finding ( du ) and ( v ), you can use the integration by parts formula to find the antiderivative of ( (2x)e^{3x} ).To find the antiderivative of ( (2x)e^{3x} ), you can use integration by parts. Integration by parts is a technique based on the product rule for differentiation. The formula for integration by parts is:

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

In this case, let ( u = 2x ) and ( dv = e^{3x} , dx ). Then, we differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ).

[ du = 2 , dx ] [ v = \frac{1}{3} e^{3x} ]

Now, we apply the integration by parts formula:

[ \int (2x)e^{3x} , dx = (2x) \left( \frac{1}{3} e^{3x} \right) - \int \frac{1}{3} e^{3x} \cdot 2 , dx ]

[ = \frac{2x}{3} e^{3x} - \frac{2}{3} \int e^{3x} , dx ]

The integral ( \int e^{3x} , dx ) is a straightforward integration:

[ \int e^{3x} , dx = \frac{1}{3} e^{3x} ]

Putting it all together:

[ \int (2x)e^{3x} , dx = \frac{2x}{3} e^{3x} - \frac{2}{9} e^{3x} + C ]

Where ( C ) is the constant of integration.