# How do you integrate #int cos^3xsinxdx#?

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To integrate ( \int \cos^3(x) \sin(x) , dx ), you can use the substitution method.

Let ( u = \cos(x) ), then ( du = -\sin(x) , dx ).

This means ( \sin(x) , dx = -du ).

Substituting ( u ) and ( du ) into the integral:

[ \int \cos^3(x) \sin(x) , dx = \int -u^3 , du ]

Now, integrate ( -u^3 ) with respect to ( u ):

[ \int -u^3 , du = -\frac{1}{4}u^4 + C ]

Finally, resubstitute ( \cos(x) ) for ( u ):

[ -\frac{1}{4}\cos^4(x) + C ]

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