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How do you find the antiderivative of #sin^3(x) cos^2(x) dx#?

1 Answer

May 3, 2018

#= - 1/3 cos^3 x + 1/5cos^5 x + C#

Explanation:

#int \ sin^3 x \ cos^2 x \ dx#

#int \ sin x( 1- cos^2 x) \ cos^2 x \ dx#

#= int \ sin x \ cos^2 x - sin x cos^4 x \ dx#

#= int \ ( - 1/3 cos^3 x)^' - ( -1/5cos^5 x)^' \ dx#

#= - 1/3 cos^3 x + 1/5cos^5 x + C#

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