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How do you find the antiderivative of #int sin^3xdx#?

1 Answer

Dec 4, 2016

#int sin^3xdx = (cos^3x)/3-cosx+C#

Explanation:

Note that:

#sin^3x = sin x*sin^2x= sin x (1-cos^2x)#

So:

#int sin^3xdx = int sin x (1-cos^2x)dx = int sin x dx -int cos^2x sinxdx #

But #-sinx dx = d cosx#

#int sin^3xdx = -int d(cosx) +int cos^2x d( cosx ) = (cos^3x)/3-cosx#

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