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How do you find the antiderivative of #cos^3 x#?

1 Answer

Jul 5, 2016

#int cos^3x dx = sinx - 1/3sin^3x + C#

Explanation:

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

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

Let #u = sinx implies du = cosxdx#

#int (1-u^2)du = u - 1/3u^3 + C = sinx - 1/3sin^3x + C#

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