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

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Answer 1 · 2016-07-05T21:02:46

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

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

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

Let $u = sinx implies du = cosxdx$

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

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