Question

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

Answer 1

`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`