Question

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

Answer 1

`sin x- 1/3 sin^3x + C`

Explanation:

`\int cos^3 x \ dx = = \int cosx(cos^2x) \ dx= \int cosx(1-sin^2x) \ dx` and that's pretty much it

because

`\int cosx(1-sin^2x) \ dx`

`= \int cosx- cosx sin^2x \ dx`

`= sin x- 1/3 sin^3x + C`