Question

How do you find the antiderivative of `sin^3(x) cos^2(x) dx`?

Answer 1

`= - 1/3 cos^3 x + 1/5cos^5 x + C`

Explanation:

`int \ sin^3 x \ cos^2 x \ dx`

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

`= int \ sin x \ cos^2 x - sin x cos^4 x \ dx`

`= int \ ( - 1/3 cos^3 x)^' - ( -1/5cos^5 x)^' \ dx`

`= - 1/3 cos^3 x + 1/5cos^5 x + C`