Question

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

Answer 1

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

Explanation:

`I = int sin^3xcos^2xdx = int sin^2xcos^2xsinxdx`
`I = int (1-cos^2x)cos^2xsinxdx`
`cosx=t => -sinxdx=dt => sinxdx=-dt`

`I = int (1-t^2)t^2(-dt) = int (t^4-t^2)dt = t^5/5-t^3/3+C`

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