Question

How do you integrate `int cosxsqrtsinx` using substitution?

Answer 1

Let `u = sinx`. Then `du = cosxdx` and `dx = (du)/cosx`.

`=int(cosxsqrt(u))/cosx du`

`=sqrt(u) du`

`= u^(1/2) du`

`=2/3u^(3/2) + C`

`=2/3(sinx)^(3/2) + C`

`=2/3sqrt(sin^3x) + C`

`=2/3sinxsqrt(sinx) + C`

Hopefully this helps!