I was solving an integral, but I am not quite sure for the final answer. If someone has the time, just take a look.

Integral from 0 to pi/2 of (x*[sin x]^2)dx

I used by parts integration; using u=(sinx)^2 du=2 sinx cosx

dv = x v = x^2/2

I used once more by parts integration and I got as a final answer pi/24.

I need some advice.

Thank you