Question

Evaluate the integral.
from 0 to π/2
sin^3(θ)cos^5(θ) dθ

Answer 1

The way this is done is to express everything in terms of sin or cos:

sin^3(θ)cos^5(θ) dθ
= sin^3θ cos^4θ cosθ dθ
= sin^3θ (1-sin^2θ)^2 cosθ dθ
Now let
u=sinθ
du = cosθ dθ
and you have

u^3 (1-u^2)^2 du

and it's a cinch...