Calculate $\int_{0}^{\pi/2} (\sin(2x))^5 dx$ I want to calculate the following integral: 
$$\int_{0}^{\pi/2} (\sin(2x))^5 dx$$I tried integration by parts but it didn't work for me. Suggestions?

$$\dfrac{d(\sin^nax\cos ax)}{dx}=an\sin^{n-1}ax(1-\sin^2ax)-a\sin^{n+1}x$$
Integrate both sides with respect to $x,$
$$\sin^nax\cos ax=anI_{n+1}-a(n+1)I_{n+1}$$
where $$I_n=\int\sin^max\ dx$$
Set $n+1=5,3,1$ one by one
