integral from 3pie/4 to pie/2 of (sinx)^5 (cosx)^3dx
Hello,
Note that $\displaystyle \cos^3x=\cos^2x\cos x=\cos x(1-\sin^2 x)$
So :
$\displaystyle \int_{3 \pi/4}^{\pi / 2} \sin^5x\cos^3x ~dx=\int_{3 \pi/4}^{\pi/2} \cos x \sin^5x (1-\sin^2x) ~dx$
$\displaystyle =\int_{3 \pi/4}^{\pi/2}\cos x\sin^5x ~dx-\int_{3 \pi/4}^{\pi/2} \cos x \sin^7x ~dx$
Substitute $\displaystyle t=\sin(x)$ in each of the integrals and you're done.