Question

sin^6(x) integration

Answer 1

sin^6(x) = (sin^2(x))^3

sin^2(x) = (1 - cos(2x))/2

expand the polynomial.

after expanding: remember that cos^2(x) = (1 + cos(2x))/2 and that to integrate sin^3(x):

you'll look at it as sin(x)*(1 - cos^2(x)) , taking u = cos(x)