The Attempt at a Solution
I've successfully solved this problem by factoring out 1 sinx and changing the sin2x to (1-cos2x then assigning u=cosx and du=-sinx and so on.
What I'm wondering is why does letting u=sin3x in the original integral not work. Then du=3cos2xdx and there is a cos2x in the original integral. Why does this fail? Please and thank you :)