Wie finden Sie das Integral von # sin ^ 3 (x) cos ^ 2 (x) dx #?

#I = int sin^3xcos^2xdx = int sin^2xcos^2xsinxdx#
#I = int (1-cos^2x)cos^2xsinxdx#
#cosx=t => -sinxdx=dt => sinxdx=-dt#

#I = int (1-t^2)t^2(-dt) = int (t^4-t^2)dt = t^5/5-t^3/3+C#

#I = 1/5cos^5x-1/3cos^3x+C#