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QUESTION
What is the integral of ##sin(2x)cos^2(2x)dx##?
##int sin(2x)*cos^2(2x) d x=-1/6cos^3(2x)+C##
##int sin(2x)*cos^2(2x) d x=?##
##"Substitute "u=cos(2x)" ; "d u=-2sin(2x)*d x##
##int sin(2x)*cos^2(2x) d x=-1/2 int u^2*d u##
##"So ;" int u^n d u=1/(n+1)u^(n+1)##
##"Apply "n=2##
##int sin(2x)*cos^2(2x) d x=-1/2*1/3 u^3##
##"Now ;undo substitution"##
##int sin(2x)*cos^2(2x) d x=-1/6cos^3(2x)+C##
