Integrate ∫ xsinxcosx dx

Answer 1

I=∫ xsinxcosx dx (subst. double angle)
=(1/2)∫ xsin(2x) dx
Integrate by parts
I=-(1/4)xcos(2x)+(1/4)∫ cos(2x) dx
=-(1/4)xcos(2x)+(1/8)sin(2x)+C

Answer 2

no