求不定积分∫sin2xcos3xdx

Question

如题所述

Answer 1

cos3x=
∫sin2xcos3xdx
=∫1/2(sin(2x+3x)+sin(2x-3x))dx
=1/2∫sin5xdx-1/2∫sinxdx
=1/10∫sin5xd5x+1/2∫dcosx
=(cosx)/2-(cos5x)/10+C