积分号sin2x乘以cos3xdx

∫sin2x*cos3xdx
=∫1/2(sin(2x+3x)+sin(2x-3x))dx
=1/2∫sin5xdx-1/2∫sinxdx
=1/2*1/5∫sin5xd5x-1/2cosx
=1/10cos5x-1/2cosx+c

积化和差即可

∫sin2x*cos3xdx
=2∫sinxcosxcos(2x+x)dx
=2∫sinxcosx(cos2xcosx-sin2xsinx)dx
=2∫sinxcosx(2cosxcosxcosx-cosx-2sinxsinxcosx)dx
=4∫[sinx(cosx)^5-sinx(cosx)^2-sinx(1-cosxcosx)cosxcosx]dx
=-4(cosx)^6/6+4(cosx)^3/3+4(cosx)^3/3-4(cosx)^5/5+C
=2(cosx)^3-(4/5)(cosx)^5+C