sin²2xsin3x的积分

sin^2xsin3x
=0.5(1-cos4x)sin3x
=0.5 sin3x-0.5sin3xcos4x
=0.5sin3x-0.25 (sin7x-sinx)
I= -1/6 cos3x + 1/28 cos7x- 1/4 cosx +C

这个先降次，然后在积化和差

sin^2(2x)=(1-cos4x)/2
sin^2(2x)sin3x=(1-cos4x)/2*sin3x=1/2*(sin3x-sin3xcos4x)=1/2(sin3x-1/2(sin7x+sin(-x))=1/2sin3x-1/4sin7x+1/4sinx
所以,积分sin^2(2x)sin3xdx=-1/2*1/3cos3x+1/4*1/7cos7x-1/4cosx+C
=-1/6cos3x+1/28cos7x-1/4cosx+C