求不定积分∫sin(3x)sin(5x)dx,求详细过程~
问题描述：
求不定积分∫sin(3x)sin(5x)dx,求详细过程~
答
sin(3x)sin(5x)
=sin(4x-x)sin(4x+x)
=(sin4xcosx-cos4xsinx)*(sin4xcosx+cos4xsinx)
= sin^4x-sin^x
=(1-cos8x)/2-(1-cosx)/2
=(cos2x-cos8x)/2
所以∫sin(3x)sin(5x)dx=sin2x/4-sin8x/16+C