∫sin3xsinxdx=?

Question

∫sin3xsinxdx=?高数

Answer 1

预备知识
cos(A-B)=cosAcosB+sinAsinB
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)-cos(A+B)=2sinAsinB
∴ sinAsinB=1/2[cos(A-B)-cos(A+B)]

∫sin3xsinxdx

=1/2 ∫(cos2x-cos4x)dx
=1/4 sin2x -1/8 sin8x +C本回答被提问者采纳