Question

大一高数～求不定积分∫sin3xsin5xdx

Answer 1

须知公式：sinAsinB = (1/2)[cos(A-B)-cos(A+B]∫sin(3x)sin(5x) dx= (1/2)∫[cos(-2x)-cos(8x)] dx= (1/2)∫cos2x dx - (1/2)∫cos8x dx= (1/4)∫cos2x d(2x) - (1/16)∫cos8x d(8x)= (1/4)sin2x - (1/16)sin8x + C

追问

3扣。。

Answer 2

积化和差
∫sin3xsin5xdx
=∫{-1/2[cos(3x 5x)-cos(5x-3x)]}dx
=-1/2(∫cos8xdx-∫cos2xdx)
-1/16∫cos8xd(8x) 1/4∫cos2xd(2x)
=1/4sin2x-1/16sin8x C