求sinxsin3x的不定积分?

2个回答

∫ (sinx * sin3x) dx
= (1/2)∫ [cos(x - 3x) - cos(x + 3x)] dx
= (1/2)∫ cos2x dx - (1/2)∫ cos4x dx
= (1/2)(1/2)sin2x - (1/2)(1/4)sin4x + C
= (1/8)(2sin2x - sin4x) + C