S (sin 5x) (sin 3x) dx =

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S (sin 5x) (sin 3x) dx =
S (sin 5x) (sin 3x) dx =

S (sin 5x) (sin 3x) dx =
∫(sin5x)(sin3x)dx
=∫1/2[cos(5x - 3x) - cos(5x + 3x)]dx
=1/2 ∫[cos2x - cos8x]dx
=1/2∫cos2xdx-1/2∫cos8xdx
=1/2*1/2∫cos2xd2x-1/2*1/8∫cos8xd8x
=1/4*sin2x-1/16*sin8x+C
C为任意常数
利用到了:sina*sinb=1/2[cos(a-b)-cos(a+b)]
和积分公式:∫cosxdx=sinx+C

∫(sin5x)(sin3x)dx = ∫1/2[cos(5x - 3x) - cos(5x + 3x)]dx = 1/2 ∫[cos2x - cos8x]dx = 1/2sin2x - (1/16sin8x) + C