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问题: 这两个不定积分不会啊!!

这是给出的答案但是没看懂,谢谢

解答:

1)x[cos(x/2)]^4dx/(sinx)^3
=x[cos(x/2)^4]dx/[2sin(x/2)cos(x/2)]^3【sin2x=2sinxcosx】
=xcos(x/2)dx/{8[sin(x/2)]^3}
=xcot(x/2)dx/{8[sin(x/2)]^2}【cotx=cosx/sinx】
2)(x+sinx)dx/(1+cosx)
=xdx/(1+cosx)+sinxdx/(1+cosx)【1+cos2x=2(cosx)^2,sin2x=2sinxcosx】
=xdx/{2cos(x/2)]^2}+tan(x/2)dx
=xdtan(x/2)+tan(x/2)dx