∫xcosx/(sinx)^3dx 用分布积分法做

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∫xcosx/(sinx)^3dx 用分布积分法做
∫xcosx/(sinx)^3dx 用分布积分法做

∫xcosx/(sinx)^3dx 用分布积分法做
∫xcosx/(sinx)^3dx =∫x/(sinx)^3dsinx =-1/2∫xd1/(sinx)^2
=-1/2(x/sin^2)+1/2∫1/(sinx)^2dx
后面的就好做了撒

=∫x/sin³xdsinx
=∫x/(-2)d[1/sin²x)]
=(-1/2)∫xd(cscx)
=-(1/2)x*csc²x+(1/2)∫csc²xdx
=-(1/2)x*csc²x-(1/2)cotx+C

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