∫(xcosx)/(sinx)^3 dx

来源：学生作业帮助网编辑：作业帮时间：2024/04/27 15:06:01

∫(xcosx)/(sinx)^3 dx
∫(xcosx)/(sinx)^3 dx

∫(xcosx)/(sinx)^3 dx
用分步积分
∫(xcosx)/(sinx)^3 dx
=∫(x)/(sinx)^3 dsinx
=-1/2∫(x) d(1/sin^2x)
=-1/2s/sin^2x+1/2∫1/sin^2xdx
=-1/2s/sin^2x+1/2∫csc^2xdx
=-1/2s/sin^2x-1/2cotx+C

这个没有积分上下限？

∫(xcosx)/(sinx)^3 dx=Sx/(sinx)^3 d(sinx)=-1/2*Sxd(sinx)^(-2)=1/2*Sxd(cscx)^2
=-1/2*x*(cscx)^2+1/2*S(cscx)^2dx
=-1/2*x*(cscx)^2-1/2*cotx+c

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