∫cos^4x/sin^3x dx=?

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∫cos^4x/sin^3x dx=?
∫cos^4x/sin^3x dx=?

∫cos^4x/sin^3x dx=?
∫(cosx)^4dx/(sinx^3)=∫(cosx)^3dsinx/sinx^3=(-1/2)∫cosx^3d(1/sinx^2)
=(-1/2)cosx^3/sinx^2-(3/2)∫(1-sinx^2)dx/sinx
=(-1/2)cosx^3/sinx^2-(3/2)cosx+(3/4)ln|(1+cosx)/(1-cosx)|+C
楼上的正负号弄错了

∫(cosx)^4dx/(sinx^3)=∫(cosx)^3dsinx/sinx^3=(-1/2)∫cosx^3d(1/sinx^2)
=(-1/2)cosx^3/sinx^2+(-3/2)∫(sinx^2-1)dx/sinx
=(-1/2)cosx^3/sinx^2+(3/2)cosx+(-3/4)ln|(1+cosx)/(1-cosx)|+C

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