∫(cot^2 x/sin^2 x)dx=?

∫(cotx)^2/ (sinx)^2 dx
= ∫(cotx)^2(cscx)^2dx
=-∫ (cotx)^2 d(cotx)
= - (cotx)^3/3 + C

原式=∫cot²xcsc²xdx
=-∫cot²x(-csc²x)dx
=-∫cot²xdcotx
=-cot³x/3+C

原式=∫[(cscx)^2-1]/(sinx)^2 dx
=∫[(cscx)^2]/(sinx)^2 dx - ∫1/(sinx)^2 dx
=∫1/(sinx)^4 dx - ∫1/(sinx)^2 dx
=∫(cscx)^4 dx - ∫(cscx)^2 dx
设t=cotx
dt=-(cscx)^2dx
(cscx)^2=-2/(cos2x-1...