∫csc x cot^2 x dx
= ∫csc x (csc^2 x -1) dx
= ∫csc^3 x dx - ∫csc x dx
You probably have handy the form for ∫csc x dx, and you can use the power reduction formulas for ∫csc^3 x dx, or note that
d/dx (cscx cotx) = -csc^3 x - csc x cot^2 x
∫csc x cot^2 xdx
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