How to integrate csc^3(x)cot(x)?

To integrate csc^3(x)cot(x), use the substitution u = csc(x) and du/dx = -csc(x)cot(x).

Integrating csc^3(x)cot(x) can be done using the substitution u = csc(x). This gives us du/dx = -csc(x)cot(x), which can be rearranged to give -du/csc(x) = cot(x)dx. Substituting these into the integral gives:

∫csc^3(x)cot(x)dx = ∫-u^3du = -1/4csc^4(x) + C

Therefore, the integral of csc^3(x)cot(x) is -1/4csc^4(x) + C.