How to integrate csc^2(x)cot(x)?

To integrate csc^2(x)cot(x), use u-substitution with u = csc(x).

To integrate csc^2(x)cot(x), we can use u-substitution with u = csc(x). This means that du/dx = -csc(x)cot(x)dx, which can be rearranged to give -du = csc(x)cot(x)dx. Substituting this into the integral gives:

∫csc^2(x)cot(x)dx = ∫-u^-2du

Integrating this gives:

∫csc^2(x)cot(x)dx = u^-1 + C

Substituting back in for u gives:

∫csc^2(x)cot(x)dx = csc(x) + C

Therefore, the integral of csc^2(x)cot(x) is csc(x) + C.