How to integrate csc^2(x)cot^3(x)?

To integrate csc^2(x)cot^3(x), use u-substitution with u = cot(x) and du = -csc^2(x)dx.

Integrating csc^2(x)cot^3(x) can be done using u-substitution. Let u = cot(x) and du = -csc^2(x)dx. Then the integral becomes:

∫csc^2(x)cot^3(x)dx = ∫-u^3du

Integrating -u^3 gives:

= -1/4u^4 + C

Substituting back in for u:

= -1/4cot^4(x) + C

Therefore, the final answer is:

∫csc^2(x)cot^3(x)dx = -1/4cot^4(x) + C