How to integrate csc^4(x)cot(x)?

To integrate csc^4(x)cot(x), use the substitution u = csc(x) and simplify.

To integrate csc^4(x)cot(x), start by using the substitution u = csc(x). This gives:

du/dx = -csc(x)cot(x) dx
dx = -du/(csc(x)cot(x))

Substituting this into the original integral gives:

∫csc^4(x)cot(x) dx = ∫-u^4 du

Integrating this gives:

= -u^5/5 + C

Substituting back in for u gives:

= -csc^5(x)/5 + C

Therefore, the final answer is:

∫csc^4(x)cot(x) dx = -csc^5(x)/5 + C