Hi, Ive been stuck on this proof problem for awile and was wondering if anyone has any ideas?

Integral (csc(x)) dx = ? expain how you get the answer.

**For example in Integral (sec(x)) dx:

Integral (Sec(x)) (tan(x) + sec(x)) / (tan(x) + sec(x))) dx =

(sec(x)tan(x) + sec^2(x)) / (tan(x) + sec (x))

Set u= tan(x) + sec(x) du= (sec^2(x) + sec(x)tan(x)) dx

If, Integral sec(x) = Integral (1 / u) = ln(abs(u))

Then, Integral sec(x) = ln(abs(tan(x) + sec(x))) + c

With the csc(x) proof I am stuck trying to find the function equaling one to times it by in the beginning that will lead to the correct answer.