Question

\[\int\limits \frac{\csc ^{2}(\frac{1}{x})}{x ^{2}}dx\]

Answer 1

let 1/x = u see what happens
probably you get answer in cot

Answer 2

From what @experimentX said
\(u = \frac{1}{x} = x^{-1}\)
\(du = (-1)x^{-2} \ \ dx \ \rightarrow \ -du = x^{-2} \ \ dx\)

See of you can find du hidden up there ;-)