Answer
$\coth (5-x) +C$
Work Step by Step
As we are given that $\int csch^2(5-x) dx$
The given integral can be re-written as follows:$\int csch^2(5-x) dx=\int csch^2(x-5) dx$
Consider $x-5=t \implies dx =dt$
This implies, $\int csch^2(5-x) dx=\int csch^2 t dt=-\coth t +C= -\coth (x-5) +C=\coth (5-x) +C$$
