Answer
$\coth (5-x) +C$
Work Step by Step
Given: $\int csch^2(5-x) dx$
This can be re-written as: $\int csch^2(5-x) dx=\int csch^2(x-5) dx$
Plug in $x-5=t$ and $dx =dt$
Thus, $\int csch^2(5-x) dx=\int csch^2 t dt=-\coth t +C$
or, $= -\coth (x-5) +C$
or, $=\coth (5-x) +C$
