## University Calculus: Early Transcendentals (3rd Edition)

$\coth (5-x) +C$
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, $=\coth (5-x) +C$