Answer
$-csch(\ln t) +C$
Work Step by Step
Given: $\int \dfrac{csch(\ln t) coth(\ln t) dt}{ t}$
This can be re-written as:$\int \dfrac{csch(\ln t) coth(\ln t) dt}{ t}= \int [csch(\ln t) coth(\ln t)](\dfrac{ dt}{ t})$
Plug $\ln t =a$ and $da= \dfrac{ dt}{ t}$
Thus, $\int [csch(\ln t) coth(\ln t)](\dfrac{ dt}{ t})= \int [(csch a ) (coth a) da]=- csch a +C=-csch(\ln t) +C$
