$\huge \int \frac{4\cosh\!\left(5x\right)}{\sinh\!\left(5x\right)} \, \d x $ $\huge \begin{align} \let u &= \sinh(5x) \\ \let \d u&= \frac{1}{5} \cosh(5x)\d x\\ \\ \int \frac{4\cosh\!\left(5x\right)}{\sinh\!\left(5x\right)} \, \d x &= \frac{4}{5} \int u^{-1}\d u\\ &=\frac{4}{5} \ln|u|+C\\ &= \frac{4}{5} \ln|\sinh(5x)| \end{align} $