Chapter 6.10, Problem 108E

(a)

To determine

To show: The statement ${\displaystyle \int \mathrm{csch}x}dx={\displaystyle \int \frac{2du}{\sinh 2u}}$ is true

(b)

To determine

To show The statement $\frac{2}{\sinh 2u}=\frac{{\mathrm{sech}}^{2}u}{\tanh u}$ is true.

(c)

To determine

The value of indefinite integral ${\displaystyle \int \frac{{\mathrm{sech}}^{2}u}{\tanh u}du}$.