Question 1:

I find the following integral formula from "Table of integrals" but I do not

know how to derive it.

$\displaystyle

\int^{\infty}_{0} \frac{\ln (x)}{\cosh^2(x)} dx = \psi(\frac{1}{2}) + \ln(\pi),

$

where $\displaystyle \psi $ is the Digamma function.

Question 2:

How to get the answer for the slightly modifed integral:

$\displaystyle

\int^{\infty}_{0} \frac{\ln (x)}{\cosh^2(x+a)} dx = ?

$