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 = ?
$