Evaluate the following integrals:

Given, $\int \sec x(\sec x+\tan x) d x$

We know that, $\int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \tan ^{-1} \frac{x}{a}$

By comparison, $a=4$

$=\frac{1}{4} \tan ^{-1} \frac{x}{4}+c$