In my solution book it says
Let
How do you figure what to use as substitution
I'm too lazy to type this out, so here's a picture.
In the circled part, how do they get from that trig expression to that?
Go this website
Type in the exact expression: integrate dx/sqrt[x^2 + a^2]
Click the equal sign at the end. What do you get?
Ckick the show steps button.