Question

Integrals:

Answer 1

http://prntscr.com/3d8fbj

Answer 2

sub \(u = \tan^{-1}(5x)\)

Answer 3

I would say the same thing, but it feels a little more obvious to say it as: \[5x=\tan \theta\] since I just seem to have a natural affinity for the trig substitution. From there it sort of seems obvious how to get rid of the inverse tan. But whatevs!