I have been working out some cases where I can't integrate through trigonometric substitutions (or at least, not easily) but I can using hyperbolic functions. See if you can solve
$ \int x^2\sqrt{x^2+1}dx $
Special points if you can solve it using trig functions.
The method and thought process
Why couldn't you substitute x^2+1 for u and say x^2 = u-1. then, distribute and just use the power rule. There is no need for trig substitution for this.
