(adsbygoogle = window.adsbygoogle || []).push({}); Does Apostol ever introduce "Trig Substitutions"?

I took Calculus before, but I am going over Apostol's Calculus Vol. 1 book. In section 5.7 he introduces Integration by Substitution, but never really discusses what was commonly referred to as "Trig Substitutions" in my Calc classes. For instance, #16 in section 5.8 is

[itex]\int(x^2+1)^{\frac{-3}{2}}dx[/itex]

Now I know (from my previous class) that I can solve this by letting [itex]x=tan\theta[/itex], but Apostol never introduced this notion. More importantly, to properly solve it in terms of [itex]x[/itex] I will need to use [itex]arctan[/itex], which isn't introduced until section 6. Just wondering if there's a way to solve it without using trig substitutions.

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# Homework Help: Does Apostol ever introduce Trig Substitutions ?

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