How does one integrate $\int \dfrac{du}{(a^2 + u^2)^{3/2}}\ ?$
The table of integrals here: http://teachers.sduhsd.k12.ca.us/abrown/classes/CalculusC/IntegralTablesStewart.pdf
Gives it as: $\frac{u}{a^2 ( a^2 + u^2)^{1/2}}\ .$
I'm getting back into calculus and very rusty. I'd like to be comfortable with some of the proofs behind various fundamental "Table of Integrals" integrals.
Looking at it, the substitution rule seems like the method of choice. What is the strategy here for choosing a substitution? It has a form similar to many trigonometric integrals, but the final result seems to suggest that they're not necessary in this case.