Lesser-known integration tricks I am currently studying for the GRE math subject test, which heavily tests calculus. I've reviewed most of the basic calculus techniques (integration by parts, trig substitutions, etc.) I am now looking for a list or reference for some lesser-known tricks or clever substitutions that are useful in integration. For example, I learned of this trick 
$$\int_a^b f(x) \, dx = \int_a^b f(a + b -x) \, dx$$
in the question Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even 
I am especially interested in tricks that can be used without an excessive amount of computation, as I believe (or hope?) that these will be what  is useful for the GRE.

I really like the so-called Schwinger trick that is based on identities like the following: 
$$ \frac{1}{\alpha^\nu}=\frac{1}{\Gamma(\nu)}\int^{\infty}_{0} \tau^{\nu-1}\mathrm{e}^{-\alpha \tau}\mathrm{d}\tau.$$
This technique is very useful, as you can see here.
