# 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

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 don’t know about “lesser known” but many calculus courses pass over hyperbolic functions. Just as the identity $$sin2(t)+cos2(t)=1\sin^2(t)+\cos^2(t)=1$$ allows one to deal with $$1−x21-x^2$$ terms, the identity $$cosh2(t)−sinh2(t)=1\cosh^2(t)-\sinh^2(t)=1$$ allows one to deal with $$1+x21+x^2$$ terms.