Smart Integration Tricks I am in the last year of my school 
and studied integration this year 
I have done several Integration techniques like Integration


*

*By substitution

*By partial fractions

*By parts

*Trigo. substitutions

*Tangent half angle substitution
and many other basic methods of integration.


So I wanted to ask about some integration tricks that might prove quite helpful.
Not something advanced which is taught at higher level of studies 
But some smart integration tricks at school level only.

Another neat trick is to add different forms of integrals to obtain a much simpler one.
For example, if we let a function $f$ be such that $f(x)f(-x)=1$ and we want to evaluate $$I=\int_{-1}^1\frac1{1+f(x)}\,dx$$ then we could replace $x$ by $-x$ giving $$I=-\int_1^{-1}\frac1{1+f(-x)}\,dx=\int_{-1}^1\frac{f(x)}{1+f(x)}\,dx$$ and adding gives $$2I=\int_{-1}^1\,dx=2\implies I=1.$$
