Euler substitution

Euler substitution is a method for evaluating integrals of the form

$${\displaystyle \int R(x,{\sqrt {ax^{2}+bx+c}})\,dx,}$$

where ${\displaystyle R}$ is a rational function of ${\displaystyle x}$ and ${\textstyle {\sqrt {ax^{2}+bx+c}}}$. It is proved that these integrals can always be rationalized using one of three Euler substitutions.