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 ${\textstyle {\sqrt {ax^{2}+bx+c}}}$. In such cases, the integrand can be changed to a rational function by using the substitutions of Euler.[1]