Euler substitution

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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]