Euler substitution

Euler substitution is a method for evaluating integrals of the form

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${\displaystyle f(a)-f(b)=\int _{b}^{a}f'(t)\,dt}$
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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.