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Integration by Partial Fractions

What euler su...

Question

What euler substitutions must be used in integrals of the form: $\sqrt{a x^{2} + b x + c}$

\pm (x + x_{1})

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\pm (- x - 2 x_{1})

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\pm (x - x_{1})

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None of these

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Solution

The correct option is C $\pm (x - x_{1})$
Given : $\sqrt{a x^{2} + b x + c}$
If the roots of the equation are real
$\sqrt{a x^{2} + b x + c} = \sqrt{a (x - x_{1}) (x - x_{2})}$
Then outer third substitution is applied.
i.e. $\pm (x - x_{1})$

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