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Integration by Partial Fractions

What euler's ...

Question

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

\pm \sqrt{b} x, a > o

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\pm \sqrt{a^{3}} x, a > o

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\pm \sqrt{a} x, a > o

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None of these

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Solution

The correct option is C $\pm \sqrt{a} x, a > o$
Given : $\sqrt{a x^{2} + b x + c}$
If the coefficient of $x^{2}$ is greater than zero
i.e. If $(a > 0)$ The outer substitution first is applied
$\pm \sqrt{a} x, a > 0$
Hence the correct answer is $\pm \sqrt{a} x, a > 0$

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