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Integration by Partial Fractions

What euler su...

Question

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

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

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+ x \pm \sqrt{b}, c > o

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+ x \pm \sqrt{c}, c > o

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None of these

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Solution

The correct option is C $+ x \pm \sqrt{c}, c > o$
Given : $\sqrt{a x^{2} + b x + c}$
If constant term of the equation is positive that is $c > 0$
Then outer second substitution is applied
i.e. $+ x \pm \sqrt{c}$
Hence the correct answer is $+ x \pm \sqrt{c}$

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