JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

The value of

I=\int \frac{d x}{\left(a+b x^2\right) \sqrt{b-a x^2}}

, is

View answer and explanation

Correct option: A

\frac{1}{\sqrt{a\left(a^2+b^2\right)}} \tan ^{-1}\left(\frac{x \sqrt{a^2+b^2}}{a \sqrt{b-a x^2}}\right)+C

Option A is correct because the integral evaluates to

\frac{1}{\sqrt{a(a^2+b^2)}} \tan ^{-1}\left(\frac{x \sqrt{a^2+b^2}}{a \sqrt{b-a x^2}}\right)+C

after using a trigonometric substitution and simplification.

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