JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{1+x^2}{\sqrt{1-x^2}} d x=

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Correct option: A

\frac{3}{2} \sin ^{-1} x-\frac{1}{2} x \sqrt{1-x^2}+c

Option A is correct because the integral evaluates to

\frac{3}{2} \sin^{-1} x - \frac{1}{2}x \sqrt{1-x^2} + c

after trigonometric substitution and simplification.

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