JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int e^x\left[\sin ^{-1} \frac{x}{a}+\frac{1}{\sqrt{a^2-x^2}}\right] d x=

View answer and explanation

Correct option: C

e^x \sin ^{-1} \frac{x}{a}+c

Option C is correct because the integral can be expressed in the form

\int e^x [f(x) + f'(x)] dx

, where

f(x) = \sin^{-1}(\frac{x}{a})

and

f'(x) = \frac{1}{\sqrt{a^2 - x^2}}

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