JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \mathrm{e}^{\tan ^{-1} \mathrm{x}}\left(1+\mathrm{x}+\mathrm{x}^2\right) \mathrm{d}\left(\cot ^{-1} \mathrm{x}\right)=

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Correct option: C

-x e^{\tan ^{-1} x}+c

Option C (

-x e^{\tan ^{-1} x}+c

) is correct because after applying integration by parts, the integral simplifies to this expression.

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