JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int e^x \frac{\left(x^3-x+2\right)}{\left(x^2+1\right)^2} d x=

View answer and explanation

Correct option: B

\frac{(x+1) e^x}{x^2+1}+c

Option C (

e^x\left(\frac{{x+1}}{{x+2}}\right)+c

) is correct because the integral can be expressed in the form

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

, where

f(x) = \frac{{x+1}}{{x+2}}

and its derivative is

\frac{{1}}{{(x+2)^2}}

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f(x)

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f\left(\frac{4}{25}\right)

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{f}\left(\frac{1}{2}\right)=2

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{C}

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