JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{e^{x-1}+x^{e-1}}{e^x+x^e} d x

is equal to

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because by substituting

t = e^x + x^e

, the integral simplifies to

\frac{1}{e} \int \frac{dt}{t}

, which integrates to

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

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