$\smallint \frac{{1\,\, + \,\,x}}{{x\,\, + \,\,{e^{ - x}}}}\,\,\;dx$ is equal to

$\log \,\,\left| {\,\left( {x\,\, - \,\,{e^{ - x}}} \right)\,} \right| + c$

$\log \,\,\left| {\,\left( {x\,\, + \,\,{e^{ - x}}} \right)\,} \right| + c$

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{{1\,\, + \,\,x}}{{x\,\, + \,\,{e^{ - x}}}}\,\,\;dx

is equal to

View answer and explanation

Correct option: C

\log \,\,\left| {\,\left( {1\,\, + \,\,x{e^x}} \right)\,} \right| + c

Option C (

\log \,|\,(1 + x{e^x})\,| + c

) is correct because by using substitution, the integral simplifies to this logarithmic form.