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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
∫  (x+1)x(1+xex)2  dx\int \,\,\frac{{\left( {x + 1} \right)}}{{x{{\left( {1 + x{e^x}} \right)}^2}}}\,\,dx is
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Correct option: A
log⁡  (xexxex+1)  +  11+xex  +  c\log \,\,\left( {\frac{{x{e^x}}}{{x{e^x} + 1}}} \right)\,\, + \,\,\frac{1}{{1 + x{e^x}}}\,\, + \,\,c
Option A is correct because the integral simplifies to a logarithmic form plus a rational term after substitution and partial fraction decomposition.

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