Evaluate : (1+x) x (1+x e^ x )^ 2 d x
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Evaluate : \(\int \frac{(1+x)}{x\left(1+x e^{x}\right)^{2}} d x\)
- \(\ln \left(\frac{\mathrm{xe}^{\mathrm{x}}}{1+\mathrm{xe}^{\mathrm{x}}}\right)+\frac{1}{1+\mathrm{xe}^{\mathrm{x}}}+\mathrm{c}\)
- \(\ln \left(\frac{1+\mathrm{xe}^{\mathrm{x}}}{\mathrm{xe}^{\mathrm{x}}}\right)+\frac{1}{\mathrm{xe}^{\mathrm{x}}+1}+\mathrm{c}\)
- \(\ln \left(\frac{\mathrm{xe}^{\mathrm{x}}}{\mathrm{xe}^{\mathrm{x}}+1}\right)-\frac{1}{\mathrm{xe}^{\mathrm{x}}+1}+\mathrm{c}\)
- None of these
Answer
(A) ( xe ^ x 1+ xe ^ x )+ 1 1+ xe ^ x + c
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