Indefinite Integration

\(\log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|+c\), where \(\mathrm{c}\) is a constant of integration.

\(\log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|-\frac{1}{1+x \mathrm{e}^x}+\mathrm{c}\), where c is a constant of integration.

\(\log \left|1+x \mathrm{e}^x\right|+\frac{1}{1+x \mathrm{e}^x}+\mathrm{c}\), where \(\mathrm{c}\) is constant of integration.

\(\log \left|\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right|+\frac{1}{1+x \mathrm{e}^x}+\mathrm{c}\), where \(\mathrm{c}\) is constant of integration.