Indefinite Integration

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

$\log \left(\frac{x \mathrm{e}^x}{1+x \mathrm{e}^x}\right)+\frac{\mathrm{e}^x}{1+x \mathrm{e}^x}+\mathrm{c}$, where 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

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