Find the anti-derivative for ex1+e2xdx\displaystyle \int\frac{{{e}^{{x}}}}{{{1}+{e}^{{{2}{x}}}}}{\left.{d}{x}\right.}=  

Evaluate the definite integral 01/8ex1+e2xdx\displaystyle {\int_{{0}}^{{\text{1/8}}}}\frac{{{e}^{{x}}}}{{{1}+{e}^{{{2}{x}}}}}{\left.{d}{x}\right.}=