Find the anti-derivative for ex1e2xdx\displaystyle \int\frac{{{e}^{{x}}}}{\sqrt{{{1}-{e}^{{{2}{x}}}}}}{\left.{d}{x}\right.}=  

Evaluate the definite integral 90ex1e2xdx\displaystyle {\int_{{-{9}}}^{{{0}}}}\frac{{{e}^{{x}}}}{\sqrt{{{1}-{e}^{{{2}{x}}}}}}{\left.{d}{x}\right.}=