Evaluate $\int{\frac{e^{2x}} {\sqrt{1-e^x}}}\ dx$ Evaluate  $$\displaystyle\int{\frac{e^{2x}} {\sqrt{1-e^x}}}\ dx.$$
I tried to solve by using integration by parts, but I couldn't find a solution. What method should I use to integrate this?

$$
\int\frac{e^x}{\sqrt{1-e^x}}\underbrace{\Big(e^x \, dx\Big)}_{\text{HINT}}
$$
After that substitution (the one that is hinted at), use another substitution, namely a rationalizing substitution.
