A calculus problem by Kïñshük Sïñgh

Calculus Level 4

\[\int _{ \infty }^{ 0 }{ \frac { x{ e }^{ -x } }{ \sqrt { 1-{ e }^{ -2x } } } } \, dx = \, ? \]

Clarification: The lower limit is indeed \(\infty\), and not \( -\infty\).