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 $-\infty$ .