# "I am Back" says Integration Part 8

Calculus Level 5

$\large \int_{-\infty}^{\infty}{xe^{nx}e^{-e^{2x}} \, dx }$

For positive constant $$n$$, the above integral can be expressed as $\dfrac{a}{b} \Gamma{\left( \dfrac{n}{c} \right)} \psi{\left( \dfrac{n}{d} \right)},$

where $$a,b,c$$ and $$d$$ are positive integers with $$a,b$$ coprime. Find $$a \times b \times c \times d$$.

Notations:

×