# "I am Back" says Integration Part 7

Calculus Level 5

$\large \int_{-\infty}^{\infty} {xe^{3x}e^{-{e}^{2x}} \, dx}$

If the above Integral can be expressed as $\dfrac{{\pi}^{A/2}}{B} \left( C - \gamma - D\ln(E)\right),$

where $$A,B,C,D, E$$ are positive integers, with $$E$$ prime, find $$A+B+C+D+E$$.

Notation: $$\gamma$$ denotes the Euler-Mascheroni constant, $$\displaystyle \gamma = \lim_{n\to\infty} \left( - \ln n + \sum_{k=1}^n \dfrac1k \right) \approx 0.5772$$.

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