# How will you solve this?

Calculus Level 5

$\large \displaystyle \int_0 ^ \infty e^{-x^2} \ln(x)\ \mathrm{d}x = -\dfrac{A}{B}\left( \gamma^C +D\ln(D) \right)\pi^E$

If the above equation is true for positive integers $$A,B,C,D$$, where $$A,B$$ are coprime to each other and $$D$$ isn't any $$m^{th}$$ power of a positive integer with $$m \in \mathbb Z,\ m \geq 2$$.

Submit the value of $$A+B+C+D+2E$$ as your answer.

Note: $$\gamma$$ is the Euler-Mascheroni Constant defined as:

$\large \gamma =\lim_{n \rightarrow \infty} \left(\displaystyle \sum_{k=1} ^{n} \dfrac{1}{k} -\ln(n) \right)$

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