# A mixed bonanza!

Calculus Level 5

$\large \displaystyle \int_{0}^{\infty}e^{-x^{8}}\cos(x^{8})x^{3}\ln(x)\, dx$ If the integral above can be expressed as $\dfrac{-\pi^{\frac{1}{A}}}{B}\left[ \sqrt{\sqrt{A}+C}\left(\gamma^{C}+\dfrac{D}{A}\ln(A)\right)+\dfrac{\pi^{C}}{E}\sqrt{\sqrt{A}-C}\right]$

with positive integers $$A,B,C,D,E$$ and all fractions are irreducible and $$A$$ being square free, then evaluate $$A+B+C+D+E$$.

 Notation: $$\gamma \approx 0.5772$$ denotes the Euler-Mascheroni constant.

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