# $$\gamma,\Gamma$$-day Problem 2

Calculus Level 5

$\large \int_0^{\infty}\frac{x^6}{e^{3x^2}}\,dx$

The integral above can be written as $$\dfrac{a\sqrt{\pi}}{b^4\cdot c^{d/2}}$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are prime numbers.

Find $$a+b+c+d$$.

This is problem for Daily challenge of Greek letters.

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