$\gamma,\Gamma$ -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 $a+b+c+d$ .

γ,Γ\gamma,\Gammaγ,Γ-day Problem 2