γ,Γ\gamma,\Gamma-day Problem 2

Calculus Level 5

0x6e3x2dx\large \int_0^{\infty}\frac{x^6}{e^{3x^2}}\,dx

The integral above can be written as aπb4cd/2\dfrac{a\sqrt{\pi}}{b^4\cdot c^{d/2}}, where aa, bb, cc, and dd are prime numbers.

Find a+b+c+da+b+c+d.


This is problem for Daily challenge of Greek letters.

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