Spooky Integrals

Calculus Level 4

Given \[ \prod_{k=1}^3\left[\int_0^\infty x^{-\frac{k}{4}}e^{-(k+1)^4x}\;dx\right]=\frac{\sqrt{a}}{b}\pi^{\frac{c}{d}}, \] what is the value of \(a+b+c+d?\)

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