We know that $\displaystyle \int_0^\infty e^{-t} \, dt = 1$ and $\large\displaystyle \int_0^\infty e^{-t^2} \, dt =\dfrac{\sqrt \pi}2$. What is the value of $\large \displaystyle \int_0^\infty e^{-t^{1/5}} \, dt$?

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