Change of Variables and Integration by Parts

Calculus Level 4

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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