Change of Variables and Integration by Parts

Calculus Level 4

We know that 0etdt=1 \displaystyle \int_0^\infty e^{-t} \, dt = 1 and 0et2dt=π2 \large\displaystyle \int_0^\infty e^{-t^2} \, dt =\dfrac{\sqrt \pi}2 . What is the value of 0et1/5dt\large \displaystyle \int_0^\infty e^{-t^{1/5}} \, dt ?

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