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 $\large \displaystyle \int_0^\infty e^{-t^{1/5}} \, dt$ ?