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We know that ∫0∞e−t dt=1 \displaystyle \int_0^\infty e^{-t} \, dt = 1 ∫0∞e−tdt=1 and ∫0∞e−t2 dt=π2 \large\displaystyle \int_0^\infty e^{-t^2} \, dt =\dfrac{\sqrt \pi}2 ∫0∞e−t2dt=2π. What is the value of ∫0∞e−t1/5 dt\large \displaystyle \int_0^\infty e^{-t^{1/5}} \, dt ∫0∞e−t1/5dt?
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