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    Integral from 0 to Infinity

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    Show that the

    integral from 0 to infinity of (t^n e^-t dt) = n!

    © BrainMass Inc. brainmass.com March 4, 2021, 5:59 pm ad1c9bdddf
    https://brainmass.com/math/integrals/integral-infinity-22445

    Solution Preview

    By parts,
    I = integral(0 to inf)[t^n e^-t dt]
    = {-t^n e^(-t)}(U=inf, L=0) + n*integration(0 to inf)[t^(n-1) e^(-t) dt]
    Here, U = upper limit = ...

    Solution Summary

    This is how to show a given integral is a factorial.

    $2.49

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