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Write this integral in terms of gamma function

  1. Mar 17, 2015 #1

    So I'm self studying mary boas's mathematical methods book and I've come across this integral:

    \int _{0}^{\infty }e^{-x^4}dx

    and I'm suppose to write this using the gamma function. The hint given states to let x^4 = u. And the answer is:

    \Gamma \left( \dfrac {5} {4}\right)

    I tried substituting u = x^4 and du = 4x^3dx, but that doesn't give the correct answer.

    I'm a bit confused as to how the book got that answer. Any ideas would be great.

  2. jcsd
  3. Mar 17, 2015 #2
    After substitution you should have something you can express as ## t \Gamma(t) ## which you can rewrite using the relation ## t\Gamma(t) = \Gamma(t+1)##.
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