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Integration Problem

  1. Nov 10, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex] \int_{0}^{\infty}x^3.e^{-x^2} \mathrm{d}x [/tex]

    3. The attempt at a solution

    I have tried substitution u=x^2, u=x^3; integration by parts; squeeze theorem; partial fraction decomp; taylor series expansion- but nothing seems to work. I know the limit of [tex]x^3.e^{-x^2}[/tex] as x tends to infinity is zero, but that doesn't help.
    Any help please?
     
  2. jcsd
  3. Nov 10, 2007 #2
    That should work.
     
  4. Nov 10, 2007 #3
    Well, ok.

    Let u = x^2 , then: du = 2x.dx. And then what? We have an x^3 in the integration, so I don't see how it works.
     
  5. Nov 10, 2007 #4
    But x3 = x.x2, isn't it?
     
  6. Nov 10, 2007 #5
    Yes, but then we would have:

    [tex]x^2.e^{-u}.du[/tex] or am I missing something?
     
  7. Nov 10, 2007 #6
    You just did the sub u=x^2 a couple of steps ago.
     
  8. Nov 10, 2007 #7
    AHA!!! Oh thank-you neutrino! I can't believe I never saw that! Gee, I feel like an idiot! Thank-you again!
     
  9. Nov 10, 2007 #8
    You're welcome. Make a hobby out of solving integrals (if you're into those kind of things), and you'll start recognising the methods with just a look at the integral. (For some of them, at least. :biggrin:)
     
  10. Nov 10, 2007 #9
    Actually I quite dislike calculus. I find it dry and boring. Or atleast that's the way my first year course presents it. But I guess you are right, I need to do more calculus problems if I want to be a mathematician :tongue:, which I do.
     
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