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Integrate (2x^2+1)e^x^2dx ( Wow, seriously?)

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Integrate: (2x^2+1)e^x^2dx

    2. Relevant equations

    3. The attempt at a solution

    I don't even know where to start , I either got to do this by basic substitution or by parts. Basic substitution doesn't help for obvious reasons, so I thought I'd do it by parts, but that would get completely messed up based upon the e^x^2 not having any anti-derivative, so I'd need basic substitution to get rid of it.

    I thought of making:

    u = e^x^2
    ln|u| = x^2
    √ln|u| = x
    du = 2xe^x^2 dx

    Therefore, my equation would be:

    (2ln|u| + 1)/(2√[ln|u|]) du

    Then I thought about breaking that up:

    integrate: (2ln|u|)/(2√[ln|u|]) + 1/(2√[ln|u|])

    Simplified to...

    (ln|u|)/(√[ln|u|]) + 1/(2√[ln|u|])

    Annnndd... now I'm stuck again because that square root is basically the most evilest thing on the entire planet. It limits partial fractions, I can't exactly do trig substitution, and the fraction kills by parts.
  2. jcsd
  3. Feb 10, 2010 #2
    Expand out the brackets of the integrand to get two terms, then try to do by parts on the first term only. Hint: [tex]dv = 2x e^{x^2}dx[/tex].
    Last edited: Feb 10, 2010
  4. Feb 10, 2010 #3
    huh... This looks a lot simpler than my way... Lets see if I can finish it :P
  5. Feb 10, 2010 #4
    Huh, wow... Thanks, I didn't even THINK about being able to cancel the integrals that result.
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