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I dont know the code for exponential

  1. Jan 3, 2006 #1
    [tex]\int \ell^{x^2} x^2 dx [/tex]

    [tex] = 1/2 \int \ell^{x^2} x^2 d(x^2) [/tex]
    [tex] = 1/2 \int \ell^{t} . t dt [/tex] (Let x^2 = t )
    [tex] = 1/2 [t.\ell^{t} - \int \ell^{t} dt] [/tex]
    [tex] = 1/2 [t.\ell^{t} - \ell^{t} + c ] [/tex]
    [tex] = 1/2 [x^2 \ell^{x^2} - \ell^{x^2} + c] [/tex]

    [tex]\ell[/tex] is actually exponential. I dont know the code for exponential. :)
    What`s the problem with the above integration I have done?
    Last edited: Jan 3, 2006
  2. jcsd
  3. Jan 3, 2006 #2
    Well you set [tex] t= x^2 [/tex] but you don't have [tex]d(x^2)[/tex] in the original integral, just integrate by parts you don't really have to make a substitution.
  4. Jan 4, 2006 #3


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    The error lies in line #2, you are changing dx into d(x2), that requires an x, that'll left you with:
    [tex]\frac{1}{2} \int x e ^ {x ^ 2} d(x ^ 2)[/tex] not [tex]\frac{1}{2} \int x ^ 2 e ^ {x ^ 2} d(x ^ 2)[/tex]. Or you can do a little bit more slowly by letting t = x2. Just try it, and see if you can get to:
    [tex]\frac{1}{2} \int x e ^ {x ^ 2} d(x ^ 2)[/tex].
    From here, you can do the same and end up with:
    [tex]\frac{1}{2} \int x e ^ {x ^ 2} d(x ^ 2) = \frac{1}{2} \int x d(e ^ {x ^ 2})[/tex].
    From here, do you know what to do next?
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