I dont know the code for exponential

  • Thread starter frozen7
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  • #1
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[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?
 
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Answers and Replies

  • #2
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frozen7 said:
[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?
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.
 
  • #3
VietDao29
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frozen7 said:
[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?
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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