Quick question antiderivative of e^x^2

  • Thread starter meee
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  • #1
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my retarded textbook has this question i need the antiderivate of e^xsquared

and i hav no idea. thanks

ps. should this be in the calculus forum?

i dont really know what calc is?
 
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  • #2
benorin
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The antiderivative of [tex]e^{x^2}[/tex] cannot be expressed using a finite number of elementary functions, however one may use power series to arrive some sort of an answer, as in:

[tex]\int e^{x^2}dx = \int \sum_{n=0}^{\infty}\frac{x^{2n}}{n!} dx = \sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)n!}+C[/tex]​

hence [tex]\sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)n!}+C[/tex] is the most general antiderivative of [tex]e^{x^2}[/tex].

Re: P.S.: If you are asking about anything involving limiting processes such as limits, derivatives, antiderivatives (a.k.a. integrals), etc., that would be calculus (excepting perhaps so-called "end-behavior" of functions which arise in some precalc courses). Hence your question about an antiderivative should indeed be posted in the calculus forum.
 
  • #3
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ok geeez thanks! i didnt think it would be that.. complex , hehe thanks! and now i know what calculus is
 
  • #4
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Also, be careful with exponential notation. e^x^2 is ambiguous because exponentiation is not associative. It could mean

[tex]e^{x^2}[/tex]

OR

[tex](e^x)^2[/tex],

which are completely different.
 
  • #5
VietDao29
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Data said:
Also, be careful with exponential notation. e^x^2 is ambiguous because exponentiation is not associative. It could mean

[tex]e^{x^2}[/tex]

OR

[tex](e^x)^2[/tex],

which are completely different.
Unlike other operations, exponents are evaluated from Right to Left. i.e, if one writes [tex]a ^ {b ^ c}[/tex], it can be taken for granted that it's the same as writing: [tex]a ^ {\left( b ^ c \right)}[/tex]
Other wise, it should be written:
[tex]{\left( a ^ b \right)} ^ c[/tex]
See Special Cases in Order of Operations. :)
 
  • #6
benorin
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yet the terminology e^xsquared was clear, no?
 
  • #7
BobG
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benorin said:
yet the terminology e^xsquared was clear, no?
No. Considering how you asked the question, I would have assumed you meant:

[tex]\int{(e^x)^2}dx[/tex]

which can be solved by u-substitution.
 
  • #8
No. Considering how you asked the question, I would have assumed you meant:

[tex]\int{(e^x)^2}dx[/tex]

which can be solved by u-substitution.

if you are referring to this question, think really hard back to indices laws x^2*x^3=x^5 ( when you multiply you add ) (e^x)^2 =(e^x)(e^x)=(e^2x)

Anti D = (1/k)*(e^2x)+c ( note 2 is K )
(1/2)*(e^2x)+c
 
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