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Quick question antiderivative of e^x^2

  1. Jul 24, 2006 #1
    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?
    Last edited: Jul 24, 2006
  2. jcsd
  3. Jul 24, 2006 #2


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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.
  4. Jul 24, 2006 #3
    ok geeez thanks! i didnt think it would be that.. complex , hehe thanks! and now i know what calculus is
  5. Jul 24, 2006 #4
    Also, be careful with exponential notation. e^x^2 is ambiguous because exponentiation is not associative. It could mean




    which are completely different.
  6. Jul 24, 2006 #5


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    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. :)
  7. Jul 24, 2006 #6


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    yet the terminology e^xsquared was clear, no?
  8. Jul 25, 2006 #7


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    No. Considering how you asked the question, I would have assumed you meant:


    which can be solved by u-substitution.
  9. Sep 29, 2009 #8
    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 )
    Last edited: Sep 29, 2009
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