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Math Help - Integrate

  1. #1
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    Integrate

    \int{e^{x^2}}\,dx

    I really don't know where to go with this

    mchalurin series?
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  2. #2
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    Quote Originally Posted by treetheta View Post
    \int{e^{x^2}}\,dx

    I really don't know where to go with this

    mchalurin series?
    maclaurin series ... yes.
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  3. #3
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    so would it be

    \begin{array}{l}<br />
 {e^x} = \sum\limits_{n = 0}^\infty  {\frac{{{x^n}}}{{n!}}}  \\ <br />
 {e^{{x^2}}} = \sum\limits_{n = 0}^\infty  {\frac{{{{({x^2})}^n}}}{{n!}}}  \\ <br />
 \end{array}<br /> <br /> <br /> <br />
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  4. #4
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    Quote Originally Posted by treetheta View Post
    so would it be

    \begin{array}{l}<br />
{e^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} \\<br />
{e^{{x^2}}} = \sum\limits_{n = 0}^\infty {\frac{{{{({x^2})}^n}}}{{n!}}} \\<br />
\end{array}
    Yes.
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  5. #5
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    How would I intergrate both sides though o.o
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  6. #6
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    Quote Originally Posted by treetheta View Post
    How would I intergrate both sides though o.o
    Where has this question come from?

    I assumed from your first post that you realise that e^{x^2} has no elementary primitive. After expressing e^{x^2} as a series, you integrate the series term-by-term.
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  7. #7
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    calculus final exam

    isn't there an easier way to do it than term by term what would the nth term in the series be?
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  8. #8
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    Quote Originally Posted by treetheta View Post
    calculus final exam

    isn't there an easier way to do it than term by term what would the nth term in the series be?
    Write the first few terms out, spot the pattern.
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