Integrate

**treetheta** · April 28th 2009, 03:00 PM

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

I really don't know where to go with this

mchalurin series?

**skeeter** · April 28th 2009, 04:18 PM

Originally Posted by treetheta

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

I really don't know where to go with this

mchalurin series?

maclaurin series ... yes.

**treetheta** · April 28th 2009, 06:38 PM

so would it be

$\begin{array}{l} {e^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} \\ {e^{{x^2}}} = \sum\limits_{n = 0}^\infty {\frac{{{{({x^2})}^n}}}{{n!}}} \\ \end{array} $

**mr fantastic** · April 28th 2009, 07:28 PM

Originally Posted by treetheta

so would it be

$\begin{array}{l} {e^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} \\ {e^{{x^2}}} = \sum\limits_{n = 0}^\infty {\frac{{{{({x^2})}^n}}}{{n!}}} \\ \end{array}$

Yes.

**treetheta** · April 28th 2009, 07:29 PM

How would I intergrate both sides though o.o

**mr fantastic** · April 28th 2009, 07:37 PM

Originally Posted by treetheta

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.

**treetheta** · April 28th 2009, 07:50 PM

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?

**mr fantastic** · April 28th 2009, 07:54 PM

Originally Posted by treetheta

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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