# Integrate

• Apr 28th 2009, 03:00 PM
treetheta
Integrate
\int{e^{x^2}}\,dx

I really don't know where to go with this

mchalurin series?
• Apr 28th 2009, 04:18 PM
skeeter
Quote:

Originally Posted by treetheta
\int{e^{x^2}}\,dx

I really don't know where to go with this

mchalurin series?

maclaurin series ... yes.
• Apr 28th 2009, 06:38 PM
treetheta
so would it be

$\displaystyle \begin{array}{l} {e^x} = \sum\limits_{n = 0}^\infty {\frac{{{x^n}}}{{n!}}} \\ {e^{{x^2}}} = \sum\limits_{n = 0}^\infty {\frac{{{{({x^2})}^n}}}{{n!}}} \\ \end{array}$
• Apr 28th 2009, 07:28 PM
mr fantastic
Quote:

Originally Posted by treetheta
so would it be

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

Yes.
• Apr 28th 2009, 07:29 PM
treetheta
How would I intergrate both sides though o.o
• Apr 28th 2009, 07:37 PM
mr fantastic
Quote:

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 $\displaystyle e^{x^2}$ has no elementary primitive. After expressing $\displaystyle e^{x^2}$ as a series, you integrate the series term-by-term.
• Apr 28th 2009, 07:50 PM
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?
• Apr 28th 2009, 07:54 PM
mr fantastic
Quote:

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.