\int{e^{x^2}}\,dx I really don't know where to go with this mchalurin series?
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Originally Posted by treetheta \int{e^{x^2}}\,dx I really don't know where to go with this mchalurin series? maclaurin series ... yes.
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} $
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.
How would I intergrate both sides though o.o
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.
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?
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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