small question: integral e^(2x^2) dx
- Thread starter spoon3457
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These types of 'e' integrals are difficult to integrate. As pka said, not by elementary means, i.e. parts, u-substitution, etc.
This can be done, but by other means, such as asymptotic series, error function, complex analysis, etc.
Anyway, I ran it through Maple and here's what she gave me:
\(\displaystyle \L\\\int{e^{4x^{2}}}dx=\frac{1}{4}\frac{\sqrt{\pi}erf(2\sqrt{-ln(e)})}{\sqrt{-ln(e)}}\)
I don't know why it displayed \(\displaystyle \sqrt{-ln(e)}\) instead of \(\displaystyle \sqrt{-1}=i\)
erf=error function
This can be done, but by other means, such as asymptotic series, error function, complex analysis, etc.
Anyway, I ran it through Maple and here's what she gave me:
\(\displaystyle \L\\\int{e^{4x^{2}}}dx=\frac{1}{4}\frac{\sqrt{\pi}erf(2\sqrt{-ln(e)})}{\sqrt{-ln(e)}}\)
I don't know why it displayed \(\displaystyle \sqrt{-ln(e)}\) instead of \(\displaystyle \sqrt{-1}=i\)
erf=error function