I am stuck in this problem of integrating $e^{x^2}$. I was solving the linear differential equation of second order for damped oscillations in which i got this to solve
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6$e^{x^2}$ or $({e^x})^2$? – Zelos Malum Mar 10 '16 at 07:37
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If you are integrating over the reals, it becomes $-i\sqrt{\pi}$ – Bobson Dugnutt Mar 10 '16 at 07:57
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The integral of the function $f(x)= e^{x^2}$ cannot be expressed in terms of elementary functions.
The integral can be given in terms of the imaginary error function, $\text{erfi}(x)$, which is defined as: $$\text{erfi}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^{x} e^{t^2} dt $$
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