Optimal. Leaf size=11 \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
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Rubi [A] time = 0.0018481, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2204} \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
Antiderivative was successfully verified.
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Rule 2204
Rubi steps
\begin{align*} \int e^{x^2} \, dx &=\frac{1}{2} \sqrt{\pi } \text{erfi}(x)\\ \end{align*}
Mathematica [A] time = 0.0017681, size = 11, normalized size = 1. \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 8, normalized size = 0.7 \begin{align*}{\frac{{\it erfi} \left ( x \right ) \sqrt{\pi }}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] time = 0.926658, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{2} i \, \sqrt{\pi } \operatorname{erf}\left (i \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.02875, size = 30, normalized size = 2.73 \begin{align*} \frac{1}{2} \, \sqrt{\pi } \operatorname{erfi}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.231137, size = 8, normalized size = 0.73 \begin{align*} \frac{\sqrt{\pi } \operatorname{erfi}{\left (x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] time = 1.08518, size = 12, normalized size = 1.09 \begin{align*} \frac{1}{2} i \, \sqrt{\pi } \operatorname{erf}\left (-i \, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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