Optimal. Leaf size=18 \[ x \text{Erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }} \]
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Rubi [A] time = 0.0053284, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {6349} \[ x \text{Erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }} \]
Antiderivative was successfully verified.
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Rule 6349
Rubi steps
\begin{align*} \int \text{erf}(x) \, dx &=\frac{e^{-x^2}}{\sqrt{\pi }}+x \text{erf}(x)\\ \end{align*}
Mathematica [A] time = 0.0066766, size = 18, normalized size = 1. \[ x \text{Erf}(x)+\frac{e^{-x^2}}{\sqrt{\pi }} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \begin{align*} x{\it Erf} \left ( x \right ) +{\frac{{{\rm e}^{-{x}^{2}}}}{\sqrt{\pi }}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928914, size = 20, normalized size = 1.11 \begin{align*} x \operatorname{erf}\left (x\right ) + \frac{e^{\left (-x^{2}\right )}}{\sqrt{\pi }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.80279, size = 51, normalized size = 2.83 \begin{align*} \frac{\pi x \operatorname{erf}\left (x\right ) + \sqrt{\pi } e^{\left (-x^{2}\right )}}{\pi } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.307698, size = 15, normalized size = 0.83 \begin{align*} x \operatorname{erf}{\left (x \right )} + \frac{e^{- x^{2}}}{\sqrt{\pi }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07719, size = 20, normalized size = 1.11 \begin{align*} x \operatorname{erf}\left (x\right ) + \frac{e^{\left (-x^{2}\right )}}{\sqrt{\pi }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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