Optimal. Leaf size=18 \[ x \text {erf}(x)+\frac {e^{-x^2}}{\sqrt {\pi }} \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, 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*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \[ x \text {erf}(x)+\frac {e^{-x^2}}{\sqrt {\pi }} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 20, normalized size = 1.11 \[ \frac {\pi x \operatorname {erf}\relax (x) + \sqrt {\pi } e^{\left (-x^{2}\right )}}{\pi } \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 15, normalized size = 0.83 \[ x \operatorname {erf}\relax (x) + \frac {e^{\left (-x^{2}\right )}}{\sqrt {\pi }} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 16, normalized size = 0.89 \[ x \erf \relax (x )+\frac {{\mathrm e}^{-x^{2}}}{\sqrt {\pi }} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 15, normalized size = 0.83 \[ x \operatorname {erf}\relax (x) + \frac {e^{\left (-x^{2}\right )}}{\sqrt {\pi }} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 15, normalized size = 0.83 \[ \frac {{\mathrm {e}}^{-x^2}}{\sqrt {\pi }}+x\,\mathrm {erf}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 15, normalized size = 0.83 \[ x \operatorname {erf}{\relax (x )} + \frac {e^{- x^{2}}}{\sqrt {\pi }} \]
Verification of antiderivative is not currently implemented for this CAS.
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