Optimal. Leaf size=11 \[ \frac {1}{2} \sqrt {\pi } \operatorname {Erfi}(x) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \frac {1}{2} \sqrt {\pi } \operatorname {Erfi}(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 7, normalized size = 0.64 \[ \frac {1}{2} \, \sqrt {\pi } \operatorname {erfi}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [C] time = 1.05, size = 9, normalized size = 0.82 \[ \frac {1}{2} i \, \sqrt {\pi } \operatorname {erf}\left (-i \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 8, normalized size = 0.73 \[ \frac {\sqrt {\pi }\, \erfi \relax (x )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.54, size = 9, normalized size = 0.82 \[ -\frac {1}{2} i \, \sqrt {\pi } \operatorname {erf}\left (i \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 0.64 \[ \frac {\sqrt {\pi }\,\mathrm {erfi}\relax (x)}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 8, normalized size = 0.73 \[ \frac {\sqrt {\pi } \operatorname {erfi}{\relax (x )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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