Optimal. Leaf size=11 \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
[Out]
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Rubi [A] time = 0.00665885, 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 \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
Antiderivative was successfully verified.
[In] Int[E^x^2,x]
[Out]
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Rubi in Sympy [A] time = 0.486834, size = 8, normalized size = 0.73 \[ \frac{\sqrt{\pi } \operatorname{erfi}{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(x**2),x)
[Out]
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Mathematica [A] time = 0.00213845, size = 11, normalized size = 1. \[ \frac{1}{2} \sqrt{\pi } \text{Erfi}(x) \]
Antiderivative was successfully verified.
[In] Integrate[E^x^2,x]
[Out]
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Maple [A] time = 0.002, size = 8, normalized size = 0.7 \[{\frac{{\it erfi} \left ( x \right ) \sqrt{\pi }}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(x^2),x)
[Out]
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Maxima [A] time = 1.45931, size = 12, normalized size = 1.09 \[ -\frac{1}{2} i \, \sqrt{\pi } \operatorname{erf}\left (i \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237532, size = 9, normalized size = 0.82 \[ \frac{1}{2} \, \sqrt{\pi } \operatorname{erfi}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.288247, size = 8, normalized size = 0.73 \[ \frac{\sqrt{\pi } \operatorname{erfi}{\left (x \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(x**2),x)
[Out]
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GIAC/XCAS [A] time = 0.201048, size = 12, normalized size = 1.09 \[ \frac{1}{2} i \, \sqrt{\pi } \operatorname{erf}\left (-i \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(x^2),x, algorithm="giac")
[Out]