Optimal. Leaf size=7 \[ e^{x^2} x \]
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Rubi [A]
time = 0.01, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2235, 2243}
\begin {gather*} e^{x^2} x \end {gather*}
Antiderivative was successfully verified.
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Rule 2235
Rule 2243
Rubi steps
\begin {align*} \int \left (e^{x^2}+2 e^{x^2} x^2\right ) \, dx &=2 \int e^{x^2} x^2 \, dx+\int e^{x^2} \, dx\\ &=e^{x^2} x+\frac {1}{2} \sqrt {\pi } \text {erfi}(x)-\int e^{x^2} \, dx\\ &=e^{x^2} x\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 7, normalized size = 1.00 \begin {gather*} e^{x^2} x \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.66, size = 7, normalized size = 1.00 \begin {gather*} x E^{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 7, normalized size = 1.00
method | result | size |
gosper | \({\mathrm e}^{x^{2}} x\) | \(7\) |
default | \({\mathrm e}^{x^{2}} x\) | \(7\) |
norman | \({\mathrm e}^{x^{2}} x\) | \(7\) |
risch | \({\mathrm e}^{x^{2}} x\) | \(7\) |
meijerg | \(\frac {\erfi \left (x \right ) \sqrt {\pi }}{2}+i \left (-i x \,{\mathrm e}^{x^{2}}+\frac {i \erfi \left (x \right ) \sqrt {\pi }}{2}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 6, normalized size = 0.86 \begin {gather*} x e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 6, normalized size = 0.86 \begin {gather*} x e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 5, normalized size = 0.71 \begin {gather*} x e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 37, normalized size = 5.29 \begin {gather*} -\frac {\sqrt {\pi } \mathrm {erf}\left (-\mathrm {i} x\right )}{\mathrm {i}\cdot 2}+2 \left (\frac {1}{2} x \mathrm {e}^{x^{2}}+\frac {\sqrt {\pi } \mathrm {erf}\left (-\mathrm {i} x\right )}{2 \mathrm {i}\cdot 2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 6, normalized size = 0.86 \begin {gather*} x\,{\mathrm {e}}^{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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