Optimal. Leaf size=15 \[ e^{x^2} \left (1+x+2 e^8 x\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 1.33, number of steps used = 6, number of rules used = 4, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.148, Rules used = {2226, 2204, 2209, 2212} \begin {gather*} \left (1+2 e^8\right ) e^{x^2} x+e^{x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2204
Rule 2209
Rule 2212
Rule 2226
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{x^2} \left (1+2 e^8\right )+2 e^{x^2} x+2 e^{x^2} \left (1+2 e^8\right ) x^2\right ) \, dx\\ &=2 \int e^{x^2} x \, dx+\left (1+2 e^8\right ) \int e^{x^2} \, dx+\left (2 \left (1+2 e^8\right )\right ) \int e^{x^2} x^2 \, dx\\ &=e^{x^2}+e^{x^2} \left (1+2 e^8\right ) x+\frac {1}{2} \left (1+2 e^8\right ) \sqrt {\pi } \text {erfi}(x)+\left (-1-2 e^8\right ) \int e^{x^2} \, dx\\ &=e^{x^2}+e^{x^2} \left (1+2 e^8\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} e^{x^2} \left (1+x+2 e^8 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 14, normalized size = 0.93 \begin {gather*} e^{\left (x^{2} + \log \left (2 \, x e^{8} + x + 1\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 20, normalized size = 1.33 \begin {gather*} 2 \, x e^{\left (x^{2} + 8\right )} + x e^{\left (x^{2}\right )} + e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 14, normalized size = 0.93
method | result | size |
risch | \(\left (2 x \,{\mathrm e}^{8}+x +1\right ) {\mathrm e}^{x^{2}}\) | \(14\) |
gosper | \({\mathrm e}^{\ln \left (2 x \,{\mathrm e}^{8}+x +1\right )+x^{2}}\) | \(17\) |
norman | \({\mathrm e}^{\ln \left (2 x \,{\mathrm e}^{8}+x +1\right )+x^{2}}\) | \(17\) |
default | \({\mathrm e}^{x^{2}} x +{\mathrm e}^{x^{2}}+{\mathrm e}^{8} \sqrt {\pi }\, \erfi \relax (x )+4 \,{\mathrm e}^{8} \left (\frac {{\mathrm e}^{x^{2}} x}{2}-\frac {\sqrt {\pi }\, \erfi \relax (x )}{4}\right )\) | \(39\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 20, normalized size = 1.33 \begin {gather*} 2 \, x e^{\left (x^{2} + 8\right )} + x e^{\left (x^{2}\right )} + e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.54, size = 13, normalized size = 0.87 \begin {gather*} {\mathrm {e}}^{x^2}\,\left (x+2\,x\,{\mathrm {e}}^8+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 14, normalized size = 0.93 \begin {gather*} \left (x + 2 x e^{8} + 1\right ) e^{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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