Optimal. Leaf size=20 \[ x^{\frac {2}{3} e^{-\left (\frac {3}{4}+e^5\right )^2} x} \]
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Rubi [F]
time = 0.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} e^{-\frac {1}{16} \left (3+4 e^5\right )^2} \int x^{\frac {2}{3} e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} (2+2 \log (x)) \, dx\\ &=e^{-\frac {1}{16} \left (3+4 e^5\right )^2} \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} (2+2 \log (3 x)) \, dx,x,\frac {x}{3}\right )\\ &=e^{-\frac {1}{16} \left (3+4 e^5\right )^2} \text {Subst}\left (\int 2\ 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} (1+\log (3 x)) \, dx,x,\frac {x}{3}\right )\\ &=\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} (1+\log (3 x)) \, dx,x,\frac {x}{3}\right )\\ &=\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int \left (3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x}+3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} \log (3 x)\right ) \, dx,x,\frac {x}{3}\right )\\ &=\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} \, dx,x,\frac {x}{3}\right )+\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} \log (3 x) \, dx,x,\frac {x}{3}\right )\\ &=\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} \, dx,x,\frac {x}{3}\right )-\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2}\right ) \text {Subst}\left (\int \frac {\int 3^{2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2} x} x^{2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2} x} \, dx}{x} \, dx,x,\frac {x}{3}\right )+\left (2 e^{-\frac {1}{16} \left (3+4 e^5\right )^2} \log (x)\right ) \text {Subst}\left (\int 3^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} x^{2 e^{\frac {1}{16} \left (-9-24 e^5-16 e^{10}\right )} x} \, dx,x,\frac {x}{3}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 22, normalized size = 1.10 \begin {gather*} x^{\frac {2}{3} e^{-\frac {1}{16} \left (3+4 e^5\right )^2} x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.18, size = 19, normalized size = 0.95
method | result | size |
risch | \(x^{\frac {2 x \,{\mathrm e}^{-{\mathrm e}^{10}-\frac {3 \,{\mathrm e}^{5}}{2}-\frac {9}{16}}}{3}}\) | \(19\) |
norman | \({\mathrm e}^{x \,{\mathrm e}^{-{\mathrm e}^{10}-\frac {3 \,{\mathrm e}^{5}}{2}-\frac {9}{16}} \ln \left (x^{\frac {2}{3}}\right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 16, normalized size = 0.80 \begin {gather*} x^{\frac {2}{3} \, x e^{\left (-e^{10} - \frac {3}{2} \, e^{5} - \frac {9}{16}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 16, normalized size = 0.80 \begin {gather*} x^{\frac {2}{3} \, x e^{\left (-e^{10} - \frac {3}{2} \, e^{5} - \frac {9}{16}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 24, normalized size = 1.20 \begin {gather*} e^{\frac {2 x \log {\left (x \right )}}{3 e^{\frac {9}{16} + \frac {3 e^{5}}{2} + e^{10}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.70, size = 16, normalized size = 0.80 \begin {gather*} x^{\frac {2}{3} \, x e^{\left (-e^{10} - \frac {3}{2} \, e^{5} - \frac {9}{16}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.46, size = 16, normalized size = 0.80 \begin {gather*} x^{\frac {2\,x\,{\mathrm {e}}^{-\frac {3\,{\mathrm {e}}^5}{2}-{\mathrm {e}}^{10}-\frac {9}{16}}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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