Optimal. Leaf size=19 \[ \frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x^2 \]
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Rubi [A] time = 0.02, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 1586, 30} \begin {gather*} \frac {1}{9} x^2 e^{\frac {e^{39/16}}{\log (3)}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 1586
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx\\ &=2 \int \frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x \, dx\\ &=\frac {1}{9} \left (2 e^{\frac {e^{39/16}}{\log (3)}}\right ) \int x \, dx\\ &=\frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{9} \, x^{2} e^{\left (\frac {e^{\frac {39}{16}}}{\log \relax (3)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.67, size = 13, normalized size = 0.68 \begin {gather*} \frac {1}{9} \, x^{2} e^{\left (\frac {e^{\frac {39}{16}}}{\log \relax (3)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.74
method | result | size |
norman | \(\frac {{\mathrm e}^{\frac {{\mathrm e}^{\frac {39}{16}}}{\ln \relax (3)}} x^{2}}{9}\) | \(14\) |
risch | \(\frac {{\mathrm e}^{\frac {{\mathrm e}^{\frac {39}{16}}}{\ln \relax (3)}} x^{2}}{9}\) | \(14\) |
gosper | \({\mathrm e}^{\frac {\ln \relax (3) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \relax (3)}}\) | \(19\) |
derivativedivides | \({\mathrm e}^{\frac {\ln \relax (3) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \relax (3)}}\) | \(19\) |
default | \({\mathrm e}^{\frac {\ln \relax (3) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \relax (3)}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (\frac {\log \relax (3) \log \left (\frac {1}{9} \, x^{2}\right ) + e^{\frac {39}{16}}}{\log \relax (3)}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.68 \begin {gather*} \frac {x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{39/16}}{\ln \relax (3)}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.74 \begin {gather*} \frac {x^{2} e^{\frac {e^{\frac {39}{16}}}{\log {\relax (3 )}}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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