Integrand size = 29, antiderivative size = 19 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x^2 \]
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Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 1600, 30} \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {1}{9} x^2 e^{\frac {e^{39/16}}{\log (3)}} \]
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Rule 12
Rule 30
Rule 1600
Rubi steps \begin{align*} \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{align*}
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {1}{9} e^{\frac {e^{39/16}}{\log (3)}} x^2 \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74
method | result | size |
norman | \(\frac {{\mathrm e}^{\frac {{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}} x^{2}}{9}\) | \(14\) |
risch | \(\frac {{\mathrm e}^{\frac {{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}} x^{2}}{9}\) | \(14\) |
gosper | \({\mathrm e}^{\frac {\ln \left (3\right ) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}}\) | \(19\) |
derivativedivides | \({\mathrm e}^{\frac {\ln \left (3\right ) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}}\) | \(19\) |
default | \({\mathrm e}^{\frac {\ln \left (3\right ) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}}\) | \(19\) |
parallelrisch | \({\mathrm e}^{\frac {\ln \left (3\right ) \ln \left (\frac {x^{2}}{9}\right )+{\mathrm e}^{\frac {39}{16}}}{\ln \left (3\right )}}\) | \(19\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {1}{9} \, x^{2} e^{\left (\frac {e^{\frac {39}{16}}}{\log \left (3\right )}\right )} \]
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Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {x^{2} e^{\frac {e^{\frac {39}{16}}}{\log {\left (3 \right )}}}}{9} \]
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Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=e^{\left (\frac {\log \left (3\right ) \log \left (\frac {1}{9} \, x^{2}\right ) + e^{\frac {39}{16}}}{\log \left (3\right )}\right )} \]
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {1}{9} \, x^{2} e^{\left (\frac {e^{\frac {39}{16}}}{\log \left (3\right )}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {2 e^{\frac {e^{39/16}+\log (3) \log \left (\frac {x^2}{9}\right )}{\log (3)}}}{x} \, dx=\frac {x^2\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{39/16}}{\ln \left (3\right )}}}{9} \]
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