Optimal. Leaf size=18 \[ e^{-3-\frac {1}{3} e^4 \log (x)+\log ^2(\log (4))} \]
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Rubi [A]
time = 0.03, antiderivative size = 19, normalized size of antiderivative = 1.06, number of steps
used = 3, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {12, 2234}
\begin {gather*} x^{-\frac {e^4}{3}} e^{\log ^2(\log (4))-3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2234
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{3} \int \frac {\exp \left (4+\frac {1}{3} \left (-9-e^4 \log (x)+3 \log ^2(\log (4))\right )\right )}{x} \, dx\right )\\ &=-\left (\frac {1}{3} \text {Subst}\left (\int e^{4+\frac {1}{3} \left (-9-e^4 x+3 \log ^2(\log (4))\right )} \, dx,x,\log (x)\right )\right )\\ &=e^{-3+\log ^2(\log (4))} x^{-\frac {e^4}{3}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.06 \begin {gather*} e^{-3+\log ^2(\log (4))} x^{-\frac {e^4}{3}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 19, normalized size = 1.06
method | result | size |
gosper | \({\mathrm e}^{\ln \left (2 \ln \left (2\right )\right )^{2}-\frac {{\mathrm e}^{4} \ln \left (x \right )}{3}-3}\) | \(19\) |
derivativedivides | \({\mathrm e}^{\ln \left (2 \ln \left (2\right )\right )^{2}-\frac {{\mathrm e}^{4} \ln \left (x \right )}{3}-3}\) | \(19\) |
default | \({\mathrm e}^{\ln \left (2 \ln \left (2\right )\right )^{2}-\frac {{\mathrm e}^{4} \ln \left (x \right )}{3}-3}\) | \(19\) |
norman | \({\mathrm e}^{\ln \left (2 \ln \left (2\right )\right )^{2}-\frac {{\mathrm e}^{4} \ln \left (x \right )}{3}-3}\) | \(19\) |
risch | \(x^{-\frac {{\mathrm e}^{4}}{3}} \ln \left (2\right )^{2 \ln \left (2\right )} {\mathrm e}^{\ln \left (2\right )^{2}-3+\ln \left (\ln \left (2\right )\right )^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 16, normalized size = 0.89 \begin {gather*} e^{\left (-\frac {1}{3} \, e^{4} \log \left (x\right ) + \log \left (2 \, \log \left (2\right )\right )^{2} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 16, normalized size = 0.89 \begin {gather*} e^{\left (-\frac {1}{3} \, e^{4} \log \left (x\right ) + \log \left (2 \, \log \left (2\right )\right )^{2} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 19, normalized size = 1.06 \begin {gather*} \frac {1}{x^{\frac {e^{4}}{3}} e^{3 - \log {\left (2 \log {\left (2 \right )} \right )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 16, normalized size = 0.89 \begin {gather*} e^{\left (-\frac {1}{3} \, e^{4} \log \left (x\right ) + \log \left (2 \, \log \left (2\right )\right )^{2} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.67, size = 29, normalized size = 1.61 \begin {gather*} \frac {2^{2\,\ln \left (\ln \left (2\right )\right )}\,{\mathrm {e}}^{{\ln \left (2\right )}^2}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{{\ln \left (\ln \left (2\right )\right )}^2}}{x^{\frac {{\mathrm {e}}^4}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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