Optimal. Leaf size=16 \[ e^{-\frac {1}{9+\frac {4 \log (x)}{3}}} x \]
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Rubi [F] time = 0.37, 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*} \int \frac {e^{-\frac {3}{27+4 \log (x)}} \left (741+216 \log (x)+16 \log ^2(x)\right )}{729+216 \log (x)+16 \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-\frac {3}{27+4 \log (x)}} \left (741+216 \log (x)+16 \log ^2(x)\right )}{(27+4 \log (x))^2} \, dx\\ &=\int \left (e^{-\frac {3}{27+4 \log (x)}}+\frac {12 e^{-\frac {3}{27+4 \log (x)}}}{(27+4 \log (x))^2}\right ) \, dx\\ &=12 \int \frac {e^{-\frac {3}{27+4 \log (x)}}}{(27+4 \log (x))^2} \, dx+\int e^{-\frac {3}{27+4 \log (x)}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 14, normalized size = 0.88 \begin {gather*} e^{-\frac {3}{27+4 \log (x)}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 13, normalized size = 0.81 \begin {gather*} x e^{\left (-\frac {3}{4 \, \log \relax (x) + 27}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.29, size = 30, normalized size = 1.88 \begin {gather*} x^{\frac {247}{9 \, {\left (4 \, \log \relax (x) + 27\right )}}} e^{\left (\frac {4 \, \log \relax (x)^{2}}{4 \, \log \relax (x) + 27} - \frac {1}{9}\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 = 0.88
method | result | size |
risch | \(x \,{\mathrm e}^{-\frac {3}{4 \ln \relax (x )+27}}\) | \(14\) |
norman | \(\frac {\left (27 x +4 x \ln \relax (x )\right ) {\mathrm e}^{-\frac {3}{4 \ln \relax (x )+27}}}{4 \ln \relax (x )+27}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 13, normalized size = 0.81 \begin {gather*} x e^{\left (-\frac {3}{4 \, \log \relax (x) + 27}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {{\mathrm {e}}^{-\frac {3}{4\,\ln \relax (x)+27}}\,\left (16\,{\ln \relax (x)}^2+216\,\ln \relax (x)+741\right )}{16\,{\ln \relax (x)}^2+216\,\ln \relax (x)+729} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.13, size = 10, normalized size = 0.62 \begin {gather*} x e^{- \frac {3}{4 \log {\relax (x )} + 27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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