Optimal. Leaf size=20 \[ e^{x+x \log \left (\frac {x^2}{(9+x) \log ^2(4)}\right )} \]
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Rubi [A] time = 0.29, antiderivative size = 21, normalized size of antiderivative = 1.05, number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6706} \begin {gather*} e^x \left (\frac {x^2}{x+9}\right )^x \log ^{-2 x}(4) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^x \left (\frac {x^2}{9+x}\right )^x \log ^{-2 x}(4)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 21, normalized size = 1.05 \begin {gather*} e^x \left (\frac {x^2}{9+x}\right )^x \log ^{-2 x}(4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 20, normalized size = 1.00 \begin {gather*} e^{\left (x \log \left (\frac {x^{2}}{4 \, {\left (x + 9\right )} \log \relax (2)^{2}}\right ) + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.54, size = 26, normalized size = 1.30 \begin {gather*} e^{\left (x \log \left (\frac {x^{2}}{4 \, {\left (x \log \relax (2)^{2} + 9 \, \log \relax (2)^{2}\right )}}\right ) + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.54, size = 20, normalized size = 1.00
method | result | size |
risch | \(\left (\frac {x^{2}}{4 \left (x +9\right ) \ln \relax (2)^{2}}\right )^{x} {\mathrm e}^{x}\) | \(20\) |
norman | \({\mathrm e}^{x \ln \left (\frac {x^{2}}{4 \left (x +9\right ) \ln \relax (2)^{2}}\right )+x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 26, normalized size = 1.30 \begin {gather*} e^{\left (-2 \, x \log \relax (2) - x \log \left (x + 9\right ) + 2 \, x \log \relax (x) - 2 \, x \log \left (\log \relax (2)\right ) + x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.25, size = 26, normalized size = 1.30 \begin {gather*} {\mathrm {e}}^x\,{\left (\frac {1}{4\,x\,{\ln \relax (2)}^2+36\,{\ln \relax (2)}^2}\right )}^x\,{\left (x^2\right )}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 19, normalized size = 0.95 \begin {gather*} e^{x \log {\left (\frac {x^{2}}{4 \left (x + 9\right ) \log {\relax (2 )}^{2}} \right )} + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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