Optimal. Leaf size=23 \[ 22-x+\log \left (2+\frac {1}{4} \left (3+e^x-\frac {2}{\log (x)}\right )\right ) \]
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Rubi [F] time = 0.84, 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 {2+2 x \log (x)-11 x \log ^2(x)}{-2 x \log (x)+\left (11 x+e^x x\right ) \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 {-2-2 x \log (x)+11 x \log ^2(x)}{x \log (x) \left (2-11 \log (x)-e^x \log (x)\right )} \, dx\\ &=\int \left (\frac {2}{-2+11 \log (x)+e^x \log (x)}+\frac {2}{x \log (x) \left (-2+11 \log (x)+e^x \log (x)\right )}-\frac {11 \log (x)}{-2+11 \log (x)+e^x \log (x)}\right ) \, dx\\ &=2 \int \frac {1}{-2+11 \log (x)+e^x \log (x)} \, dx+2 \int \frac {1}{x \log (x) \left (-2+11 \log (x)+e^x \log (x)\right )} \, dx-11 \int \frac {\log (x)}{-2+11 \log (x)+e^x \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 23, normalized size = 1.00 \begin {gather*} -x-\log (\log (x))+\log \left (2-11 \log (x)-e^x \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 31, normalized size = 1.35 \begin {gather*} -x + \log \left (\frac {{\left (e^{x} + 11\right )} \log \relax (x) - 2}{e^{x} + 11}\right ) + \log \left (e^{x} + 11\right ) - \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 21, normalized size = 0.91 \begin {gather*} -x + \log \left (e^{x} \log \relax (x) + 11 \, \log \relax (x) - 2\right ) - \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 22, normalized size = 0.96
method | result | size |
norman | \(-x -\ln \left (\ln \relax (x )\right )+\ln \left ({\mathrm e}^{x} \ln \relax (x )+11 \ln \relax (x )-2\right )\) | \(22\) |
risch | \(-x +\ln \left ({\mathrm e}^{x}+11\right )-\ln \left (\ln \relax (x )\right )+\ln \left (\ln \relax (x )-\frac {2}{{\mathrm e}^{x}+11}\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 21, normalized size = 0.91 \begin {gather*} -x + \log \left (\frac {e^{x} \log \relax (x) + 11 \, \log \relax (x) - 2}{\log \relax (x)}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.60, size = 21, normalized size = 0.91 \begin {gather*} \ln \left (11\,\ln \relax (x)+{\mathrm {e}}^x\,\ln \relax (x)-2\right )-x-\ln \left (\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 15, normalized size = 0.65 \begin {gather*} - x + \log {\left (\frac {11 \log {\relax (x )} - 2}{\log {\relax (x )}} + e^{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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