Optimal. Leaf size=22 \[ \log (8+e) \left (1+x+\frac {-1+x+\log \left (\frac {\log (4)}{x}\right )}{x}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 31, normalized size of antiderivative = 1.41, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14, 2304} \begin {gather*} x \log (8+e)+\frac {\log (8+e) \log \left (\frac {\log (4)}{x}\right )}{x}-\frac {\log (8+e)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2304
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\log (8+e)-\frac {\log (8+e) \log \left (\frac {\log (4)}{x}\right )}{x^2}\right ) \, dx\\ &=x \log (8+e)-\log (8+e) \int \frac {\log \left (\frac {\log (4)}{x}\right )}{x^2} \, dx\\ &=-\frac {\log (8+e)}{x}+x \log (8+e)+\frac {\log (8+e) \log \left (\frac {\log (4)}{x}\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 31, normalized size = 1.41 \begin {gather*} -\frac {\log (8+e)}{x}+x \log (8+e)+\frac {\log (8+e) \log \left (\frac {\log (4)}{x}\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 30, normalized size = 1.36 \begin {gather*} \frac {{\left (x^{2} - 1\right )} \log \left (e + 8\right ) + \log \left (\frac {2 \, \log \relax (2)}{x}\right ) \log \left (e + 8\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.43, size = 52, normalized size = 2.36 \begin {gather*} \frac {{\left (\log \relax (2)^{2} \log \left (e + 8\right ) + \frac {\log \relax (2)^{2} \log \left (\frac {2 \, \log \relax (2)}{x}\right ) \log \left (e + 8\right )}{x^{2}} - \frac {\log \relax (2)^{2} \log \left (e + 8\right )}{x^{2}}\right )} x}{\log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 33, normalized size = 1.50
method | result | size |
risch | \(\frac {\ln \left ({\mathrm e}+8\right ) \ln \left (\frac {2 \ln \relax (2)}{x}\right )}{x}+\frac {\ln \left ({\mathrm e}+8\right ) \left (x^{2}-1\right )}{x}\) | \(33\) |
derivativedivides | \(\frac {\ln \left ({\mathrm e}+8\right ) \ln \left (\frac {2 \ln \relax (2)}{x}\right )}{x}-\frac {\ln \left ({\mathrm e}+8\right )}{x}+x \ln \left ({\mathrm e}+8\right )\) | \(36\) |
default | \(\frac {\ln \left ({\mathrm e}+8\right ) \ln \left (\frac {2 \ln \relax (2)}{x}\right )}{x}-\frac {\ln \left ({\mathrm e}+8\right )}{x}+x \ln \left ({\mathrm e}+8\right )\) | \(36\) |
norman | \(\frac {x^{2} \ln \left ({\mathrm e}+8\right )+\ln \left ({\mathrm e}+8\right ) \ln \left (\frac {2 \ln \relax (2)}{x}\right )-\ln \left ({\mathrm e}+8\right )}{x}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 40, normalized size = 1.82 \begin {gather*} x \log \left (e + 8\right ) + \frac {{\left (\frac {\log \relax (2) \log \left (\frac {2 \, \log \relax (2)}{x}\right )}{x} - \frac {\log \relax (2)}{x}\right )} \log \left (e + 8\right )}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.35, size = 22, normalized size = 1.00 \begin {gather*} \frac {\ln \left (\mathrm {e}+8\right )\,\left (\ln \left (\frac {2\,\ln \relax (2)}{x}\right )+x^2-1\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 32, normalized size = 1.45 \begin {gather*} x \log {\left (e + 8 \right )} + \frac {\log {\left (\frac {2 \log {\relax (2 )}}{x} \right )} \log {\left (e + 8 \right )}}{x} - \frac {\log {\left (e + 8 \right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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