Optimal. Leaf size=23 \[ 2 \left (-\log (x)+\frac {x}{\log \left (67+x-\log \left (4 x^2\right )\right )}\right ) \]
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Rubi [F]
time = 0.33, 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 {-4 x+2 x^2+\left (-134 x-2 x^2+2 x \log \left (4 x^2\right )\right ) \log \left (67+x-\log \left (4 x^2\right )\right )+\left (134+2 x-2 \log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )}{\left (-67 x-x^2+x \log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 2 \left (-\frac {1}{x}+\frac {2-x}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )}+\frac {1}{\log \left (67+x-\log \left (4 x^2\right )\right )}\right ) \, dx\\ &=2 \int \left (-\frac {1}{x}+\frac {2-x}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )}+\frac {1}{\log \left (67+x-\log \left (4 x^2\right )\right )}\right ) \, dx\\ &=-2 \log (x)+2 \int \frac {2-x}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )} \, dx+2 \int \frac {1}{\log \left (67+x-\log \left (4 x^2\right )\right )} \, dx\\ &=-2 \log (x)+2 \int \left (\frac {2}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )}-\frac {x}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )}\right ) \, dx+2 \int \frac {1}{\log \left (67+x-\log \left (4 x^2\right )\right )} \, dx\\ &=-2 \log (x)-2 \int \frac {x}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )} \, dx+2 \int \frac {1}{\log \left (67+x-\log \left (4 x^2\right )\right )} \, dx+4 \int \frac {1}{\left (67+x-\log \left (4 x^2\right )\right ) \log ^2\left (67+x-\log \left (4 x^2\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 23, normalized size = 1.00 \begin {gather*} 2 \left (-\log (x)+\frac {x}{\log \left (67+x-\log \left (4 x^2\right )\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (-2 \ln \left (4 x^{2}\right )+2 x +134\right ) \ln \left (-\ln \left (4 x^{2}\right )+x +67\right )^{2}+\left (2 x \ln \left (4 x^{2}\right )-2 x^{2}-134 x \right ) \ln \left (-\ln \left (4 x^{2}\right )+x +67\right )+2 x^{2}-4 x}{\left (x \ln \left (4 x^{2}\right )-x^{2}-67 x \right ) \ln \left (-\ln \left (4 x^{2}\right )+x +67\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, size = 22, normalized size = 0.96 \begin {gather*} \frac {2 \, x}{\log \left (x - 2 \, \log \left (2\right ) - 2 \, \log \left (x\right ) + 67\right )} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 39, normalized size = 1.70 \begin {gather*} -\frac {\log \left (4 \, x^{2}\right ) \log \left (x - \log \left (4 \, x^{2}\right ) + 67\right ) - 2 \, x}{\log \left (x - \log \left (4 \, x^{2}\right ) + 67\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 19, normalized size = 0.83 \begin {gather*} \frac {2 x}{\log {\left (x - \log {\left (4 x^{2} \right )} + 67 \right )}} - 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.50, size = 22, normalized size = 0.96 \begin {gather*} \frac {2 \, x}{\log \left (x - \log \left (4 \, x^{2}\right ) + 67\right )} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.83, size = 78, normalized size = 3.39 \begin {gather*} 2\,x-6\,\ln \left (x\right )+\frac {276}{x-2}-\frac {4\,\ln \left (4\,x^2\right )}{x-2}+\frac {2\,x-\frac {2\,x\,\ln \left (x-\ln \left (4\,x^2\right )+67\right )\,\left (x-\ln \left (4\,x^2\right )+67\right )}{x-2}}{\ln \left (x-\ln \left (4\,x^2\right )+67\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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