Optimal. Leaf size=25 \[ \log \left (5 x^2 \left (-3+\log \left (x \log \left (\frac {x}{80-x^2}\right )\right )\right )^2\right ) \]
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Rubi [A] time = 0.29, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 117, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6688, 12, 6685} \begin {gather*} 2 \log \left (-x \left (3-\log \left (x \log \left (\frac {x}{80-x^2}\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6685
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-80-x^2+\left (-80+x^2\right ) \log \left (-\frac {x}{-80+x^2}\right ) \left (-2+\log \left (x \log \left (-\frac {x}{-80+x^2}\right )\right )\right )\right )}{x \left (80-x^2\right ) \log \left (-\frac {x}{-80+x^2}\right ) \left (3-\log \left (x \log \left (-\frac {x}{-80+x^2}\right )\right )\right )} \, dx\\ &=2 \int \frac {-80-x^2+\left (-80+x^2\right ) \log \left (-\frac {x}{-80+x^2}\right ) \left (-2+\log \left (x \log \left (-\frac {x}{-80+x^2}\right )\right )\right )}{x \left (80-x^2\right ) \log \left (-\frac {x}{-80+x^2}\right ) \left (3-\log \left (x \log \left (-\frac {x}{-80+x^2}\right )\right )\right )} \, dx\\ &=2 \log \left (-x \left (3-\log \left (x \log \left (\frac {x}{80-x^2}\right )\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 24, normalized size = 0.96 \begin {gather*} 2 \left (\log (x)+\log \left (3-\log \left (x \log \left (-\frac {x}{-80+x^2}\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 24, normalized size = 0.96 \begin {gather*} 2 \, \log \relax (x) + 2 \, \log \left (\log \left (x \log \left (-\frac {x}{x^{2} - 80}\right )\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left ({\left (x^{2} - 80\right )} \log \left (x \log \left (-\frac {x}{x^{2} - 80}\right )\right ) \log \left (-\frac {x}{x^{2} - 80}\right ) - x^{2} - 2 \, {\left (x^{2} - 80\right )} \log \left (-\frac {x}{x^{2} - 80}\right ) - 80\right )}}{{\left (x^{3} - 80 \, x\right )} \log \left (x \log \left (-\frac {x}{x^{2} - 80}\right )\right ) \log \left (-\frac {x}{x^{2} - 80}\right ) - 3 \, {\left (x^{3} - 80 \, x\right )} \log \left (-\frac {x}{x^{2} - 80}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (2 x^{2}-160\right ) \ln \left (-\frac {x}{x^{2}-80}\right ) \ln \left (x \ln \left (-\frac {x}{x^{2}-80}\right )\right )+\left (-4 x^{2}+320\right ) \ln \left (-\frac {x}{x^{2}-80}\right )-2 x^{2}-160}{\left (x^{3}-80 x \right ) \ln \left (-\frac {x}{x^{2}-80}\right ) \ln \left (x \ln \left (-\frac {x}{x^{2}-80}\right )\right )+\left (-3 x^{3}+240 x \right ) \ln \left (-\frac {x}{x^{2}-80}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 26, normalized size = 1.04 \begin {gather*} 2 \, \log \relax (x) + 2 \, \log \left (\log \relax (x) + \log \left (-\log \left (-x^{2} + 80\right ) + \log \relax (x)\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.48, size = 24, normalized size = 0.96 \begin {gather*} 2\,\ln \relax (x)+2\,\ln \left (\ln \left (x\,\ln \left (-\frac {x}{x^2-80}\right )\right )-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.59, size = 22, normalized size = 0.88 \begin {gather*} 2 \log {\relax (x )} + 2 \log {\left (\log {\left (x \log {\left (- \frac {x}{x^{2} - 80} \right )} \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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