Optimal. Leaf size=21 \[ \log \left (\frac {9-\log ^2(36)+\frac {\log ^2(x)}{x^2}}{x}\right ) \]
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Rubi [A] time = 0.41, antiderivative size = 23, normalized size of antiderivative = 1.10, number of steps used = 6, number of rules used = 4, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {6, 2561, 6742, 2541} \begin {gather*} \log \left (x^2 \left (9-\log ^2(36)\right )+\log ^2(x)\right )-3 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 2541
Rule 2561
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2 \left (-9+\log ^2(36)\right )+2 \log (x)-3 \log ^2(x)}{9 x^3-x^3 \log ^2(36)+x \log ^2(x)} \, dx\\ &=\int \frac {x^2 \left (-9+\log ^2(36)\right )+2 \log (x)-3 \log ^2(x)}{x^3 \left (9-\log ^2(36)\right )+x \log ^2(x)} \, dx\\ &=\int \frac {x^2 \left (-9+\log ^2(36)\right )+2 \log (x)-3 \log ^2(x)}{x \left (x^2 \left (9-\log ^2(36)\right )+\log ^2(x)\right )} \, dx\\ &=\int \left (-\frac {3}{x}+\frac {2 \left (9 x^2 \left (1-\frac {\log ^2(36)}{9}\right )+\log (x)\right )}{x \left (9 x^2 \left (1-\frac {\log ^2(36)}{9}\right )+\log ^2(x)\right )}\right ) \, dx\\ &=-3 \log (x)+2 \int \frac {9 x^2 \left (1-\frac {\log ^2(36)}{9}\right )+\log (x)}{x \left (9 x^2 \left (1-\frac {\log ^2(36)}{9}\right )+\log ^2(x)\right )} \, dx\\ &=-3 \log (x)+\log \left (x^2 \left (9-\log ^2(36)\right )+\log ^2(x)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 23, normalized size = 1.10 \begin {gather*} -3 \log (x)+\log \left (x^2 \left (-9+\log ^2(36)\right )-\log ^2(x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 25, normalized size = 1.19 \begin {gather*} \log \left (-4 \, x^{2} \log \relax (6)^{2} + 9 \, x^{2} + \log \relax (x)^{2}\right ) - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 27, normalized size = 1.29 \begin {gather*} \log \left (4 \, x^{2} \log \relax (6)^{2} - 9 \, x^{2} - \log \relax (x)^{2}\right ) - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 1.33
method | result | size |
norman | \(-3 \ln \relax (x )+\ln \left (4 x^{2} \ln \relax (6)^{2}-9 x^{2}-\ln \relax (x )^{2}\right )\) | \(28\) |
risch | \(-3 \ln \relax (x )+\ln \left (-4 x^{2} \ln \relax (2)^{2}-8 \ln \relax (2) \ln \relax (3) x^{2}-4 x^{2} \ln \relax (3)^{2}+9 x^{2}+\ln \relax (x )^{2}\right )\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 36, normalized size = 1.71 \begin {gather*} \log \left (-{\left (4 \, \log \relax (3)^{2} + 8 \, \log \relax (3) \log \relax (2) + 4 \, \log \relax (2)^{2} - 9\right )} x^{2} + \log \relax (x)^{2}\right ) - 3 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.06, size = 25, normalized size = 1.19 \begin {gather*} \ln \left ({\ln \relax (x)}^2-4\,x^2\,{\ln \relax (6)}^2+9\,x^2\right )-3\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 26, normalized size = 1.24 \begin {gather*} - 3 \log {\relax (x )} + \log {\left (- 4 x^{2} \log {\relax (6 )}^{2} + 9 x^{2} + \log {\relax (x )}^{2} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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