Optimal. Leaf size=24 \[ \log \left (\frac {\frac {11}{2}+e^4}{(5+x+\log (3)) \left (-5+\log \left (x^2\right )\right )}\right ) \]
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Rubi [A] time = 0.39, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 6, number of rules used = 5, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.102, Rules used = {6, 6741, 6742, 2302, 29} \begin {gather*} -\log \left (5-\log \left (x^2\right )\right )-\log (x+5+\log (3)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 29
Rule 2302
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-10+3 x-2 \log (3)-x \log \left (x^2\right )}{-5 x^2+x (-25-5 \log (3))+\left (5 x+x^2+x \log (3)\right ) \log \left (x^2\right )} \, dx\\ &=\int \frac {-3 x+10 \left (1+\frac {\log (3)}{5}\right )+x \log \left (x^2\right )}{x (5+x+\log (3)) \left (5-\log \left (x^2\right )\right )} \, dx\\ &=\int \left (\frac {1}{-5-x-\log (3)}-\frac {2}{x \left (-5+\log \left (x^2\right )\right )}\right ) \, dx\\ &=-\log (5+x+\log (3))-2 \int \frac {1}{x \left (-5+\log \left (x^2\right )\right )} \, dx\\ &=-\log (5+x+\log (3))-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,-5+\log \left (x^2\right )\right )\\ &=-\log (5+x+\log (3))-\log \left (5-\log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 20, normalized size = 0.83 \begin {gather*} -\log (5+x+\log (3))-\log \left (5-\log \left (x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 18, normalized size = 0.75 \begin {gather*} -\log \left (x + \log \relax (3) + 5\right ) - \log \left (\log \left (x^{2}\right ) - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 18, normalized size = 0.75 \begin {gather*} -\log \left (x + \log \relax (3) + 5\right ) - \log \left (\log \left (x^{2}\right ) - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 19, normalized size = 0.79
method | result | size |
norman | \(-\ln \left (\ln \left (x^{2}\right )-5\right )-\ln \left (\ln \relax (3)+5+x \right )\) | \(19\) |
risch | \(-\ln \left (\ln \left (x^{2}\right )-5\right )-\ln \left (\ln \relax (3)+5+x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 16, normalized size = 0.67 \begin {gather*} -\log \left (x + \log \relax (3) + 5\right ) - \log \left (\log \relax (x) - \frac {5}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 18, normalized size = 0.75 \begin {gather*} -\ln \left (\ln \left (x^2\right )-5\right )-\ln \left (x+\ln \relax (3)+5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 17, normalized size = 0.71 \begin {gather*} - \log {\left (\log {\left (x^{2} \right )} - 5 \right )} - \log {\left (x + \log {\relax (3 )} + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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