Optimal. Leaf size=20 \[ \log \left (x \left (-3-(1-x) x+\log \left (\frac {3}{\log (5)}\right )\right )\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 1.15, number of steps used = 2, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6, 1587} \begin {gather*} \log \left (-x^3+x^2+x \left (3-\log \left (\frac {3}{\log (5)}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3-2 x+3 x^2+\log \left (\frac {3}{\log (5)}\right )}{-x^2+x^3+x \left (-3+\log \left (\frac {3}{\log (5)}\right )\right )} \, dx\\ &=\log \left (x^2-x^3+x \left (3-\log \left (\frac {3}{\log (5)}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.05 \begin {gather*} \log (x)+\log \left (3+x-x^2-\log \left (\frac {3}{\log (5)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 22, normalized size = 1.10 \begin {gather*} \log \left (x^{3} - x^{2} + x \log \left (\frac {3}{\log \relax (5)}\right ) - 3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 23, normalized size = 1.15 \begin {gather*} \log \left ({\left | x^{3} - x^{2} + x \log \left (\frac {3}{\log \relax (5)}\right ) - 3 \, x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 19, normalized size = 0.95
method | result | size |
default | \(\ln \left (x \left (x^{2}+\ln \left (\frac {3}{\ln \relax (5)}\right )-x -3\right )\right )\) | \(19\) |
norman | \(\ln \relax (x )+\ln \left (x^{2}+\ln \left (\frac {3}{\ln \relax (5)}\right )-x -3\right )\) | \(20\) |
risch | \(\ln \left (x^{3}-x^{2}+\left (\ln \relax (3)-\ln \left (\ln \relax (5)\right )-3\right ) x \right )\) | \(22\) |
derivativedivides | \(\ln \left (x \ln \left (\frac {3}{\ln \relax (5)}\right )+x^{3}-x^{2}-3 x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 22, normalized size = 1.10 \begin {gather*} \log \left (x^{3} - x^{2} + x \log \left (\frac {3}{\log \relax (5)}\right ) - 3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 22, normalized size = 1.10 \begin {gather*} \ln \left (x^3-x^2+\left (\ln \relax (3)-\ln \left (\ln \relax (5)\right )-3\right )\,x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 19, normalized size = 0.95 \begin {gather*} \log {\left (x^{3} - x^{2} + x \left (-3 - \log {\left (\log {\relax (5 )} \right )} + \log {\relax (3 )}\right ) \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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