Optimal. Leaf size=21 \[ \frac {1}{5} (-5+4 x)+\log \left (\frac {x-\log (3)}{x}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 3, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {1593, 1820} \begin {gather*} \frac {4 x}{5}-\log (x)+\log (x-\log (3)) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 x^2+(-5+4 x) \log (3)}{x (-5 x+5 \log (3))} \, dx\\ &=\int \left (\frac {4}{5}-\frac {1}{x}+\frac {1}{x-\log (3)}\right ) \, dx\\ &=\frac {4 x}{5}-\log (x)+\log (x-\log (3))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 0.81 \begin {gather*} \frac {4 x}{5}-\log (x)+\log (x-\log (3)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.02, size = 15, normalized size = 0.71 \begin {gather*} \frac {4}{5} \, x + \log \left (x - \log \relax (3)\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 17, normalized size = 0.81 \begin {gather*} \frac {4}{5} \, x + \log \left ({\left | x - \log \relax (3) \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 16, normalized size = 0.76
method | result | size |
default | \(\frac {4 x}{5}-\ln \relax (x )+\ln \left (-\ln \relax (3)+x \right )\) | \(16\) |
norman | \(\frac {4 x}{5}-\ln \relax (x )+\ln \left (\ln \relax (3)-x \right )\) | \(16\) |
risch | \(\frac {4 x}{5}-\ln \relax (x )+\ln \left (-\ln \relax (3)+x \right )\) | \(16\) |
meijerg | \(-\ln \relax (x )+\ln \left (\ln \relax (3)\right )-i \pi +\ln \left (1-\frac {x}{\ln \relax (3)}\right )-\frac {4 \ln \relax (3) \ln \left (1-\frac {x}{\ln \relax (3)}\right )}{5}-\frac {4 \ln \relax (3) \left (-\frac {x}{\ln \relax (3)}-\ln \left (1-\frac {x}{\ln \relax (3)}\right )\right )}{5}\) | \(61\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 15, normalized size = 0.71 \begin {gather*} \frac {4}{5} \, x + \log \left (x - \log \relax (3)\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 16, normalized size = 0.76 \begin {gather*} \frac {4\,x}{5}-2\,\mathrm {atanh}\left (\frac {2\,x}{\ln \relax (3)}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 14, normalized size = 0.67 \begin {gather*} \frac {4 x}{5} - \log {\relax (x )} + \log {\left (x - \log {\relax (3 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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