Optimal. Leaf size=21 \[ \log \left (2 x+x \left (-5+\frac {1}{x}+\frac {2 x}{\log \left (\frac {5}{3}\right )}\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 0.81, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {1587} \begin {gather*} \log \left (2 x^2+(1-3 x) \log \left (\frac {5}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (2 x^2+(1-3 x) \log \left (\frac {5}{3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 0.86 \begin {gather*} \log \left (2 x^2+\log \left (\frac {5}{3}\right )-3 x \log \left (\frac {5}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 16, normalized size = 0.76 \begin {gather*} \log \left (2 \, x^{2} - {\left (3 \, x - 1\right )} \log \left (\frac {5}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 14, normalized size = 0.67 \begin {gather*} \log \left (2 \, x^{2} - 3 \, x \log \left (\frac {5}{3}\right ) + \log \left (\frac {5}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.73, size = 16, normalized size = 0.76
method | result | size |
derivativedivides | \(\ln \left (\left (3 x -1\right ) \ln \left (\frac {5}{3}\right )-2 x^{2}\right )\) | \(16\) |
default | \(\ln \left (3 \ln \left (\frac {5}{3}\right ) x -2 x^{2}-\ln \left (\frac {5}{3}\right )\right )\) | \(17\) |
norman | \(\ln \left (3 \ln \left (\frac {5}{3}\right ) x -2 x^{2}-\ln \left (\frac {5}{3}\right )\right )\) | \(17\) |
risch | \(\ln \left (2 x^{2}+\left (3 \ln \relax (3)-3 \ln \relax (5)\right ) x +\ln \relax (5)-\ln \relax (3)\right )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 16, normalized size = 0.76 \begin {gather*} \log \left (2 \, x^{2} - {\left (3 \, x - 1\right )} \log \left (\frac {5}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 14, normalized size = 0.67 \begin {gather*} \ln \left (2\,x^2-3\,\ln \left (\frac {5}{3}\right )\,x+\ln \left (\frac {5}{3}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 24, normalized size = 1.14 \begin {gather*} \log {\left (2 x^{2} + x \left (- 3 \log {\relax (5 )} + 3 \log {\relax (3 )}\right ) - \log {\relax (3 )} + \log {\relax (5 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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