Optimal. Leaf size=22 \[ 6 \log \left (\log \left (\frac {5}{4+\frac {1-x}{x}+x^2}\right )\right ) \]
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Rubi [A] time = 0.15, antiderivative size = 17, normalized size of antiderivative = 0.77, number of steps used = 2, number of rules used = 2, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {1594, 6684} \begin {gather*} 6 \log \left (\log \left (\frac {5 x}{x^3+3 x+1}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1594
Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6-12 x^3}{x \left (1+3 x+x^3\right ) \log \left (\frac {5 x}{1+3 x+x^3}\right )} \, dx\\ &=6 \log \left (\log \left (\frac {5 x}{1+3 x+x^3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.10, size = 17, normalized size = 0.77 \begin {gather*} 6 \log \left (\log \left (\frac {5 x}{1+3 x+x^3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 17, normalized size = 0.77 \begin {gather*} 6 \, \log \left (\log \left (\frac {5 \, x}{x^{3} + 3 \, x + 1}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 17, normalized size = 0.77 \begin {gather*} 6 \, \log \left (\log \left (\frac {5 \, x}{x^{3} + 3 \, x + 1}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 0.82
method | result | size |
norman | \(6 \ln \left (\ln \left (\frac {5 x}{x^{3}+3 x +1}\right )\right )\) | \(18\) |
risch | \(6 \ln \left (\ln \left (\frac {5 x}{x^{3}+3 x +1}\right )\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 21, normalized size = 0.95 \begin {gather*} 6 \, \log \left (-\log \relax (5) + \log \left (x^{3} + 3 \, x + 1\right ) - \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.16, size = 17, normalized size = 0.77 \begin {gather*} 6\,\ln \left (\ln \left (\frac {5\,x}{x^3+3\,x+1}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 15, normalized size = 0.68 \begin {gather*} 6 \log {\left (\log {\left (\frac {5 x}{x^{3} + 3 x + 1} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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