Optimal. Leaf size=18 \[ 4 \log \left (4-\log \left (\log \left (5+2 \left (-16+\frac {1}{x}\right )\right )\right )\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {12, 6688, 6684} \begin {gather*} 4 \log \left (4-\log \left (\log \left (\frac {2}{x}-27\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=8 \int \frac {1}{\left (8 x-108 x^2\right ) \log \left (\frac {2-27 x}{x}\right )+\left (-2 x+27 x^2\right ) \log \left (\frac {2-27 x}{x}\right ) \log \left (\log \left (\frac {2-27 x}{x}\right )\right )} \, dx\\ &=8 \int \frac {1}{(2-27 x) x \log \left (-27+\frac {2}{x}\right ) \left (4-\log \left (\log \left (-27+\frac {2}{x}\right )\right )\right )} \, dx\\ &=4 \log \left (4-\log \left (\log \left (-27+\frac {2}{x}\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 5.02, size = 14, normalized size = 0.78 \begin {gather*} 4 \log \left (-4+\log \left (\log \left (-27+\frac {2}{x}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 17, normalized size = 0.94 \begin {gather*} 4 \, \log \left (\log \left (\log \left (-\frac {27 \, x - 2}{x}\right )\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {8}{{\left (27 \, x^{2} - 2 \, x\right )} \log \left (-\frac {27 \, x - 2}{x}\right ) \log \left (\log \left (-\frac {27 \, x - 2}{x}\right )\right ) - 4 \, {\left (27 \, x^{2} - 2 \, x\right )} \log \left (-\frac {27 \, x - 2}{x}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 17, normalized size = 0.94
method | result | size |
norman | \(4 \ln \left (\ln \left (\ln \left (\frac {-27 x +2}{x}\right )\right )-4\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 17, normalized size = 0.94 \begin {gather*} 4 \, \log \left (\log \left (-\log \relax (x) + \log \left (-27 \, x + 2\right )\right ) - 4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.82, size = 14, normalized size = 0.78 \begin {gather*} 4\,\ln \left (\ln \left (\ln \left (\frac {2}{x}-27\right )\right )-4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 14, normalized size = 0.78 \begin {gather*} 4 \log {\left (\log {\left (\log {\left (\frac {2 - 27 x}{x} \right )} \right )} - 4 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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