Optimal. Leaf size=20 \[ \left (3+\log \left (\log \left (\frac {4 \left (-1+4 x^3\right )}{9 x^3}\right )\right )\right )^2 \]
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Rubi [A]
time = 0.09, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {1607, 6818}
\begin {gather*} \left (\log \left (\log \left (-\frac {4 \left (1-4 x^3\right )}{9 x^3}\right )\right )+3\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 6818
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18+6 \log \left (\log \left (\frac {-4+16 x^3}{9 x^3}\right )\right )}{x \left (-1+4 x^3\right ) \log \left (\frac {-4+16 x^3}{9 x^3}\right )} \, dx\\ &=\left (3+\log \left (\log \left (-\frac {4 \left (1-4 x^3\right )}{9 x^3}\right )\right )\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 0.85 \begin {gather*} \left (3+\log \left (\log \left (\frac {4}{9} \left (4-\frac {1}{x^3}\right )\right )\right )\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs.
\(2(18)=36\).
time = 0.68, size = 46, normalized size = 2.30
method | result | size |
default | \(\ln \left (2 \ln \left (2\right )-2 \ln \left (3\right )+\ln \left (\frac {4 x^{3}-1}{x^{3}}\right )\right )^{2}+6 \ln \left (2 \ln \left (2\right )-2 \ln \left (3\right )+\ln \left (4-\frac {1}{x^{3}}\right )\right )\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 84 vs.
\(2 (18) = 36\).
time = 0.51, size = 84, normalized size = 4.20 \begin {gather*} -\log \left (-2 \, \log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (4 \, x^{3} - 1\right ) - 3 \, \log \left (x\right )\right )^{2} + 2 \, \log \left (-2 \, \log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (4 \, x^{3} - 1\right ) - 3 \, \log \left (x\right )\right ) \log \left (\log \left (-\frac {4}{9 \, x^{3}} + \frac {16}{9}\right )\right ) + 6 \, \log \left (-2 \, \log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (4 \, x^{3} - 1\right ) - 3 \, \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 33, normalized size = 1.65 \begin {gather*} \log \left (\log \left (\frac {4 \, {\left (4 \, x^{3} - 1\right )}}{9 \, x^{3}}\right )\right )^{2} + 6 \, \log \left (\log \left (\frac {4 \, {\left (4 \, x^{3} - 1\right )}}{9 \, x^{3}}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 36, normalized size = 1.80 \begin {gather*} \log {\left (\log {\left (\frac {\frac {16 x^{3}}{9} - \frac {4}{9}}{x^{3}} \right )} \right )}^{2} + 6 \log {\left (\log {\left (\frac {\frac {16 x^{3}}{9} - \frac {4}{9}}{x^{3}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 77 vs.
\(2 (18) = 36\).
time = 0.45, size = 77, normalized size = 3.85 \begin {gather*} -\log \left (-\log \left (9 \, x^{3}\right ) + \log \left (16 \, x^{3} - 4\right )\right )^{2} + 2 \, \log \left (-\log \left (9 \, x^{3}\right ) + \log \left (16 \, x^{3} - 4\right )\right ) \log \left (\log \left (\frac {4 \, {\left (4 \, x^{3} - 1\right )}}{9 \, x^{3}}\right )\right ) + 6 \, \log \left (-\log \left (9 \, x^{3}\right ) + \log \left (16 \, x^{3} - 4\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.52, size = 29, normalized size = 1.45 \begin {gather*} \ln \left (\ln \left (\frac {\frac {16\,x^3}{9}-\frac {4}{9}}{x^3}\right )\right )\,\left (\ln \left (\ln \left (\frac {\frac {16\,x^3}{9}-\frac {4}{9}}{x^3}\right )\right )+6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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