Optimal. Leaf size=32 \[ \frac {3}{\log \left (\log \left (\frac {3 \log (x)}{x+\frac {x+\frac {x}{\log (x)}}{\frac {2}{3}-x}}\right )\right )} \]
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Rubi [F]
time = 26.32, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-36+54 x+\left (-12+63 x-27 x^2\right ) \log (x)+\left (30-36 x+27 x^2\right ) \log ^2(x)}{\left (\left (6 x-9 x^2\right ) \log (x)+\left (10 x-21 x^2+9 x^3\right ) \log ^2(x)\right ) \log \left (\frac {(-6+9 x) \log ^2(x)}{-3 x+\left (-5 x+3 x^2\right ) \log (x)}\right ) \log ^2\left (\log \left (\frac {(-6+9 x) \log ^2(x)}{-3 x+\left (-5 x+3 x^2\right ) \log (x)}\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-36+54 x+\left (-12+63 x-27 x^2\right ) \log (x)+\left (30-36 x+27 x^2\right ) \log ^2(x)}{(2-3 x) x \log (x) (3+5 \log (x)-3 x \log (x)) \log \left (\frac {(-6+9 x) \log ^2(x)}{-3 x+\left (-5 x+3 x^2\right ) \log (x)}\right ) \log ^2\left (\log \left (\frac {(-6+9 x) \log ^2(x)}{-3 x+\left (-5 x+3 x^2\right ) \log (x)}\right )\right )} \, dx\\ &=\int \left (-\frac {3 \left (-12+18 x-4 \log (x)+21 x \log (x)-9 x^2 \log (x)+10 \log ^2(x)-12 x \log ^2(x)+9 x^2 \log ^2(x)\right )}{2 x \log (x) (-3-5 \log (x)+3 x \log (x)) \log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right ) \log ^2\left (\log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right )\right )}+\frac {9 \left (-12+18 x-4 \log (x)+21 x \log (x)-9 x^2 \log (x)+10 \log ^2(x)-12 x \log ^2(x)+9 x^2 \log ^2(x)\right )}{2 (-2+3 x) \log (x) (-3-5 \log (x)+3 x \log (x)) \log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right ) \log ^2\left (\log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right )\right )}\right ) \, dx\\ &=-\left (\frac {3}{2} \int \frac {-12+18 x-4 \log (x)+21 x \log (x)-9 x^2 \log (x)+10 \log ^2(x)-12 x \log ^2(x)+9 x^2 \log ^2(x)}{x \log (x) (-3-5 \log (x)+3 x \log (x)) \log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right ) \log ^2\left (\log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right )\right )} \, dx\right )+\frac {9}{2} \int \frac {-12+18 x-4 \log (x)+21 x \log (x)-9 x^2 \log (x)+10 \log ^2(x)-12 x \log ^2(x)+9 x^2 \log ^2(x)}{(-2+3 x) \log (x) (-3-5 \log (x)+3 x \log (x)) \log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right ) \log ^2\left (\log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 32, normalized size = 1.00 \begin {gather*} \frac {3}{\log \left (\log \left (\frac {3 (-2+3 x) \log ^2(x)}{x (-3+(-5+3 x) \log (x))}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 4.06, size = 350, normalized size = 10.94
method | result | size |
default | \(\frac {3}{\ln \left (\ln \left (3\right )+2 \ln \left (\ln \left (x \right )\right )-\ln \left (x \right )-\ln \left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right )+\ln \left (x -\frac {2}{3}\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )}\right )+\mathrm {csgn}\left (\frac {i}{-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )}\right )+\mathrm {csgn}\left (i \left (x -\frac {2}{3}\right )\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{x \left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right )}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{x \left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right )}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{x \left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right )}\right )+\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )}\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right ) \left (-\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )+\mathrm {csgn}\left (i \ln \left (x \right )\right )\right )^{2}}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{\left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right ) x}\right ) \left (-\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{\left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right ) x}\right )+\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{\left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right ) x}\right )+\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{x \left (-1+\left (x -\frac {5}{3}\right ) \ln \left (x \right )\right )}\right )\right )}{2}\right )}\) | \(350\) |
risch | \(\frac {3}{\ln \left (\ln \left (3\right )-\ln \left (x \right )+2 \ln \left (\ln \left (x \right )\right )+\ln \left (x -\frac {2}{3}\right )-\ln \left (-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}\right )-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )+\mathrm {csgn}\left (i \left (x -\frac {2}{3}\right )\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )+\mathrm {csgn}\left (\frac {i}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right ) \left (-\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )+\mathrm {csgn}\left (i \ln \left (x \right )\right )\right )^{2}}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right ) \left (-\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )+\mathrm {csgn}\left (i \ln \left (x \right )^{2}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )+\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right ) \ln \left (x \right )^{2}}{x \left (-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}\right )}\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right ) \ln \left (x \right )^{2}}{x \left (-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}\right )}\right )+\mathrm {csgn}\left (\frac {i}{x}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i \left (x -\frac {2}{3}\right ) \ln \left (x \right )^{2}}{x \left (-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}\right )}\right )+\mathrm {csgn}\left (\frac {i \ln \left (x \right )^{2} \left (x -\frac {2}{3}\right )}{-1+x \ln \left (x \right )-\frac {5 \ln \left (x \right )}{3}}\right )\right )}{2}\right )}\) | \(380\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.56, size = 36, normalized size = 1.12 \begin {gather*} \frac {3}{\log \left (\log \left (3\right ) - \log \left ({\left (3 \, x - 5\right )} \log \left (x\right ) - 3\right ) + \log \left (3 \, x - 2\right ) - \log \left (x\right ) + 2 \, \log \left (\log \left (x\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 35, normalized size = 1.09 \begin {gather*} \frac {3}{\log \left (\log \left (\frac {3 \, {\left (3 \, x - 2\right )} \log \left (x\right )^{2}}{{\left (3 \, x^{2} - 5 \, x\right )} \log \left (x\right ) - 3 \, x}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.79, size = 29, normalized size = 0.91 \begin {gather*} \frac {3}{\log {\left (\log {\left (\frac {\left (9 x - 6\right ) \log {\left (x \right )}^{2}}{- 3 x + \left (3 x^{2} - 5 x\right ) \log {\left (x \right )}} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.76, size = 39, normalized size = 1.22 \begin {gather*} \frac {3}{\log \left (\log \left (9 \, x \log \left (x\right )^{2} - 6 \, \log \left (x\right )^{2}\right ) - \log \left (3 \, x \log \left (x\right ) - 5 \, \log \left (x\right ) - 3\right ) - \log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.94, size = 35, normalized size = 1.09 \begin {gather*} \frac {3}{\ln \left (\ln \left (-\frac {{\ln \left (x\right )}^2\,\left (9\,x-6\right )}{3\,x+\ln \left (x\right )\,\left (5\,x-3\,x^2\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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