Optimal. Leaf size=22 \[ \log \left (\log \left (6 x \left (-(-1+x)^2+x\right ) (-3+\log (4)) (-3+\log (x))\right )\right ) \]
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Rubi [F] time = 21.45, 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 {-2+15 x-8 x^2+\left (1-6 x+3 x^2\right ) \log (x)}{\left (-3 x+9 x^2-3 x^3+\left (x-3 x^2+x^3\right ) \log (x)\right ) \log \left (-54 x+162 x^2-54 x^3+\left (18 x-54 x^2+18 x^3\right ) \log (4)+\left (18 x-54 x^2+18 x^3+\left (-6 x+18 x^2-6 x^3\right ) \log (4)\right ) \log (x)\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 {2-15 x+8 x^2-\left (1-6 x+3 x^2\right ) \log (x)}{x \left (1-3 x+x^2\right ) (3-\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx\\ &=\int \left (\frac {-2+15 x-8 x^2+\log (x)-6 x \log (x)+3 x^2 \log (x)}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {(-3+x) \left (-2+15 x-8 x^2+\log (x)-6 x \log (x)+3 x^2 \log (x)\right )}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}\right ) \, dx\\ &=\int \frac {-2+15 x-8 x^2+\log (x)-6 x \log (x)+3 x^2 \log (x)}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-\int \frac {(-3+x) \left (-2+15 x-8 x^2+\log (x)-6 x \log (x)+3 x^2 \log (x)\right )}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx\\ &=\int \left (\frac {15}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {2}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {8 x}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {6 \log (x)}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}+\frac {\log (x)}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}+\frac {3 x \log (x)}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}\right ) \, dx-\int \left (\frac {6}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {47 x}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}+\frac {39 x^2}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {8 x^3}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {3 \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}+\frac {19 x \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}-\frac {15 x^2 \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}+\frac {3 x^3 \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )}\right ) \, dx\\ &=-\left (2 \int \frac {1}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx\right )+3 \int \frac {x \log (x)}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+3 \int \frac {\log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-3 \int \frac {x^3 \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-6 \int \frac {1}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-6 \int \frac {\log (x)}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-8 \int \frac {x}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+8 \int \frac {x^3}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+15 \int \frac {1}{(-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+15 \int \frac {x^2 \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-19 \int \frac {x \log (x)}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx-39 \int \frac {x^2}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+47 \int \frac {x}{\left (1-3 x+x^2\right ) (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx+\int \frac {\log (x)}{x (-3+\log (x)) \log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.32, size = 21, normalized size = 0.95 \begin {gather*} \log \left (\log \left (-6 x \left (1-3 x+x^2\right ) (-3+\log (4)) (-3+\log (x))\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 62, normalized size = 2.82 \begin {gather*} \log \left (\log \left (-54 \, x^{3} + 162 \, x^{2} + 36 \, {\left (x^{3} - 3 \, x^{2} + x\right )} \log \relax (2) + 6 \, {\left (3 \, x^{3} - 9 \, x^{2} - 2 \, {\left (x^{3} - 3 \, x^{2} + x\right )} \log \relax (2) + 3 \, x\right )} \log \relax (x) - 54 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 71, normalized size = 3.23 \begin {gather*} \log \left (\log \relax (2) + \log \left (-6 \, x^{2} \log \relax (2) \log \relax (x) + 18 \, x^{2} \log \relax (2) + 9 \, x^{2} \log \relax (x) + 18 \, x \log \relax (2) \log \relax (x) - 27 \, x^{2} - 54 \, x \log \relax (2) - 27 \, x \log \relax (x) - 6 \, \log \relax (2) \log \relax (x) + 81 \, x + 18 \, \log \relax (2) + 9 \, \log \relax (x) - 27\right ) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.19, size = 309, normalized size = 14.05
method | result | size |
risch | \(\ln \left (\ln \left (x^{2}-3 x +1\right )+\frac {i \left (-2 \pi \mathrm {csgn}\left (i x \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )+\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )-3\right )\right ) \mathrm {csgn}\left (i \left (x^{2}-3 x +1\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )+\pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )-3\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{2}+\pi \,\mathrm {csgn}\left (i \left (x^{2}-3 x +1\right )\right ) \mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{2}-\pi \mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{3}+\pi \,\mathrm {csgn}\left (i \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{2}+\pi \mathrm {csgn}\left (i x \left (\ln \relax (x )-3\right ) \left (x^{2}-3 x +1\right )\right )^{3}-2 i \ln \left (\ln \relax (x )-3\right )-2 i \ln \relax (3)-2 i \ln \relax (x )-2 i \ln \relax (2)+2 \pi \right )}{2}\right )\) | \(309\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.79, size = 32, normalized size = 1.45 \begin {gather*} \log \left (i \, \pi + \log \relax (3) + \log \relax (2) + \log \left (x^{2} - 3 \, x + 1\right ) + \log \relax (x) + \log \left (2 \, \log \relax (2) - 3\right ) + \log \left (\log \relax (x) - 3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.03, size = 69, normalized size = 3.14 \begin {gather*} \ln \left (\ln \left (\ln \relax (x)\,\left (18\,x-2\,\ln \relax (2)\,\left (6\,x^3-18\,x^2+6\,x\right )-54\,x^2+18\,x^3\right )-54\,x+2\,\ln \relax (2)\,\left (18\,x^3-54\,x^2+18\,x\right )+162\,x^2-54\,x^3\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.04, size = 66, normalized size = 3.00 \begin {gather*} \log {\left (\log {\left (- 54 x^{3} + 162 x^{2} - 54 x + \left (36 x^{3} - 108 x^{2} + 36 x\right ) \log {\relax (2 )} + \left (18 x^{3} - 54 x^{2} + 18 x + \left (- 12 x^{3} + 36 x^{2} - 12 x\right ) \log {\relax (2 )}\right ) \log {\relax (x )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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