Integrand size = 490, antiderivative size = 30 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x+\log \left (5-\left (-\log ^2(x)+\frac {6}{-x+\log (2+3 x)}\right )^2\right ) \]
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Timed out. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Leaf count is larger than twice the leaf count of optimal. \(95\) vs. \(2(30)=60\).
Time = 0.46 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x-2 \log (x-\log (2+3 x))+\log \left (36-5 x^2+12 x \log ^2(x)+x^2 \log ^4(x)+10 x \log (2+3 x)-12 \log ^2(x) \log (2+3 x)-2 x \log ^4(x) \log (2+3 x)-5 \log ^2(2+3 x)+\log ^4(x) \log ^2(2+3 x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(95\) vs. \(2(32)=64\).
Time = 11.30 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.20
method | result | size |
default | \(\ln \left (\ln \left (x \right )^{4}-5\right )+x -2 \ln \left (-x +\ln \left (2+3 x \right )\right )+\ln \left (\ln \left (2+3 x \right )^{2}-\frac {2 \left (x \ln \left (x \right )^{4}+6 \ln \left (x \right )^{2}-5 x \right ) \ln \left (2+3 x \right )}{\ln \left (x \right )^{4}-5}+\frac {x^{2} \ln \left (x \right )^{4}+12 x \ln \left (x \right )^{2}-5 x^{2}+36}{\ln \left (x \right )^{4}-5}\right )\) | \(96\) |
risch | \(\ln \left (\ln \left (x \right )^{4}-5\right )+x -2 \ln \left (-x +\ln \left (2+3 x \right )\right )+\ln \left (\ln \left (2+3 x \right )^{2}-\frac {2 \left (x \ln \left (x \right )^{4}+6 \ln \left (x \right )^{2}-5 x \right ) \ln \left (2+3 x \right )}{\ln \left (x \right )^{4}-5}+\frac {x^{2} \ln \left (x \right )^{4}+12 x \ln \left (x \right )^{2}-5 x^{2}+36}{\ln \left (x \right )^{4}-5}\right )\) | \(96\) |
parallelrisch | \(-\frac {4}{3}-2 \ln \left (x -\ln \left (2+3 x \right )\right )+\ln \left (x^{2} \ln \left (x \right )^{4}-2 \ln \left (x \right )^{4} \ln \left (2+3 x \right ) x +\ln \left (x \right )^{4} \ln \left (2+3 x \right )^{2}+12 x \ln \left (x \right )^{2}-12 \ln \left (x \right )^{2} \ln \left (2+3 x \right )-5 x^{2}+10 \ln \left (2+3 x \right ) x -5 \ln \left (2+3 x \right )^{2}+36\right )+x\) | \(97\) |
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Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (28) = 56\).
Time = 0.29 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.10 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (\log \left (x\right )^{4} - 5\right ) - 2 \, \log \left (-x + \log \left (3 \, x + 2\right )\right ) + \log \left (\frac {x^{2} \log \left (x\right )^{4} + {\left (\log \left (x\right )^{4} - 5\right )} \log \left (3 \, x + 2\right )^{2} + 12 \, x \log \left (x\right )^{2} - 5 \, x^{2} - 2 \, {\left (x \log \left (x\right )^{4} + 6 \, \log \left (x\right )^{2} - 5 \, x\right )} \log \left (3 \, x + 2\right ) + 36}{\log \left (x\right )^{4} - 5}\right ) \]
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Exception generated. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\text {Exception raised: PolynomialError} \]
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Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (28) = 56\).
Time = 0.40 (sec) , antiderivative size = 93, normalized size of antiderivative = 3.10 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (\log \left (x\right )^{4} - 5\right ) - 2 \, \log \left (-x + \log \left (3 \, x + 2\right )\right ) + \log \left (\frac {x^{2} \log \left (x\right )^{4} + {\left (\log \left (x\right )^{4} - 5\right )} \log \left (3 \, x + 2\right )^{2} + 12 \, x \log \left (x\right )^{2} - 5 \, x^{2} - 2 \, {\left (x \log \left (x\right )^{4} + 6 \, \log \left (x\right )^{2} - 5 \, x\right )} \log \left (3 \, x + 2\right ) + 36}{\log \left (x\right )^{4} - 5}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 95 vs. \(2 (28) = 56\).
Time = 0.84 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.17 \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=x + \log \left (x^{2} \log \left (x\right )^{4} - 2 \, x \log \left (3 \, x + 2\right ) \log \left (x\right )^{4} + \log \left (3 \, x + 2\right )^{2} \log \left (x\right )^{4} + 12 \, x \log \left (x\right )^{2} - 12 \, \log \left (3 \, x + 2\right ) \log \left (x\right )^{2} - 5 \, x^{2} + 10 \, x \log \left (3 \, x + 2\right ) - 5 \, \log \left (3 \, x + 2\right )^{2} + 36\right ) - 2 \, \log \left (x - \log \left (3 \, x + 2\right )\right ) \]
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Timed out. \[ \int \frac {-72 x+144 x^2-108 x^3+10 x^4+15 x^5+\left (-48 x^2-72 x^3\right ) \log (x)+\left (-12 x^2+12 x^3-36 x^4\right ) \log ^2(x)+\left (-8 x^3-12 x^4\right ) \log ^3(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (96 x+144 x^2\right ) \log (x)+\left (12 x+12 x^2+72 x^3\right ) \log ^2(x)+\left (24 x^2+36 x^3\right ) \log ^3(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+(-48-72 x) \log (x)+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-24 x-36 x^2\right ) \log ^3(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+(8+12 x) \log ^3(x)+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)}{-72 x^2-108 x^3+10 x^4+15 x^5+\left (-24 x^3-36 x^4\right ) \log ^2(x)+\left (-2 x^4-3 x^5\right ) \log ^4(x)+\left (72 x+108 x^2-30 x^3-45 x^4+\left (48 x^2+72 x^3\right ) \log ^2(x)+\left (6 x^3+9 x^4\right ) \log ^4(x)\right ) \log (2+3 x)+\left (30 x^2+45 x^3+\left (-24 x-36 x^2\right ) \log ^2(x)+\left (-6 x^2-9 x^3\right ) \log ^4(x)\right ) \log ^2(2+3 x)+\left (-10 x-15 x^2+\left (2 x+3 x^2\right ) \log ^4(x)\right ) \log ^3(2+3 x)} \, dx=\int \frac {72\,x+\ln \left (x\right )\,\left (72\,x^3+48\,x^2\right )+{\ln \left (3\,x+2\right )}^2\,\left ({\ln \left (x\right )}^2\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^3\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^3+6\,x^2\right )+\ln \left (x\right )\,\left (72\,x+48\right )-30\,x^2-45\,x^3\right )+{\ln \left (x\right )}^4\,\left (3\,x^5+2\,x^4\right )+{\ln \left (x\right )}^3\,\left (12\,x^4+8\,x^3\right )+{\ln \left (x\right )}^2\,\left (36\,x^4-12\,x^3+12\,x^2\right )-\ln \left (3\,x+2\right )\,\left (72\,x+{\ln \left (x\right )}^2\,\left (72\,x^3+12\,x^2+12\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^4+6\,x^3\right )+{\ln \left (x\right )}^3\,\left (36\,x^3+24\,x^2\right )+\ln \left (x\right )\,\left (144\,x^2+96\,x\right )+108\,x^2-30\,x^3-45\,x^4\right )+{\ln \left (3\,x+2\right )}^3\,\left (10\,x-{\ln \left (x\right )}^4\,\left (3\,x^2+2\,x\right )+15\,x^2-{\ln \left (x\right )}^3\,\left (12\,x+8\right )\right )-144\,x^2+108\,x^3-10\,x^4-15\,x^5}{{\ln \left (x\right )}^4\,\left (3\,x^5+2\,x^4\right )+{\ln \left (x\right )}^2\,\left (36\,x^4+24\,x^3\right )+{\ln \left (3\,x+2\right )}^2\,\left ({\ln \left (x\right )}^2\,\left (36\,x^2+24\,x\right )+{\ln \left (x\right )}^4\,\left (9\,x^3+6\,x^2\right )-30\,x^2-45\,x^3\right )-\ln \left (3\,x+2\right )\,\left (72\,x+{\ln \left (x\right )}^4\,\left (9\,x^4+6\,x^3\right )+{\ln \left (x\right )}^2\,\left (72\,x^3+48\,x^2\right )+108\,x^2-30\,x^3-45\,x^4\right )+72\,x^2+108\,x^3-10\,x^4-15\,x^5+{\ln \left (3\,x+2\right )}^3\,\left (10\,x-{\ln \left (x\right )}^4\,\left (3\,x^2+2\,x\right )+15\,x^2\right )} \,d x \]
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