Integrand size = 166, antiderivative size = 28 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (2-x-\frac {x}{(9-x)^2}-\log \left (\frac {5}{3+x}\right )\right ) \]
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Time = 11.42 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54, number of steps used = 46, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6874, 6820, 2629} \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (\frac {-x^3+20 x^2-118 x-(9-x)^2 \log \left (\frac {5}{x+3}\right )+162}{(9-x)^2}\right ) \]
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Rule 2629
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {1485 x}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )}-\frac {255 x^2}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )}+\frac {188 x^3}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )}-\frac {25 x^4}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )}+\frac {x^5}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )}+\log \left (-\frac {-162+118 x-20 x^2+x^3+(-9+x)^2 \log \left (\frac {5}{3+x}\right )}{(-9+x)^2}\right )\right ) \, dx \\ & = -\left (25 \int \frac {x^4}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx\right )+188 \int \frac {x^3}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx-255 \int \frac {x^2}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx-1485 \int \frac {x}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx+\int \frac {x^5}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+81 \log \left (\frac {5}{3+x}\right )-18 x \log \left (\frac {5}{3+x}\right )+x^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx+\int \log \left (-\frac {-162+118 x-20 x^2+x^3+(-9+x)^2 \log \left (\frac {5}{3+x}\right )}{(-9+x)^2}\right ) \, dx \\ & = x \log \left (\frac {162-118 x+20 x^2-x^3-(9-x)^2 \log \left (\frac {5}{3+x}\right )}{(9-x)^2}\right )-25 \int \frac {x^4}{(9-x) (3+x) \left (162-118 x+20 x^2-x^3-(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx+188 \int \frac {x^3}{(9-x) (3+x) \left (162-118 x+20 x^2-x^3-(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx-255 \int \frac {x^2}{(9-x) (3+x) \left (162-118 x+20 x^2-x^3-(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx-1485 \int \frac {x}{(9-x) (3+x) \left (162-118 x+20 x^2-x^3-(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx+\int \frac {x^5}{(9-x) (3+x) \left (162-118 x+20 x^2-x^3-(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx-\int \frac {x \left (-1485-255 x+188 x^2-25 x^3+x^4\right )}{(-9+x) (3+x) \left (-162+118 x-20 x^2+x^3+(-9+x)^2 \log \left (\frac {5}{3+x}\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.14 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (-\frac {-162+118 x-20 x^2+x^3+(-9+x)^2 \log \left (\frac {5}{3+x}\right )}{(-9+x)^2}\right ) \]
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Time = 5.49 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75
method | result | size |
parallelrisch | \(\ln \left (\frac {\left (-x^{2}+18 x -81\right ) \ln \left (\frac {5}{3+x}\right )-x^{3}+20 x^{2}-118 x +162}{x^{2}-18 x +81}\right ) x\) | \(49\) |
default | \(\ln \left (\frac {-x^{2} \ln \left (5\right )-x^{2} \ln \left (\frac {1}{3+x}\right )-x^{3}+18 x \ln \left (5\right )+18 x \ln \left (\frac {1}{3+x}\right )+20 x^{2}-81 \ln \left (5\right )-81 \ln \left (\frac {1}{3+x}\right )-118 x +162}{x^{2}-18 x +81}\right ) x\) | \(74\) |
parts | \(\ln \left (\frac {-x^{2} \ln \left (5\right )-x^{2} \ln \left (\frac {1}{3+x}\right )-x^{3}+18 x \ln \left (5\right )+18 x \ln \left (\frac {1}{3+x}\right )+20 x^{2}-81 \ln \left (5\right )-81 \ln \left (\frac {1}{3+x}\right )-118 x +162}{x^{2}-18 x +81}\right ) x\) | \(74\) |
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Time = 0.24 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (-\frac {x^{3} - 20 \, x^{2} + {\left (x^{2} - 18 \, x + 81\right )} \log \left (\frac {5}{x + 3}\right ) + 118 \, x - 162}{x^{2} - 18 \, x + 81}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (19) = 38\).
Time = 0.69 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.54 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=\left (x - 1\right ) \log {\left (\frac {- x^{3} + 20 x^{2} - 118 x + \left (- x^{2} + 18 x - 81\right ) \log {\left (\frac {5}{x + 3} \right )} + 162}{x^{2} - 18 x + 81} \right )} + \log {\left (\log {\left (\frac {5}{x + 3} \right )} + \frac {x^{3} - 20 x^{2} + 118 x - 162}{x^{2} - 18 x + 81} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (26) = 52\).
Time = 0.31 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (-x^{3} - x^{2} {\left (\log \left (5\right ) - \log \left (x + 3\right ) - 20\right )} + 2 \, x {\left (9 \, \log \left (5\right ) - 9 \, \log \left (x + 3\right ) - 59\right )} - 81 \, \log \left (5\right ) + 81 \, \log \left (x + 3\right ) + 162\right ) - 2 \, x \log \left (x - 9\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (26) = 52\).
Time = 0.58 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.32 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x \log \left (-x^{3} - x^{2} \log \left (\frac {5}{x + 3}\right ) + 20 \, x^{2} + 18 \, x \log \left (\frac {5}{x + 3}\right ) - 118 \, x - 81 \, \log \left (\frac {5}{x + 3}\right ) + 162\right ) - x \log \left (x^{2} - 18 \, x + 81\right ) \]
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Time = 11.38 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.61 \[ \int \frac {-1485 x-255 x^2+188 x^3-25 x^4+x^5+\left (4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )\right ) \log \left (\frac {162-118 x+20 x^2-x^3+\left (-81+18 x-x^2\right ) \log \left (\frac {5}{3+x}\right )}{81-18 x+x^2}\right )}{4374-2214 x-330 x^2+211 x^3-26 x^4+x^5+\left (-2187+162 x^2-24 x^3+x^4\right ) \log \left (\frac {5}{3+x}\right )} \, dx=x\,\ln \left (-\frac {118\,x+\ln \left (\frac {5}{x+3}\right )\,\left (x^2-18\,x+81\right )-20\,x^2+x^3-162}{x^2-18\,x+81}\right ) \]
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