Integrand size = 211, antiderivative size = 29 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=x+\frac {x}{e^{\frac {-9+\log (x)}{(-2+x) x}}-x}+\log ^2(x) \]
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\[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=\int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx \]
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Rubi steps Aborted
\[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=\int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx \]
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Time = 1.35 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03
method | result | size |
risch | \(\ln \left (x \right )^{2}+x -\frac {x}{x -{\mathrm e}^{\frac {\ln \left (x \right )-9}{\left (-2+x \right ) x}}}\) | \(30\) |
parallelrisch | \(\frac {x \ln \left (x \right )^{2}-\ln \left (x \right )^{2} {\mathrm e}^{\frac {\ln \left (x \right )-9}{\left (-2+x \right ) x}}+x^{2}-{\mathrm e}^{\frac {\ln \left (x \right )-9}{\left (-2+x \right ) x}} x +7 x -8 \,{\mathrm e}^{\frac {\ln \left (x \right )-9}{\left (-2+x \right ) x}}}{x -{\mathrm e}^{\frac {\ln \left (x \right )-9}{\left (-2+x \right ) x}}}\) | \(88\) |
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Time = 0.27 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.00 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=\frac {x \log \left (x\right )^{2} + x^{2} - {\left (\log \left (x\right )^{2} + x\right )} e^{\left (\frac {\log \left (x\right ) - 9}{x^{2} - 2 \, x}\right )} - x}{x - e^{\left (\frac {\log \left (x\right ) - 9}{x^{2} - 2 \, x}\right )}} \]
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Time = 0.27 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=x + \frac {x}{- x + e^{\frac {\log {\left (x \right )} - 9}{x^{2} - 2 x}}} + \log {\left (x \right )}^{2} \]
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Leaf count of result is larger than twice the leaf count of optimal. 96 vs. \(2 (29) = 58\).
Time = 0.33 (sec) , antiderivative size = 96, normalized size of antiderivative = 3.31 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=-\frac {{\left (\log \left (x\right )^{2} + x\right )} e^{\left (\frac {\log \left (x\right )}{2 \, {\left (x - 2\right )}} + \frac {9}{2 \, x}\right )} - {\left (x \log \left (x\right )^{2} + x^{2} - x\right )} e^{\left (\frac {\log \left (x\right )}{2 \, x} + \frac {9}{2 \, {\left (x - 2\right )}}\right )}}{x e^{\left (\frac {\log \left (x\right )}{2 \, x} + \frac {9}{2 \, {\left (x - 2\right )}}\right )} - e^{\left (\frac {\log \left (x\right )}{2 \, {\left (x - 2\right )}} + \frac {9}{2 \, x}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 74 vs. \(2 (29) = 58\).
Time = 0.67 (sec) , antiderivative size = 74, normalized size of antiderivative = 2.55 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=\frac {x \log \left (x\right )^{2} - e^{\left (\frac {\log \left (x\right ) - 9}{x^{2} - 2 \, x}\right )} \log \left (x\right )^{2} + x^{2} - x e^{\left (\frac {\log \left (x\right ) - 9}{x^{2} - 2 \, x}\right )} - x}{x - e^{\left (\frac {\log \left (x\right ) - 9}{x^{2} - 2 \, x}\right )}} \]
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Time = 16.16 (sec) , antiderivative size = 123, normalized size of antiderivative = 4.24 \[ \int \frac {4 x^3-4 x^4+x^5+\left (8 x^2-8 x^3+2 x^4\right ) \log (x)+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3+\left (8-8 x+2 x^2\right ) \log (x)\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (20-15 x-12 x^2+9 x^3-2 x^4+\left (-2-14 x+16 x^2-4 x^3\right ) \log (x)\right )}{4 x^3-4 x^4+x^5+e^{\frac {2 (-9+\log (x))}{-2 x+x^2}} \left (4 x-4 x^2+x^3\right )+e^{\frac {-9+\log (x)}{-2 x+x^2}} \left (-8 x^2+8 x^3-2 x^4\right )} \, dx=\frac {{\mathrm {e}}^{\frac {9}{2\,x-x^2}}\,{\ln \left (x\right )}^2+x\,{\mathrm {e}}^{\frac {9}{2\,x-x^2}}+x\,x^{\frac {1}{2\,x-x^2}}-x^{\frac {1}{2\,x-x^2}}\,x^2-x\,x^{\frac {1}{2\,x-x^2}}\,{\ln \left (x\right )}^2}{{\mathrm {e}}^{\frac {9}{2\,x-x^2}}-x\,x^{\frac {1}{2\,x-x^2}}} \]
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