Integrand size = 107, antiderivative size = 25 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=e^{\frac {x}{\frac {x}{27-x}+\frac {4 \log (2)}{x^3}}} x \]
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\[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=\int \frac {\exp \left (\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}\right ) \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx \\ & = \int \left (\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right )-\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x+\frac {48 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) (-36+x) (-27+x)^2 \log ^2(2)}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2}+\frac {8 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \left (1458-81 x+x^2\right ) \log (2)}{x^4+108 \log (2)-4 x \log (2)}\right ) \, dx \\ & = (8 \log (2)) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \left (1458-81 x+x^2\right )}{x^4+108 \log (2)-4 x \log (2)} \, dx+\left (48 \log ^2(2)\right ) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) (-36+x) (-27+x)^2}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx+\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \, dx-\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x \, dx \\ & = (8 \log (2)) \int \left (\frac {1458 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right )}{x^4+108 \log (2)-4 x \log (2)}-\frac {81 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x}{x^4+108 \log (2)-4 x \log (2)}+\frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^2}{x^4+108 \log (2)-4 x \log (2)}\right ) \, dx+\left (48 \log ^2(2)\right ) \int \left (-\frac {26244 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right )}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2}+\frac {2673 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2}-\frac {90 \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^2}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2}+\frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^3}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2}\right ) \, dx+\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \, dx-\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x \, dx \\ & = (8 \log (2)) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^2}{x^4+108 \log (2)-4 x \log (2)} \, dx-(648 \log (2)) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x}{x^4+108 \log (2)-4 x \log (2)} \, dx+(11664 \log (2)) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right )}{x^4+108 \log (2)-4 x \log (2)} \, dx+\left (48 \log ^2(2)\right ) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^3}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx-\left (4320 \log ^2(2)\right ) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x^2}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx+\left (128304 \log ^2(2)\right ) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx-\left (1259712 \log ^2(2)\right ) \int \frac {\exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right )}{\left (x^4+108 \log (2)-4 x \log (2)\right )^2} \, dx+\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) \, dx-\int \exp \left (\frac {(-27+x) x^4}{-x^4-108 \log (2)+4 x \log (2)}\right ) x \, dx \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.32 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=2^{-\frac {4 (-27+x)^2}{x^4+108 \log (2)-4 x \log (2)}} e^{27-x} x \]
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Time = 1.52 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12
method | result | size |
gosper | \(x \,{\mathrm e}^{\frac {x^{4} \left (x -27\right )}{-x^{4}+4 x \ln \left (2\right )-108 \ln \left (2\right )}}\) | \(28\) |
risch | \(x \,{\mathrm e}^{\frac {x^{4} \left (x -27\right )}{-x^{4}+4 x \ln \left (2\right )-108 \ln \left (2\right )}}\) | \(28\) |
parallelrisch | \(x \,{\mathrm e}^{\frac {x^{4} \left (x -27\right )}{-x^{4}+4 x \ln \left (2\right )-108 \ln \left (2\right )}}\) | \(28\) |
norman | \(\frac {-x^{5} {\mathrm e}^{\frac {x^{5}-27 x^{4}}{\left (4 x -108\right ) \ln \left (2\right )-x^{4}}}-108 x \ln \left (2\right ) {\mathrm e}^{\frac {x^{5}-27 x^{4}}{\left (4 x -108\right ) \ln \left (2\right )-x^{4}}}+4 x^{2} \ln \left (2\right ) {\mathrm e}^{\frac {x^{5}-27 x^{4}}{\left (4 x -108\right ) \ln \left (2\right )-x^{4}}}}{-x^{4}+4 x \ln \left (2\right )-108 \ln \left (2\right )}\) | \(118\) |
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Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=x e^{\left (-\frac {x^{5} - 27 \, x^{4}}{x^{4} - 4 \, {\left (x - 27\right )} \log \left (2\right )}\right )} \]
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Timed out. \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=\text {Timed out} \]
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (23) = 46\).
Time = 0.49 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=x e^{\left (-\frac {4 \, x^{2} \log \left (2\right )}{x^{4} - 4 \, x \log \left (2\right ) + 108 \, \log \left (2\right )} - x + \frac {216 \, x \log \left (2\right )}{x^{4} - 4 \, x \log \left (2\right ) + 108 \, \log \left (2\right )} - \frac {2916 \, \log \left (2\right )}{x^{4} - 4 \, x \log \left (2\right ) + 108 \, \log \left (2\right )} + 27\right )} \]
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Time = 0.36 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=x e^{\left (-\frac {x^{5} - 27 \, x^{4}}{x^{4} - 4 \, x \log \left (2\right ) + 108 \, \log \left (2\right )}\right )} \]
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Time = 15.29 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.20 \[ \int \frac {e^{\frac {-27 x^4+x^5}{-x^4+(-108+4 x) \log (2)}} \left (x^8-x^9+\left (11880 x^4-872 x^5+16 x^6\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)\right )}{x^8+\left (216 x^4-8 x^5\right ) \log (2)+\left (11664-864 x+16 x^2\right ) \log ^2(2)} \, dx=x\,{\mathrm {e}}^{\frac {27\,x^4-x^5}{x^4-4\,\ln \left (2\right )\,x+108\,\ln \left (2\right )}} \]
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