Integrand size = 117, antiderivative size = 24 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=4+\log \left (x-\log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )\right ) \]
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Time = 0.42 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {6, 6873, 6816} \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log \left (x-\log \left (-e^{\frac {e^4}{x^6}}+x+3+\log (4)\right )\right ) \]
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Rule 6
Rule 6816
Rule 6873
Rubi steps \begin{align*} \text {integral}& = \int \frac {x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 (2+\log (4))}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx \\ & = \int \frac {x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 (2+\log (4))}{-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 (3+\log (4))+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx \\ & = \int \frac {-x^8-e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )-x^7 (2+\log (4))}{x^7 \left (e^{\frac {e^4}{x^6}}-x-3 \left (1+\frac {2 \log (2)}{3}\right )\right ) \left (x-\log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )\right )} \, dx \\ & = \log \left (x-\log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )\right ) \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log \left (x-\log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )\right ) \]
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Time = 62.79 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96
method | result | size |
risch | \(\ln \left (\ln \left (-{\mathrm e}^{\frac {{\mathrm e}^{4}}{x^{6}}}+2 \ln \left (2\right )+3+x \right )-x \right )\) | \(23\) |
parallelrisch | \(\ln \left (x -\ln \left (-{\mathrm e}^{\frac {{\mathrm e}^{4}}{x^{6}}}+2 \ln \left (2\right )+3+x \right )\right )\) | \(23\) |
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Time = 0.25 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log \left (-x + \log \left (x - e^{\left (\frac {e^{4}}{x^{6}}\right )} + 2 \, \log \left (2\right ) + 3\right )\right ) \]
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Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log {\left (- x + \log {\left (x - e^{\frac {e^{4}}{x^{6}}} + 2 \log {\left (2 \right )} + 3 \right )} \right )} \]
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Time = 0.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log \left (-x + \log \left (x - e^{\left (\frac {e^{4}}{x^{6}}\right )} + 2 \, \log \left (2\right ) + 3\right )\right ) \]
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Time = 0.36 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.62 \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\log \left (x - \log \left ({\left (x e^{4} + 2 \, e^{4} \log \left (2\right ) + 3 \, e^{4} - e^{\left (\frac {4 \, x^{6} + e^{4}}{x^{6}}\right )}\right )} e^{\left (-4\right )}\right )\right ) \]
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Timed out. \[ \int \frac {2 x^7+x^8+e^{\frac {e^4}{x^6}} \left (-6 e^4-x^7\right )+x^7 \log (4)}{3 x^8-e^{\frac {e^4}{x^6}} x^8+x^9+x^8 \log (4)+\left (-3 x^7+e^{\frac {e^4}{x^6}} x^7-x^8-x^7 \log (4)\right ) \log \left (3-e^{\frac {e^4}{x^6}}+x+\log (4)\right )} \, dx=\int \frac {2\,x^7\,\ln \left (2\right )-{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^6}}\,\left (x^7+6\,{\mathrm {e}}^4\right )+2\,x^7+x^8}{2\,x^8\,\ln \left (2\right )-x^8\,{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^6}}-\ln \left (x-{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^6}}+2\,\ln \left (2\right )+3\right )\,\left (2\,x^7\,\ln \left (2\right )-x^7\,{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^6}}+3\,x^7+x^8\right )+3\,x^8+x^9} \,d x \]
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