Integrand size = 288, antiderivative size = 34 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\frac {-e^{\frac {1}{3 \left (x+\log (2)+\frac {1}{9} x^2 (x-\log (x))\right )}}+\log (x)}{x} \]
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\[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx \\ & = \int \left (\frac {81}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {18 x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {18 \left (9+x^2\right ) \log (2)}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {81 \log ^2(2)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right ) \log (x)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \log ^2(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {x^2 \log ^3(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (78 x^2+18 x^4+x^6+81 \log ^2(2)+9 x^3 (1+\log (4))+27 x (1+\log (64))-18 x^3 \log (x)-2 x^5 \log (x)-6 x^2 (1+\log (8)) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}\right ) \, dx \\ & = 18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \frac {9+x^2}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right ) \log (x)}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \log ^2(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^3(x)}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (78 x^2+18 x^4+x^6+81 \log ^2(2)+9 x^3 (1+\log (4))+27 x (1+\log (64))-18 x^3 \log (x)-2 x^5 \log (x)-6 x^2 (1+\log (8)) \log (x)+x^4 \log ^2(x)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx \\ & = 18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \left (\frac {9}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {x}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}\right ) \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \left (\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2}+\frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (-27 x-3 x^2+3 x^3+81 \log ^2(2)+\log ^2(512)-\log (512) \log (262144)-\log (18014398509481984)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}+\frac {6 e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx+\int \left (\frac {18 x+x^2+2 x^3+18 \log (2)}{x^4}+\frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {2 \left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx-\int \left (\frac {2 \left (9 x+x^3+\log (512)\right )}{x^4}+\frac {\log (x)}{x^2}+\frac {\left (9 x+x^3+\log (512)\right )^3}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {3 \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx-\int \left (\frac {\left (9 x+x^3+\log (512)\right )^2 \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2}-\frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )}\right ) \, dx \\ & = -\left (2 \int \frac {9 x+x^3+\log (512)}{x^4} \, dx\right )-2 \int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+3 \int \frac {\left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+6 \int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx+18 \int \frac {x^2}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+81 \int \frac {1}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(18 \log (2)) \int \frac {x}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+(162 \log (2)) \int \frac {1}{x \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\left (81 \log ^2(2)\right ) \int \frac {1}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}}}{x^2} \, dx+\int \frac {18 x+x^2+2 x^3+18 \log (2)}{x^4} \, dx-\int \frac {\log (x)}{x^2} \, dx+\int \frac {x^4}{\left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (18 x+x^2+2 x^3+18 \log (2)\right ) \left (9 x+x^3+\log (512)\right )^2}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right )^3}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx-\int \frac {\left (9 x+x^3+\log (512)\right )^2 \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {e^{\frac {3}{9 x+x^3+\log (512)-x^2 \log (x)}} \left (-27 x-3 x^2+3 x^3+81 \log ^2(2)+\log ^2(512)-\log (512) \log (262144)-\log (18014398509481984)\right )}{x^2 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )^2} \, dx+\int \frac {\left (9 x+x^3+\log (512)\right ) \left (9 x+2 x^2+x^3+\log (512)\right )}{x^4 \left (9 x+x^3+\log (512)-x^2 \log (x)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
\[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx \]
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Time = 49.88 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.06
method | result | size |
risch | \(\frac {\ln \left (x \right )}{x}-\frac {{\mathrm e}^{\frac {3}{-x^{2} \ln \left (x \right )+x^{3}+9 \ln \left (2\right )+9 x}}}{x}\) | \(36\) |
parallelrisch | \(\frac {4 x +\ln \left (x \right )-{\mathrm e}^{\frac {3}{-x^{2} \ln \left (x \right )+x^{3}+9 \ln \left (2\right )+9 x}}}{x}\) | \(36\) |
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Time = 0.25 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.97 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=-\frac {e^{\left (\frac {3}{x^{3} - x^{2} \log \left (x\right ) + 9 \, x + 9 \, \log \left (2\right )}\right )} - \log \left (x\right )}{x} \]
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Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: TypeError} \]
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Exception generated. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\text {Exception raised: RuntimeError} \]
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Time = 0.68 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.85 \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=-\frac {e^{\left (-\frac {x^{3} - x^{2} \log \left (x\right ) + 9 \, x}{3 \, {\left (x^{3} \log \left (2\right ) - x^{2} \log \left (2\right ) \log \left (x\right ) + 9 \, x \log \left (2\right ) + 9 \, \log \left (2\right )^{2}\right )}} + \frac {1}{3 \, \log \left (2\right )}\right )} - \log \left (x\right )}{x} \]
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Timed out. \[ \int \frac {81 x^2+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-81 x^2-18 x^3-18 x^4-2 x^5-x^6+\left (-162 x-18 x^2-18 x^3\right ) \log (2)-81 \log ^2(2)\right ) \log (x)+\left (18 x^3+x^4+2 x^5+18 x^2 \log (2)\right ) \log ^2(x)-x^4 \log ^3(x)+e^{-\frac {3}{-9 x-x^3-9 \log (2)+x^2 \log (x)}} \left (27 x+78 x^2+9 x^3+18 x^4+x^6+\left (162 x+18 x^3\right ) \log (2)+81 \log ^2(2)+\left (-6 x^2-18 x^3-2 x^5-18 x^2 \log (2)\right ) \log (x)+x^4 \log ^2(x)\right )}{81 x^4+18 x^6+x^8+\left (162 x^3+18 x^5\right ) \log (2)+81 x^2 \log ^2(2)+\left (-18 x^5-2 x^7-18 x^4 \log (2)\right ) \log (x)+x^6 \log ^2(x)} \, dx=\int \frac {\ln \left (2\right )\,\left (18\,x^3+162\,x\right )-x^4\,{\ln \left (x\right )}^3+81\,{\ln \left (2\right )}^2+81\,x^2+18\,x^4+x^6+{\ln \left (x\right )}^2\,\left (2\,x^5+x^4+18\,x^3+18\,\ln \left (2\right )\,x^2\right )-\ln \left (x\right )\,\left (\ln \left (2\right )\,\left (18\,x^3+18\,x^2+162\,x\right )+81\,{\ln \left (2\right )}^2+81\,x^2+18\,x^3+18\,x^4+2\,x^5+x^6\right )+{\mathrm {e}}^{\frac {3}{9\,x+9\,\ln \left (2\right )-x^2\,\ln \left (x\right )+x^3}}\,\left (27\,x+\ln \left (2\right )\,\left (18\,x^3+162\,x\right )+x^4\,{\ln \left (x\right )}^2+81\,{\ln \left (2\right )}^2+78\,x^2+9\,x^3+18\,x^4+x^6-\ln \left (x\right )\,\left (18\,x^2\,\ln \left (2\right )+6\,x^2+18\,x^3+2\,x^5\right )\right )}{81\,x^2\,{\ln \left (2\right )}^2+x^6\,{\ln \left (x\right )}^2+\ln \left (2\right )\,\left (18\,x^5+162\,x^3\right )-\ln \left (x\right )\,\left (2\,x^7+18\,x^5+18\,\ln \left (2\right )\,x^4\right )+81\,x^4+18\,x^6+x^8} \,d x \]
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