Integrand size = 199, antiderivative size = 25 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=x \left (x+\log (3)+\frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}\right ) \]
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\[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=\int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-\left (\left (-1+e^{e^x+x}\right ) x^2\right )-x (9+x) \left (2+e^{e^x+x} (-2+x)+e^{e^x+2 x} x\right ) \log (9+x)+\left (2 \left (-1+e^{e^x+x}\right )^2 x^2+9 \left (-1+e^{e^x+x}\right )^2 \log (3)+x \left (18+\log (3)+e^{2 \left (e^x+x\right )} (18+\log (3))-e^{e^x+x} (36+\log (9))\right )\right ) \log ^2(9+x)}{\left (1-e^{e^x+x}\right )^2 (9+x) \log ^2(9+x)} \, dx \\ & = \int \left (-\frac {e^{-e^x} \left (1+e^{e^x}\right ) x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)}-\frac {e^{-e^x} x \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)}+\frac {e^{-e^x} \left (-x^2+2 e^{e^x} x \log (9+x)+e^{e^x} \log (3) \log (9+x)\right )}{\log (9+x)}\right ) \, dx \\ & = -\int \frac {e^{-e^x} \left (1+e^{e^x}\right ) x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx+\int \frac {e^{-e^x} \left (-x^2+2 e^{e^x} x \log (9+x)+e^{e^x} \log (3) \log (9+x)\right )}{\log (9+x)} \, dx \\ & = \int \left (2 x+\log (3)-\frac {e^{-e^x} x^2}{\log (9+x)}\right ) \, dx-\int \left (\frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)}+\frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)}\right ) \, dx-\int \frac {e^{-e^x} x \left (-e^{e^x} x-(9+x) \left (e^{e^x} (-2+x)+2 x\right ) \log (9+x)\right )}{\left (1-e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx \\ & = x^2+x \log (3)-\int \frac {e^{-e^x} x^2}{\log (9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \left (\frac {e^{-e^x} \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)}-\frac {9 e^{-e^x} \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)}\right ) \, dx \\ & = x^2+x \log (3)+9 \int \frac {e^{-e^x} \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx-\int \left (\frac {81 e^{-e^x}}{\log (9+x)}-\frac {18 e^{-e^x} (9+x)}{\log (9+x)}+\frac {e^{-e^x} (9+x)^2}{\log (9+x)}\right ) \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} \left (e^{e^x} x-18 e^{e^x} \log (9+x)+18 x \log (9+x)+7 e^{e^x} x \log (9+x)+2 x^2 \log (9+x)+e^{e^x} x^2 \log (9+x)\right )}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)} \, dx \\ & = x^2+x \log (3)+9 \int \frac {e^{-e^x} \left (-e^{e^x} x-(9+x) \left (e^{e^x} (-2+x)+2 x\right ) \log (9+x)\right )}{\left (1-e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx+18 \int \frac {e^{-e^x} (9+x)}{\log (9+x)} \, dx-81 \int \frac {e^{-e^x}}{\log (9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} (9+x)^2}{\log (9+x)} \, dx-\int \frac {e^{-e^x} \left (-e^{e^x} x-(9+x) \left (e^{e^x} (-2+x)+2 x\right ) \log (9+x)\right )}{\left (1-e^{e^x+x}\right ) \log ^2(9+x)} \, dx \\ & = x^2+x \log (3)+9 \int \left (\frac {x}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)}-\frac {18}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}+\frac {7 x}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}+\frac {18 e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}+\frac {x^2}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}+\frac {2 e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}\right ) \, dx+18 \int \frac {e^{-e^x} (9+x)}{\log (9+x)} \, dx-81 \int \frac {e^{-e^x}}{\log (9+x)} \, dx-\int \left (\frac {x}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)}-\frac {18}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {7 x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {18 e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {2 e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)}\right ) \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} (9+x)^2}{\log (9+x)} \, dx \\ & = x^2+x \log (3)-2 \int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-7 \int \frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+9 \int \frac {x}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx+9 \int \frac {x^2}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx+18 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-18 \int \frac {e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+18 \int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx+18 \int \frac {e^{-e^x} (9+x)}{\log (9+x)} \, dx+63 \int \frac {x}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx-81 \int \frac {e^{-e^x}}{\log (9+x)} \, dx-162 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx+162 \int \frac {e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx-\int \frac {x}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-\int \frac {e^{-e^x} (9+x)^2}{\log (9+x)} \, dx \\ & = x^2+x \log (3)-2 \int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-7 \int \frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+9 \int \left (\frac {1}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)}-\frac {9}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)}\right ) \, dx+9 \int \left (-\frac {9}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {81}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}\right ) \, dx+18 \int \left (-\frac {9 e^{-e^x}}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}+\frac {81 e^{-e^x}}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}\right ) \, dx+18 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-18 \int \frac {e^{-e^x} x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+18 \int \frac {e^{-e^x} (9+x)}{\log (9+x)} \, dx+63 \int \left (\frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)}-\frac {9}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}\right ) \, dx-81 \int \frac {e^{-e^x}}{\log (9+x)} \, dx+162 \int \left (\frac {e^{-e^x}}{\left (-1+e^{e^x+x}\right ) \log (9+x)}-\frac {9 e^{-e^x}}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)}\right ) \, dx-162 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx-\int \frac {x}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-\int \frac {e^{-e^x} (9+x)^2}{\log (9+x)} \, dx \\ & = x^2+x \log (3)-2 \int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-7 \int \frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+9 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)} \, dx+9 \int \frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+18 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx+18 \int \frac {e^{-e^x} (9+x)}{\log (9+x)} \, dx+63 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-81 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log ^2(9+x)} \, dx-81 \int \frac {e^{-e^x}}{\log (9+x)} \, dx-81 \int \frac {1}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-162 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx-567 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx+729 \int \frac {1}{\left (-1+e^{e^x+x}\right ) (9+x) \log (9+x)} \, dx-\int \frac {x}{\left (-1+e^{e^x+x}\right ) \log ^2(9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {e^{-e^x} x^2}{\left (-1+e^{e^x+x}\right )^2 \log (9+x)} \, dx-\int \frac {x^2}{\left (-1+e^{e^x+x}\right ) \log (9+x)} \, dx-\int \frac {e^{-e^x} (9+x)^2}{\log (9+x)} \, dx \\ \end{align*}
Time = 0.31 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.00 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=x \left (x+\log (3)+\frac {x}{\left (-1+e^{e^x+x}\right ) \log (9+x)}\right ) \]
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Time = 4.72 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12
method | result | size |
risch | \(x \ln \left (3\right )+x^{2}+\frac {x^{2}}{\ln \left (x +9\right ) \left ({\mathrm e}^{{\mathrm e}^{x}+x}-1\right )}\) | \(28\) |
parallelrisch | \(\frac {x \ln \left (x +9\right ) {\mathrm e}^{{\mathrm e}^{x}+x} \ln \left (3\right )+\ln \left (x +9\right ) {\mathrm e}^{{\mathrm e}^{x}+x} x^{2}-\ln \left (x +9\right ) x \ln \left (3\right )-18 \ln \left (3\right ) \ln \left (x +9\right ) {\mathrm e}^{{\mathrm e}^{x}+x}-\ln \left (x +9\right ) x^{2}+18 \ln \left (3\right ) \ln \left (x +9\right )+x^{2}-81 \ln \left (x +9\right ) {\mathrm e}^{{\mathrm e}^{x}+x}+81 \ln \left (x +9\right )}{\left ({\mathrm e}^{{\mathrm e}^{x}+x}-1\right ) \ln \left (x +9\right )}\) | \(103\) |
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.24 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=\frac {{\left (x^{2} + x \log \left (3\right )\right )} e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) + x^{2} - {\left (x^{2} + x \log \left (3\right )\right )} \log \left (x + 9\right )}{e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) - \log \left (x + 9\right )} \]
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Time = 0.17 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=x^{2} + \frac {x^{2}}{e^{x + e^{x}} \log {\left (x + 9 \right )} - \log {\left (x + 9 \right )}} + x \log {\left (3 \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (23) = 46\).
Time = 0.33 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.24 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=\frac {{\left (x^{2} + x \log \left (3\right )\right )} e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) + x^{2} - {\left (x^{2} + x \log \left (3\right )\right )} \log \left (x + 9\right )}{e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) - \log \left (x + 9\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (23) = 46\).
Time = 0.31 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=\frac {x^{2} e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) + x e^{\left (x + e^{x}\right )} \log \left (3\right ) \log \left (x + 9\right ) - x^{2} \log \left (x + 9\right ) - x \log \left (3\right ) \log \left (x + 9\right ) + x^{2}}{e^{\left (x + e^{x}\right )} \log \left (x + 9\right ) - \log \left (x + 9\right )} \]
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Time = 10.81 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.28 \[ \int \frac {x^2+\left (-18 x-2 x^2\right ) \log (9+x)+\left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{2 e^x+2 x} \left (18 x+2 x^2+(9+x) \log (3)\right ) \log ^2(9+x)+e^{e^x+x} \left (-x^2+\left (18 x-7 x^2-x^3+e^x \left (-9 x^2-x^3\right )\right ) \log (9+x)+\left (-36 x-4 x^2+(-18-2 x) \log (3)\right ) \log ^2(9+x)\right )}{e^{e^x+x} (-18-2 x) \log ^2(9+x)+(9+x) \log ^2(9+x)+e^{2 e^x+2 x} (9+x) \log ^2(9+x)} \, dx=\frac {x\,\left (x-\ln \left (x+9\right )\,\ln \left (3\right )-x\,\ln \left (x+9\right )+\ln \left (x+9\right )\,{\mathrm {e}}^{x+{\mathrm {e}}^x}\,\ln \left (3\right )+x\,\ln \left (x+9\right )\,{\mathrm {e}}^{x+{\mathrm {e}}^x}\right )}{\ln \left (x+9\right )\,\left ({\mathrm {e}}^{x+{\mathrm {e}}^x}-1\right )} \]
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