Integrand size = 178, antiderivative size = 32 \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=\frac {6 e^x}{x \left (-\sqrt {e}-x-x^2+(3+\log (2))^2\right )} \]
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Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 9.66 (sec) , antiderivative size = 1976, normalized size of antiderivative = 61.75, number of steps used = 32, number of rules used = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.039, Rules used = {6, 6820, 12, 6874, 2208, 2209, 6860} \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx =\text {Too large to display} \]
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Rule 6
Rule 12
Rule 2208
Rule 2209
Rule 6820
Rule 6860
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{(81+e) x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx \\ & = \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+x^2 \log ^4(2)+x^2 \left (81+e+12 \log ^3(2)\right )} \, dx \\ & = \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+x^2 \left (81+e+12 \log ^3(2)+\log ^4(2)\right )} \, dx \\ & = \int \frac {6 e^x \left (-9+\sqrt {e}+2 x^2-x^3-\log ^2(2)-\log (64)+x \left (11-\sqrt {e}+\log ^2(2)+\log (64)\right )\right )}{x^2 \left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2} \, dx \\ & = 6 \int \frac {e^x \left (-9+\sqrt {e}+2 x^2-x^3-\log ^2(2)-\log (64)+x \left (11-\sqrt {e}+\log ^2(2)+\log (64)\right )\right )}{x^2 \left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2} \, dx \\ & = 6 \int \left (\frac {e^x \left (-9+\sqrt {e}-\log ^2(2)-\log (64)\right )}{x^2 \left (\sqrt {e}-(3+\log (2))^2\right )^2}+\frac {e^x x \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3 \left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )}+\frac {e^x \left (-81-e-66 \log (2)-6 \log ^3(2)-\log ^4(2)-7 \log (64)-\log ^2(64)-\log ^2(2) (18+\log (64))+2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{x \left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {e^x \left (171+2 e+228 \log (2)+109 \log ^2(2)+24 \log ^3(2)+2 \log ^4(2)-\sqrt {e} \left (37+24 \log (2)+4 \log ^2(2)\right )-\log (64)+x \left (9-\sqrt {e}-6 \log ^3(2)-\log ^2(2) (35-\log (64))+\log (64)+\log ^2(64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^2 \left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2}\right ) \, dx \\ & = \frac {6 \int \frac {e^x \left (171+2 e+228 \log (2)+109 \log ^2(2)+24 \log ^3(2)+2 \log ^4(2)-\sqrt {e} \left (37+24 \log (2)+4 \log ^2(2)\right )-\log (64)+x \left (9-\sqrt {e}-6 \log ^3(2)-\log ^2(2) (35-\log (64))+\log (64)+\log ^2(64)\right )\right )}{\left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}+\frac {\left (6 \left (-9+\sqrt {e}-\log ^2(2)-\log (64)\right )\right ) \int \frac {e^x}{x^2} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {\left (6 \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )\right ) \int \frac {e^x}{x} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {\left (6 \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )\right ) \int \frac {e^x x}{\sqrt {e}+x+x^2-(3+\log (2))^2} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^3} \\ & = \frac {6 e^x \left (9-\sqrt {e}+\log ^2(2)+\log (64)\right )}{x \left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {6 \text {Ei}(x) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {6 \int \left (\frac {171 e^x \left (1+\frac {1}{171} \left (2 e+228 \log (2)+109 \log ^2(2)+24 \log ^3(2)+2 \log ^4(2)-\sqrt {e} \left (37+24 \log (2)+4 \log ^2(2)\right )-\log (64)\right )\right )}{\left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2}+\frac {e^x x \left (9-\sqrt {e}-6 \log ^3(2)-\log ^2(2) (35-\log (64))+\log (64)+\log ^2(64)\right )}{\left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2}\right ) \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}+\frac {\left (6 \left (-9+\sqrt {e}-\log ^2(2)-\log (64)\right )\right ) \int \frac {e^x}{x} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}+\frac {\left (6 \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )\right ) \int \left (\frac {e^x \left (1-\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right )}{1+2 x-\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}+\frac {e^x \left (1+\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right )}{1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right ) \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^3} \\ & = \frac {6 e^x \left (9-\sqrt {e}+\log ^2(2)+\log (64)\right )}{x \left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {6 \text {Ei}(x) \left (9-\sqrt {e}+\log ^2(2)+\log (64)\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {6 \text {Ei}(x) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}-\frac {6 \int \frac {e^x x}{\left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2} \, dx}{\sqrt {e}-(3+\log (2))^2}+\frac {\left (6 \left (171+2 e+228 \log (2)+109 \log ^2(2)+24 \log ^3(2)+2 \log ^4(2)-\sqrt {e} \left (37+24 \log (2)+4 \log ^2(2)\right )-\log (64)\right )\right ) \int \frac {e^x}{\left (\sqrt {e}+x+x^2-(3+\log (2))^2\right )^2} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}+\frac {\left (6 \left (1-\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right ) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )\right ) \int \frac {e^x}{1+2 x-\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {\left (6 \left (1+\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right ) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )\right ) \int \frac {e^x}{1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}} \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^3} \\ & = \frac {6 e^x \left (9-\sqrt {e}+\log ^2(2)+\log (64)\right )}{x \left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {6 \text {Ei}(x) \left (9-\sqrt {e}+\log ^2(2)+\log (64)\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^2}-\frac {6 \text {Ei}(x) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {3 e^{\frac {1}{2} \left (-1+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )} \text {Ei}\left (\frac {1}{2} \left (1+2 x-\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )\right ) \left (1-\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right ) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}+\frac {3 e^{\frac {1}{2} \left (-1-\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )} \text {Ei}\left (\frac {1}{2} \left (1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )\right ) \left (1+\frac {1}{\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}}\right ) \left (81+e+66 \log (2)+6 \log ^3(2)+\log ^4(2)+7 \log (64)+\log ^2(64)+\log ^2(2) (18+\log (64))-2 \sqrt {e} \left (9+\log ^2(2)+\log (64)\right )\right )}{\left (\sqrt {e}-(3+\log (2))^2\right )^3}-\frac {6 \int \left (\frac {2 e^x \left (-1+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right ) \left (-1-2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )^2}-\frac {2 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right )^{3/2} \left (-1-2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}+\frac {2 e^x \left (-1-\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right ) \left (1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )^2}-\frac {2 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right )^{3/2} \left (1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}\right ) \, dx}{\sqrt {e}-(3+\log (2))^2}+\frac {\left (6 \left (171+2 e+228 \log (2)+109 \log ^2(2)+24 \log ^3(2)+2 \log ^4(2)-\sqrt {e} \left (37+24 \log (2)+4 \log ^2(2)\right )-\log (64)\right )\right ) \int \left (\frac {4 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right ) \left (-1-2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )^2}+\frac {4 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right )^{3/2} \left (-1-2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}+\frac {4 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right ) \left (1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )^2}+\frac {4 e^x}{\left (37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)\right )^{3/2} \left (1+2 x+\sqrt {37-4 \sqrt {e}+24 \log (2)+4 \log ^2(2)}\right )}\right ) \, dx}{\left (\sqrt {e}-(3+\log (2))^2\right )^2} \\ & = \text {Too large to display} \\ \end{align*}
\[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=\int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx \]
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Time = 0.43 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88
method | result | size |
gosper | \(-\frac {6 \,{\mathrm e}^{x}}{x \left (-\ln \left (2\right )^{2}+x^{2}+{\mathrm e}^{\frac {1}{2}}-6 \ln \left (2\right )+x -9\right )}\) | \(28\) |
norman | \(-\frac {6 \,{\mathrm e}^{x}}{x \left (-\ln \left (2\right )^{2}+x^{2}+{\mathrm e}^{\frac {1}{2}}-6 \ln \left (2\right )+x -9\right )}\) | \(28\) |
risch | \(-\frac {6 \,{\mathrm e}^{x}}{x \left (-\ln \left (2\right )^{2}+x^{2}+{\mathrm e}^{\frac {1}{2}}-6 \ln \left (2\right )+x -9\right )}\) | \(28\) |
parallelrisch | \(-\frac {6 \,{\mathrm e}^{x}}{x \left (-\ln \left (2\right )^{2}+x^{2}+{\mathrm e}^{\frac {1}{2}}-6 \ln \left (2\right )+x -9\right )}\) | \(28\) |
default | \(\text {Expression too large to display}\) | \(40397\) |
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Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=-\frac {6 \, e^{x}}{x^{3} - x \log \left (2\right )^{2} + x^{2} + x e^{\frac {1}{2}} - 6 \, x \log \left (2\right ) - 9 \, x} \]
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Timed out. \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=\text {Timed out} \]
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Time = 0.63 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=-\frac {6 \, e^{x}}{x^{3} - {\left (\log \left (2\right )^{2} - e^{\frac {1}{2}} + 6 \, \log \left (2\right ) + 9\right )} x + x^{2}} \]
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Time = 0.46 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=-\frac {12 \, e^{x}}{x^{3} - x \log \left (2\right )^{2} + x^{2} + x e^{\frac {1}{2}} - 6 \, x \log \left (2\right ) - 9 \, x} \]
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Time = 15.58 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \frac {e^x \left (-54+\sqrt {e} (6-6 x)+66 x+12 x^2-6 x^3+(-36+36 x) \log (2)+(-6+6 x) \log ^2(2)\right )}{81 x^2+e x^2-18 x^3-17 x^4+2 x^5+x^6+\sqrt {e} \left (-18 x^2+2 x^3+2 x^4\right )+\left (108 x^2-12 \sqrt {e} x^2-12 x^3-12 x^4\right ) \log (2)+\left (54 x^2-2 \sqrt {e} x^2-2 x^3-2 x^4\right ) \log ^2(2)+12 x^2 \log ^3(2)+x^2 \log ^4(2)} \, dx=-\frac {6\,{\mathrm {e}}^x}{x^3+x^2+\left (\sqrt {\mathrm {e}}-\ln \left (64\right )-{\ln \left (2\right )}^2-9\right )\,x} \]
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