Integrand size = 389, antiderivative size = 34 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\frac {5}{16 x^2 \left (2-x+\frac {3}{4} (3+x)^2 \left (-e^x+x\right )-\log (2)\right )^2} \]
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\[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )+x^3 \left (-512+64 \log ^3(2)\right )} \, dx \\ & = \int \frac {10 \left (-46 x-54 x^2-12 x^3+3 e^x \left (9+21 x+9 x^2+x^3\right )-8 \left (1-\frac {\log (2)}{2}\right )\right )}{x^3 \left (23 x+18 x^2+3 x^3-3 e^x (3+x)^2+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx \\ & = 10 \int \frac {-46 x-54 x^2-12 x^3+3 e^x \left (9+21 x+9 x^2+x^3\right )-8 \left (1-\frac {\log (2)}{2}\right )}{x^3 \left (23 x+18 x^2+3 x^3-3 e^x (3+x)^2+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx \\ & = 10 \int \left (\frac {-3-6 x-x^2}{x^3 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}+\frac {29-50 x^2-24 x^3-3 x^4+20 \log (2)+4 x (2+\log (2))}{x^2 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}\right ) \, dx \\ & = 10 \int \frac {-3-6 x-x^2}{x^3 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+10 \int \frac {29-50 x^2-24 x^3-3 x^4+20 \log (2)+4 x (2+\log (2))}{x^2 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx \\ & = 10 \int \left (\frac {2}{9 (-3-x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}-\frac {1}{x^3 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}-\frac {5}{3 x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}+\frac {2}{9 x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2}\right ) \, dx+10 \int \left (\frac {15}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {3 x}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {8 (-5+\log (2))}{9 (3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {29+20 \log (2)}{3 x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}+\frac {-5-\log (256)}{9 x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3}\right ) \, dx \\ & = \frac {20}{9} \int \frac {1}{(-3-x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+\frac {20}{9} \int \frac {1}{x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx-10 \int \frac {1}{x^3 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx-\frac {50}{3} \int \frac {1}{x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^2} \, dx+30 \int \frac {x}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx+150 \int \frac {1}{\left (-27 e^x+23 x-18 e^x x+18 x^2-3 e^x x^2+3 x^3+8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx-\frac {1}{9} (80 (5-\log (2))) \int \frac {1}{(3+x) \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx+\frac {1}{3} (10 (29+20 \log (2))) \int \frac {1}{x^2 \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx-\frac {1}{9} (10 (5+\log (256))) \int \frac {1}{x \left (27 e^x-23 x+18 e^x x-18 x^2+3 e^x x^2-3 x^3-8 \left (1-\frac {\log (2)}{2}\right )\right )^3} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(34)=68\).
Time = 3.33 (sec) , antiderivative size = 93, normalized size of antiderivative = 2.74 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=-\frac {5 \left (29-50 x^2-24 x^3-3 x^4+x (8+\log (16))+\log (1048576)\right )^3}{x^2 \left (-29+50 x^2+24 x^3+3 x^4-20 \log (2)-4 x (2+\log (2))\right )^3 \left (8+23 x+18 x^2+3 x^3-3 e^x (3+x)^2-\log (16)\right )^2} \]
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Time = 1.22 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.26
method | result | size |
risch | \(\frac {5}{x^{2} \left (3 \,{\mathrm e}^{x} x^{2}-3 x^{3}+18 \,{\mathrm e}^{x} x -18 x^{2}+4 \ln \left (2\right )+27 \,{\mathrm e}^{x}-23 x -8\right )^{2}}\) | \(43\) |
parallelrisch | \(\frac {5}{x^{2} \left (64+9 \,{\mathrm e}^{2 x} x^{4}+368 x +216 \,{\mathrm e}^{x} \ln \left (2\right )+108 \,{\mathrm e}^{2 x} x^{3}+486 \,{\mathrm e}^{2 x} x^{2}+972 x \,{\mathrm e}^{2 x}-216 \,{\mathrm e}^{x} x^{4}-184 x \ln \left (2\right )-144 x^{2} \ln \left (2\right )-24 x^{3} \ln \left (2\right )-1848 \,{\mathrm e}^{x} x^{2}-948 \,{\mathrm e}^{x} x^{3}-1530 \,{\mathrm e}^{x} x -18 x^{5} {\mathrm e}^{x}+144 x \ln \left (2\right ) {\mathrm e}^{x}+729 \,{\mathrm e}^{2 x}+24 x^{2} \ln \left (2\right ) {\mathrm e}^{x}-64 \ln \left (2\right )+16 \ln \left (2\right )^{2}+9 x^{6}+108 x^{5}+462 x^{4}+876 x^{3}+817 x^{2}-432 \,{\mathrm e}^{x}\right )}\) | \(166\) |
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Leaf count of result is larger than twice the leaf count of optimal. 157 vs. \(2 (29) = 58\).
Time = 0.29 (sec) , antiderivative size = 157, normalized size of antiderivative = 4.62 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\frac {5}{9 \, x^{8} + 108 \, x^{7} + 462 \, x^{6} + 876 \, x^{5} + 817 \, x^{4} + 16 \, x^{2} \log \left (2\right )^{2} + 368 \, x^{3} + 64 \, x^{2} + 9 \, {\left (x^{6} + 12 \, x^{5} + 54 \, x^{4} + 108 \, x^{3} + 81 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{7} + 36 \, x^{6} + 158 \, x^{5} + 308 \, x^{4} + 255 \, x^{3} + 72 \, x^{2} - 4 \, {\left (x^{4} + 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )\right )} e^{x} - 8 \, {\left (3 \, x^{5} + 18 \, x^{4} + 23 \, x^{3} + 8 \, x^{2}\right )} \log \left (2\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (31) = 62\).
Time = 0.63 (sec) , antiderivative size = 170, normalized size of antiderivative = 5.00 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\frac {5}{9 x^{8} + 108 x^{7} + 462 x^{6} - 24 x^{5} \log {\left (2 \right )} + 876 x^{5} - 144 x^{4} \log {\left (2 \right )} + 817 x^{4} - 184 x^{3} \log {\left (2 \right )} + 368 x^{3} - 64 x^{2} \log {\left (2 \right )} + 16 x^{2} \log {\left (2 \right )}^{2} + 64 x^{2} + \left (9 x^{6} + 108 x^{5} + 486 x^{4} + 972 x^{3} + 729 x^{2}\right ) e^{2 x} + \left (- 18 x^{7} - 216 x^{6} - 948 x^{5} - 1848 x^{4} + 24 x^{4} \log {\left (2 \right )} - 1530 x^{3} + 144 x^{3} \log {\left (2 \right )} - 432 x^{2} + 216 x^{2} \log {\left (2 \right )}\right ) e^{x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 145 vs. \(2 (29) = 58\).
Time = 1.12 (sec) , antiderivative size = 145, normalized size of antiderivative = 4.26 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\frac {5}{9 \, x^{8} + 108 \, x^{7} + 462 \, x^{6} - 12 \, x^{5} {\left (2 \, \log \left (2\right ) - 73\right )} - x^{4} {\left (144 \, \log \left (2\right ) - 817\right )} - 184 \, x^{3} {\left (\log \left (2\right ) - 2\right )} + 16 \, {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) + 4\right )} x^{2} + 9 \, {\left (x^{6} + 12 \, x^{5} + 54 \, x^{4} + 108 \, x^{3} + 81 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (3 \, x^{7} + 36 \, x^{6} + 158 \, x^{5} - 4 \, x^{4} {\left (\log \left (2\right ) - 77\right )} - 3 \, x^{3} {\left (8 \, \log \left (2\right ) - 85\right )} - 36 \, x^{2} {\left (\log \left (2\right ) - 2\right )}\right )} e^{x}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 191 vs. \(2 (29) = 58\).
Time = 0.64 (sec) , antiderivative size = 191, normalized size of antiderivative = 5.62 \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\frac {5}{9 \, x^{8} - 18 \, x^{7} e^{x} + 108 \, x^{7} + 9 \, x^{6} e^{\left (2 \, x\right )} - 216 \, x^{6} e^{x} + 462 \, x^{6} + 108 \, x^{5} e^{\left (2 \, x\right )} - 948 \, x^{5} e^{x} - 24 \, x^{5} \log \left (2\right ) + 24 \, x^{4} e^{x} \log \left (2\right ) + 876 \, x^{5} + 486 \, x^{4} e^{\left (2 \, x\right )} - 1848 \, x^{4} e^{x} - 144 \, x^{4} \log \left (2\right ) + 144 \, x^{3} e^{x} \log \left (2\right ) + 817 \, x^{4} + 972 \, x^{3} e^{\left (2 \, x\right )} - 1530 \, x^{3} e^{x} - 184 \, x^{3} \log \left (2\right ) + 216 \, x^{2} e^{x} \log \left (2\right ) + 16 \, x^{2} \log \left (2\right )^{2} + 368 \, x^{3} + 729 \, x^{2} e^{\left (2 \, x\right )} - 432 \, x^{2} e^{x} - 64 \, x^{2} \log \left (2\right ) + 64 \, x^{2}} \]
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Timed out. \[ \int \frac {80+460 x+540 x^2+120 x^3+e^x \left (-270-630 x-270 x^2-30 x^3\right )-40 \log (2)}{-512 x^3-4416 x^4-16152 x^5-32615 x^6-39654 x^7-29709 x^8-13500 x^9-3537 x^{10}-486 x^{11}-27 x^{12}+e^{3 x} \left (19683 x^3+39366 x^4+32805 x^5+14580 x^6+3645 x^7+486 x^8+27 x^9\right )+\left (768 x^3+4416 x^4+9804 x^5+10512 x^6+5544 x^7+1296 x^8+108 x^9\right ) \log (2)+\left (-384 x^3-1104 x^4-864 x^5-144 x^6\right ) \log ^2(2)+64 x^3 \log ^3(2)+e^{2 x} \left (-17496 x^3-73629 x^4-118098 x^5-95175 x^6-42660 x^7-10827 x^8-1458 x^9-81 x^{10}+\left (8748 x^3+11664 x^4+5832 x^5+1296 x^6+108 x^7\right ) \log (2)\right )+e^x \left (5184 x^3+33264 x^4+86625 x^5+118386 x^6+92079 x^7+41580 x^8+10719 x^9+1458 x^{10}+81 x^{11}+\left (-5184 x^3-18360 x^4-22176 x^5-11376 x^6-2592 x^7-216 x^8\right ) \log (2)+\left (1296 x^3+864 x^4+144 x^5\right ) \log ^2(2)\right )} \, dx=\int -\frac {460\,x-40\,\ln \left (2\right )+540\,x^2+120\,x^3-{\mathrm {e}}^x\,\left (30\,x^3+270\,x^2+630\,x+270\right )+80}{{\ln \left (2\right )}^2\,\left (144\,x^6+864\,x^5+1104\,x^4+384\,x^3\right )-{\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2\,\left (144\,x^5+864\,x^4+1296\,x^3\right )-\ln \left (2\right )\,\left (216\,x^8+2592\,x^7+11376\,x^6+22176\,x^5+18360\,x^4+5184\,x^3\right )+5184\,x^3+33264\,x^4+86625\,x^5+118386\,x^6+92079\,x^7+41580\,x^8+10719\,x^9+1458\,x^{10}+81\,x^{11}\right )-64\,x^3\,{\ln \left (2\right )}^3-{\mathrm {e}}^{3\,x}\,\left (27\,x^9+486\,x^8+3645\,x^7+14580\,x^6+32805\,x^5+39366\,x^4+19683\,x^3\right )-\ln \left (2\right )\,\left (108\,x^9+1296\,x^8+5544\,x^7+10512\,x^6+9804\,x^5+4416\,x^4+768\,x^3\right )+512\,x^3+4416\,x^4+16152\,x^5+32615\,x^6+39654\,x^7+29709\,x^8+13500\,x^9+3537\,x^{10}+486\,x^{11}+27\,x^{12}+{\mathrm {e}}^{2\,x}\,\left (17496\,x^3-\ln \left (2\right )\,\left (108\,x^7+1296\,x^6+5832\,x^5+11664\,x^4+8748\,x^3\right )+73629\,x^4+118098\,x^5+95175\,x^6+42660\,x^7+10827\,x^8+1458\,x^9+81\,x^{10}\right )} \,d x \]
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