Integrand size = 260, antiderivative size = 26 \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=e^{e^{\left (-4+\frac {4 x^2}{4-x+\log (4)}\right )^2} x^2} \]
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Timed out. \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
\[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=\int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx \]
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Time = 10.03 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.38
method | result | size |
risch | \({\mathrm e}^{x^{2} {\mathrm e}^{\frac {16 \left (-x^{2}+2 \ln \left (2\right )-x +4\right )^{2}}{\left (4+2 \ln \left (2\right )-x \right )^{2}}}}\) | \(36\) |
parallelrisch | \({\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}-4 x \ln \left (2\right )+x^{2}+16 \ln \left (2\right )-8 x +16}}}\) | \(73\) |
norman | \(\frac {x^{2} {\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}+\left (4 \ln \left (2\right )^{2}+16 \ln \left (2\right )+16\right ) {\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}+\left (-4 \ln \left (2\right )-8\right ) x \,{\mathrm e}^{x^{2} {\mathrm e}^{\frac {64 \ln \left (2\right )^{2}+2 \left (-32 x^{2}-32 x +128\right ) \ln \left (2\right )+16 x^{4}+32 x^{3}-112 x^{2}-128 x +256}{4 \ln \left (2\right )^{2}+2 \left (-2 x +8\right ) \ln \left (2\right )+x^{2}-8 x +16}}}}{\left (4+2 \ln \left (2\right )-x \right )^{2}}\) | \(255\) |
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Leaf count of result is larger than twice the leaf count of optimal. 218 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 218, normalized size of antiderivative = 8.38 \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=e^{\left (\frac {16 \, x^{4} + 32 \, x^{3} - 112 \, x^{2} + {\left (x^{4} + 4 \, x^{2} \log \left (2\right )^{2} - 8 \, x^{3} + 16 \, x^{2} - 4 \, {\left (x^{3} - 4 \, x^{2}\right )} \log \left (2\right )\right )} e^{\left (\frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )} - 64 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 64 \, \log \left (2\right )^{2} - 128 \, x + 256}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16} - \frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (22) = 44\).
Time = 1.81 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.69 \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=e^{x^{2} e^{\frac {16 x^{4} + 32 x^{3} - 112 x^{2} - 128 x + \left (- 64 x^{2} - 64 x + 256\right ) \log {\left (2 \right )} + 64 \log {\left (2 \right )}^{2} + 256}{x^{2} - 8 x + \left (16 - 4 x\right ) \log {\left (2 \right )} + 4 \log {\left (2 \right )}^{2} + 16}}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 226 vs. \(2 (25) = 50\).
Time = 3.79 (sec) , antiderivative size = 226, normalized size of antiderivative = 8.69 \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=e^{\left (28638903918474961204418783933674838490721739172170652529441449702311064005352904159345284265824628375429359509218999720074396860757073376700445026041564579620512874307979212102266801261478978776245040008231745247475930553606737583615358787106474295296 \, x^{2} e^{\left (\frac {256 \, \log \left (2\right )^{4}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + 16 \, x^{2} + 64 \, x \log \left (2\right ) + 192 \, \log \left (2\right )^{2} + \frac {2048 \, \log \left (2\right )^{3}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {512 \, \log \left (2\right )^{3}}{x - 2 \, \log \left (2\right ) - 4} + 160 \, x + \frac {6144 \, \log \left (2\right )^{2}}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {3200 \, \log \left (2\right )^{2}}{x - 2 \, \log \left (2\right ) - 4} + \frac {8192 \, \log \left (2\right )}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {6656 \, \log \left (2\right )}{x - 2 \, \log \left (2\right ) - 4} + \frac {4096}{x^{2} - 4 \, x {\left (\log \left (2\right ) + 2\right )} + 4 \, \log \left (2\right )^{2} + 16 \, \log \left (2\right ) + 16} + \frac {4608}{x - 2 \, \log \left (2\right ) - 4} + 912\right )}\right )} \]
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\[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx=\int { \frac {2 \, {\left (16 \, x^{6} - 112 \, x^{5} - 191 \, x^{4} - 8 \, x \log \left (2\right )^{3} + 500 \, x^{3} + 4 \, {\left (32 \, x^{3} + 3 \, x^{2} - 12 \, x\right )} \log \left (2\right )^{2} + 48 \, x^{2} - 2 \, {\left (32 \, x^{5} + 48 \, x^{4} - 253 \, x^{3} - 24 \, x^{2} + 48 \, x\right )} \log \left (2\right ) - 64 \, x\right )} e^{\left (x^{2} e^{\left (\frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )} + \frac {16 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 4 \, {\left (x^{2} + x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16\right )}}{x^{2} - 4 \, {\left (x - 4\right )} \log \left (2\right ) + 4 \, \log \left (2\right )^{2} - 8 \, x + 16}\right )}}{x^{3} + 12 \, {\left (x - 4\right )} \log \left (2\right )^{2} - 8 \, \log \left (2\right )^{3} - 12 \, x^{2} - 6 \, {\left (x^{2} - 8 \, x + 16\right )} \log \left (2\right ) + 48 \, x - 64} \,d x } \]
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Time = 28.11 (sec) , antiderivative size = 221, normalized size of antiderivative = 8.50 \[ \int \frac {e^{e^{\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} x^2+\frac {256-128 x-112 x^2+32 x^3+16 x^4+\left (128-32 x-32 x^2\right ) \log (4)+16 \log ^2(4)}{16-8 x+x^2+(8-2 x) \log (4)+\log ^2(4)}} \left (128 x-96 x^2-1000 x^3+382 x^4+224 x^5-32 x^6+\left (96 x-48 x^2-506 x^3+96 x^4+64 x^5\right ) \log (4)+\left (24 x-6 x^2-64 x^3\right ) \log ^2(4)+2 x \log ^3(4)\right )}{64-48 x+12 x^2-x^3+\left (48-24 x+3 x^2\right ) \log (4)+(12-3 x) \log ^2(4)+\log ^3(4)} \, dx={\mathrm {e}}^{{\left (\frac {1}{18446744073709551616}\right )}^{\frac {x^2+x-4}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,x^2\,{\mathrm {e}}^{\frac {64\,{\ln \left (2\right )}^2}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {16\,x^4}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {32\,x^3}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{-\frac {112\,x^2}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{\frac {256}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}\,{\mathrm {e}}^{-\frac {128\,x}{16\,\ln \left (2\right )-8\,x-4\,x\,\ln \left (2\right )+4\,{\ln \left (2\right )}^2+x^2+16}}} \]
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