Integrand size = 141, antiderivative size = 29 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=(1+5 x) \left (4+\frac {10 \left (-e^{\frac {16}{\left (-4+x+x^2\right )^2}}+x\right )}{x^2}\right ) \]
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\[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=\int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {10 \left (x \left (-1+2 x^2\right )+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{\left (-4+x+x^2\right )^3}\right )}{x^3} \, dx \\ & = 10 \int \frac {x \left (-1+2 x^2\right )+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{\left (-4+x+x^2\right )^3}}{x^3} \, dx \\ & = 10 \int \left (\frac {-1+2 x^2}{x^2}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{x^3 \left (-4+x+x^2\right )^3}\right ) \, dx \\ & = 10 \int \frac {-1+2 x^2}{x^2} \, dx+10 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-128-192 x+536 x^2+454 x^3-133 x^4-39 x^5+17 x^6+5 x^7\right )}{x^3 \left (-4+x+x^2\right )^3} \, dx \\ & = 10 \int \left (2-\frac {1}{x^2}\right ) \, dx+10 \int \left (\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3}+\frac {9 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{2 x^2}-\frac {31 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{8 x}+\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}} (193+29 x)}{\left (-4+x+x^2\right )^3}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (-17-15 x)}{\left (-4+x+x^2\right )^2}+\frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (35+31 x)}{8 \left (-4+x+x^2\right )}\right ) \, dx \\ & = \frac {10}{x}+20 x+\frac {5}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (35+31 x)}{-4+x+x^2} \, dx+10 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (-17-15 x)}{\left (-4+x+x^2\right )^2} \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} (193+29 x)}{\left (-4+x+x^2\right )^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx \\ & = \frac {10}{x}+20 x+\frac {5}{4} \int \left (\frac {\left (31+\frac {39}{\sqrt {17}}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x}+\frac {\left (31-\frac {39}{\sqrt {17}}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x}\right ) \, dx+10 \int \left (-\frac {17 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^2}-\frac {15 e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^2}\right ) \, dx+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx+20 \int \left (\frac {193 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^3}+\frac {29 e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^3}\right ) \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx \\ & = \frac {10}{x}+20 x+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx-150 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^2} \, dx-170 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^2} \, dx+580 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}} x}{\left (-4+x+x^2\right )^3} \, dx+3860 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-4+x+x^2\right )^3} \, dx+\frac {1}{68} \left (5 \left (527-39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx+\frac {1}{68} \left (5 \left (527+39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x} \, dx \\ & = \frac {10}{x}+20 x+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx-150 \int \left (\frac {2 \left (-1+\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \left (-1+\sqrt {17}-2 x\right )^2}-\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )}+\frac {2 \left (-1-\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \left (1+\sqrt {17}+2 x\right )^2}-\frac {2 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (1+\sqrt {17}+2 x\right )}\right ) \, dx-170 \int \left (\frac {4 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \left (-1+\sqrt {17}-2 x\right )^2}+\frac {4 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )}+\frac {4 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \left (1+\sqrt {17}+2 x\right )^2}+\frac {4 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (1+\sqrt {17}+2 x\right )}\right ) \, dx+580 \int \left (\frac {4 \left (1-\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )^3}+\frac {2 \left (3-\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \left (-1+\sqrt {17}-2 x\right )^2}+\frac {6 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )}+\frac {4 \left (1+\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (1+\sqrt {17}+2 x\right )^3}+\frac {2 \left (3+\sqrt {17}\right ) e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \left (1+\sqrt {17}+2 x\right )^2}+\frac {6 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \sqrt {17} \left (1+\sqrt {17}+2 x\right )}\right ) \, dx+3860 \int \left (-\frac {8 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )^3}-\frac {12 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \left (-1+\sqrt {17}-2 x\right )^2}-\frac {12 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \sqrt {17} \left (-1+\sqrt {17}-2 x\right )}-\frac {8 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{17 \sqrt {17} \left (1+\sqrt {17}+2 x\right )^3}-\frac {12 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \left (1+\sqrt {17}+2 x\right )^2}-\frac {12 e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{289 \sqrt {17} \left (1+\sqrt {17}+2 x\right )}\right ) \, dx+\frac {1}{68} \left (5 \left (527-39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx+\frac {1}{68} \left (5 \left (527+39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x} \, dx \\ & = \frac {10}{x}+20 x+20 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^3} \, dx-\frac {155}{4} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x} \, dx-40 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^2} \, dx-40 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^2} \, dx+45 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{x^2} \, dx-\frac {46320}{289} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^2} \, dx-\frac {46320}{289} \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^2} \, dx+\frac {3480 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{-1+\sqrt {17}-2 x} \, dx}{289 \sqrt {17}}+\frac {3480 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx}{289 \sqrt {17}}+\frac {300 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{-1+\sqrt {17}-2 x} \, dx}{17 \sqrt {17}}+\frac {300 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx}{17 \sqrt {17}}-\frac {40 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{-1+\sqrt {17}-2 x} \, dx}{\sqrt {17}}-\frac {40 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx}{\sqrt {17}}-\frac {46320 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{-1+\sqrt {17}-2 x} \, dx}{289 \sqrt {17}}-\frac {46320 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx}{289 \sqrt {17}}-\frac {30880 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^3} \, dx}{17 \sqrt {17}}-\frac {30880 \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^3} \, dx}{17 \sqrt {17}}+\frac {1}{68} \left (5 \left (527-39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1+\sqrt {17}+2 x} \, dx+\frac {1}{17} \left (300 \left (1-\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^2} \, dx+\frac {1}{289} \left (1160 \left (3-\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^2} \, dx-\frac {1}{289} \left (2320 \left (17-\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (-1+\sqrt {17}-2 x\right )^3} \, dx+\frac {1}{17} \left (300 \left (1+\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^2} \, dx+\frac {1}{289} \left (1160 \left (3+\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^2} \, dx+\frac {1}{289} \left (2320 \left (17+\sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{\left (1+\sqrt {17}+2 x\right )^3} \, dx+\frac {1}{68} \left (5 \left (527+39 \sqrt {17}\right )\right ) \int \frac {e^{\frac {16}{\left (-4+x+x^2\right )^2}}}{1-\sqrt {17}+2 x} \, dx \\ \end{align*}
Time = 1.13 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.14 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=10 \left (e^{\frac {16}{\left (-4+x+x^2\right )^2}} \left (-\frac {1}{x^2}-\frac {5}{x}\right )+\frac {1}{x}+2 x\right ) \]
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Time = 0.82 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07
method | result | size |
risch | \(20 x +\frac {10}{x}-\frac {10 \left (1+5 x \right ) {\mathrm e}^{\frac {16}{\left (x^{2}+x -4\right )^{2}}}}{x^{2}}\) | \(31\) |
parallelrisch | \(\frac {2000 x^{3}+210 x^{2}-5000 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x +1000 x -1000 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}}}{100 x^{2}}\) | \(71\) |
parts | \(20 x +\frac {10}{x}+\frac {-720 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x +470 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{2}+330 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{3}-110 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{4}-50 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{5}-160 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}}}{x^{2} \left (x^{2}+x -4\right )^{2}}\) | \(186\) |
norman | \(\frac {-720 x^{2}-210 x^{5}+140 x^{4}+570 x^{3}+160 x +20 x^{7}-720 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x +470 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{2}+330 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{3}-110 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{4}-50 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}} x^{5}-160 \,{\mathrm e}^{\frac {16}{x^{4}+2 x^{3}-7 x^{2}-8 x +16}}}{x^{2} \left (x^{2}+x -4\right )^{2}}\) | \(205\) |
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Time = 0.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=\frac {10 \, {\left (2 \, x^{3} - {\left (5 \, x + 1\right )} e^{\left (\frac {16}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16}\right )} + x\right )}}{x^{2}} \]
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Time = 0.11 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=20 x + \frac {10}{x} + \frac {\left (- 50 x - 10\right ) e^{\frac {16}{x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 16}}}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 377 vs. \(2 (29) = 58\).
Time = 0.37 (sec) , antiderivative size = 377, normalized size of antiderivative = 13.00 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=20 \, x + \frac {10 \, {\left (567 \, x^{4} + 1284 \, x^{3} - 3013 \, x^{2} - 4466 \, x + 4624\right )}}{289 \, {\left (x^{5} + 2 \, x^{4} - 7 \, x^{3} - 8 \, x^{2} + 16 \, x\right )}} - \frac {10 \, {\left (4134 \, x^{3} - 1891 \, x^{2} - 17512 \, x + 17232\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} + \frac {30 \, {\left (924 \, x^{3} - 1793 \, x^{2} - 4696 \, x + 7536\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} + \frac {95 \, {\left (386 \, x^{3} + x^{2} - 1096 \, x + 656\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {30 \, {\left (29 \, x^{3} + 188 \, x^{2} + 9 \, x - 942\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {245 \, {\left (24 \, x^{3} - 253 \, x^{2} - 152 \, x + 496\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {405 \, {\left (14 \, x^{3} + 21 \, x^{2} + 104 \, x - 96\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {820 \, {\left (12 \, x^{3} + 18 \, x^{2} - 76 \, x - 41\right )}}{289 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {35 \, {\left (6 \, x^{3} + 9 \, x^{2} - 38 \, x + 124\right )}}{17 \, {\left (x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16\right )}} - \frac {10 \, {\left (5 \, x + 1\right )} e^{\left (\frac {16}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16}\right )}}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 101 vs. \(2 (29) = 58\).
Time = 0.31 (sec) , antiderivative size = 101, normalized size of antiderivative = 3.48 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=\frac {10 \, {\left (2 \, x^{3} - 5 \, x e^{\left (-\frac {x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16} + 1\right )} + x - e^{\left (-\frac {x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x}{x^{4} + 2 \, x^{3} - 7 \, x^{2} - 8 \, x + 16} + 1\right )}\right )}}{x^{2}} \]
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Time = 11.75 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {640 x-480 x^2-1640 x^3+1190 x^4+810 x^5-490 x^6-190 x^7+60 x^8+20 x^9+e^{\frac {16}{16-8 x-7 x^2+2 x^3+x^4}} \left (-1280-1920 x+5360 x^2+4540 x^3-1330 x^4-390 x^5+170 x^6+50 x^7\right )}{-64 x^3+48 x^4+36 x^5-23 x^6-9 x^7+3 x^8+x^9} \, dx=20\,x+\frac {10}{x}-\frac {{\mathrm {e}}^{\frac {16}{x^4+2\,x^3-7\,x^2-8\,x+16}}\,\left (50\,x+10\right )}{x^2} \]
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