Integrand size = 84, antiderivative size = 22 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=2-e^{\frac {1}{7-x+x^2}}+2 x+x^6 \] Output:
2+2*x+x^6-exp(1/(x^2-x+7))
Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=-e^{\frac {1}{7-x+x^2}}+2 x+x^6 \] Input:
Integrate[(98 - 28*x + 30*x^2 - 4*x^3 + 2*x^4 + 294*x^5 - 84*x^6 + 90*x^7 - 12*x^8 + 6*x^9 + E^(7 - x + x^2)^(-1)*(-1 + 2*x))/(49 - 14*x + 15*x^2 - 2*x^3 + x^4),x]
Output:
-E^(7 - x + x^2)^(-1) + 2*x + x^6
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {6 x^9-12 x^8+90 x^7-84 x^6+294 x^5+2 x^4-4 x^3+30 x^2+e^{\frac {1}{x^2-x+7}} (2 x-1)-28 x+98}{x^4-2 x^3+15 x^2-14 x+49} \, dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {4 i \left (6 x^9-12 x^8+90 x^7-84 x^6+294 x^5+2 x^4-4 x^3+30 x^2+e^{\frac {1}{x^2-x+7}} (2 x-1)-28 x+98\right )}{81 \sqrt {3} \left (-2 x+3 i \sqrt {3}+1\right )}+\frac {4 i \left (6 x^9-12 x^8+90 x^7-84 x^6+294 x^5+2 x^4-4 x^3+30 x^2+e^{\frac {1}{x^2-x+7}} (2 x-1)-28 x+98\right )}{81 \sqrt {3} \left (2 x+3 i \sqrt {3}-1\right )}-\frac {4 \left (6 x^9-12 x^8+90 x^7-84 x^6+294 x^5+2 x^4-4 x^3+30 x^2+e^{\frac {1}{x^2-x+7}} (2 x-1)-28 x+98\right )}{27 \left (-2 x+3 i \sqrt {3}+1\right )^2}-\frac {4 \left (6 x^9-12 x^8+90 x^7-84 x^6+294 x^5+2 x^4-4 x^3+30 x^2+e^{\frac {1}{x^2-x+7}} (2 x-1)-28 x+98\right )}{27 \left (2 x+3 i \sqrt {3}-1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{324} \left (9+i \sqrt {3}\right ) x^8+\frac {1}{324} \left (9-i \sqrt {3}\right ) x^8-\frac {x^8}{18}+\frac {2}{567} \left (9+13 i \sqrt {3}\right ) x^7+\frac {2}{567} \left (9-13 i \sqrt {3}\right ) x^7-\frac {2}{63} \left (1+3 i \sqrt {3}\right ) x^7-\frac {2}{63} \left (1-3 i \sqrt {3}\right ) x^7-\frac {4}{567} \left (9+i \sqrt {3}\right ) x^7-\frac {4}{567} \left (9-i \sqrt {3}\right ) x^7+\frac {8 x^7}{63}-\frac {2}{243} \left (9+13 i \sqrt {3}\right ) x^6-\frac {2}{243} \left (9-13 i \sqrt {3}\right ) x^6-\frac {2}{243} \left (27+10 i \sqrt {3}\right ) x^6-\frac {2}{243} \left (27-10 i \sqrt {3}\right ) x^6+\frac {1}{18} \left (13+3 i \sqrt {3}\right ) x^6+\frac {2}{27} \left (1+3 i \sqrt {3}\right ) x^6+\frac {1}{18} \left (13-3 i \sqrt {3}\right ) x^6+\frac {2}{27} \left (1-3 i \sqrt {3}\right ) x^6+\frac {5}{81} \left (9+i \sqrt {3}\right ) x^6+\frac {5}{81} \left (9-i \sqrt {3}\right ) x^6-\frac {10 x^6}{9}-\frac {2}{405} \left (117+71 i \sqrt {3}\right ) x^5-\frac {2}{405} \left (117-71 i \sqrt {3}\right ) x^5+\frac {2}{27} \left (9+13 i \sqrt {3}\right ) x^5+\frac {2}{27} \left (9-13 i \sqrt {3}\right ) x^5+\frac {8}{405} \left (27+10 i \sqrt {3}\right ) x^5+\frac {8}{405} \left (27-10 i \sqrt {3}\right ) x^5+\frac {8}{45} \left (10+9 i \sqrt {3}\right ) x^5+\frac {8}{45} \left (10-9 i \sqrt {3}\right ) x^5-\frac {2}{15} \left (13+3 i \sqrt {3}\right ) x^5-\frac {2}{3} \left (1+3 i \sqrt {3}\right ) x^5-\frac {2}{15} \left (13-3 i \sqrt {3}\right ) x^5-\frac {2}{3} \left (1-3 i \sqrt {3}\right ) x^5-\frac {28}{405} \left (9+i \sqrt {3}\right ) x^5-\frac {28}{405} \left (9-i \sqrt {3}\right ) x^5+\frac {56 x^5}{45}+\frac {\left (i+3 \sqrt {3}\right )^5 x^4}{864 \sqrt {3}}-\frac {5}{288} \left (i+3 \sqrt {3}\right )^4 x^4+\frac {1}{81} \left (117+71 i \sqrt {3}\right ) x^4+\frac {1}{81} \left (117-71 i \sqrt {3}\right ) x^4-\frac {5}{36} \left (71-39 i \sqrt {3}\right ) x^4-\frac {7}{81} \left (9+13 i \sqrt {3}\right ) x^4-\frac {7}{81} \left (9-13 i \sqrt {3}\right ) x^4-\frac {5}{27} \left (27+10 i \sqrt {3}\right ) x^4-\frac {5}{27} \left (27-10 i \sqrt {3}\right ) x^4-\frac {4}{9} \left (10+9 i \sqrt {3}\right ) x^4-\frac {4}{9} \left (10-9 i \sqrt {3}\right ) x^4+\frac {5}{4} \left (13+3 i \sqrt {3}\right ) x^4+\frac {7}{9} \left (1+3 i \sqrt {3}\right ) x^4+\frac {5}{4} \left (13-3 i \sqrt {3}\right ) x^4+\frac {7}{9} \left (1-3 i \sqrt {3}\right ) x^4+\frac {49}{162} \left (9+i \sqrt {3}\right ) x^4+\frac {49}{162} \left (9-i \sqrt {3}\right ) x^4-\frac {\left (i-3 \sqrt {3}\right )^5 x^4}{864 \sqrt {3}}-\frac {49 x^4}{9}-\frac {\left (i+3 \sqrt {3}\right )^5 x^3}{324 \sqrt {3}}+\frac {5}{108} \left (i+3 \sqrt {3}\right )^4 x^3+\frac {4}{243} \left (540+143 i \sqrt {3}\right ) x^3+\frac {4}{243} \left (540-143 i \sqrt {3}\right ) x^3-\frac {10}{81} \left (117+71 i \sqrt {3}\right ) x^3-\frac {10}{81} \left (117-71 i \sqrt {3}\right ) x^3+\frac {10}{27} \left (71-39 i \sqrt {3}\right ) x^3+\frac {98}{243} \left (9+13 i \sqrt {3}\right ) x^3+\frac {98}{243} \left (9-13 i \sqrt {3}\right ) x^3+\frac {56}{243} \left (27+10 i \sqrt {3}\right ) x^3+\frac {56}{243} \left (27-10 i \sqrt {3}\right ) x^3+\frac {40}{9} \left (10+9 i \sqrt {3}\right ) x^3+\frac {40}{9} \left (10-9 i \sqrt {3}\right ) x^3-\frac {14}{9} \left (13+3 i \sqrt {3}\right ) x^3-\frac {1}{72} \left (1+3 i \sqrt {3}\right )^5 x^3-\frac {98}{27} \left (1+3 i \sqrt {3}\right ) x^3-\frac {14}{9} \left (13-3 i \sqrt {3}\right ) x^3-\frac {1}{72} \left (1-3 i \sqrt {3}\right )^5 x^3-\frac {98}{27} \left (1-3 i \sqrt {3}\right ) x^3+\frac {2}{729} \left (9+i \sqrt {3}\right ) x^3+\frac {2}{729} \left (9-i \sqrt {3}\right ) x^3+\frac {\left (i-3 \sqrt {3}\right )^5 x^3}{324 \sqrt {3}}-\frac {4 x^3}{81}-\frac {\left (i+3 \sqrt {3}\right )^7 x^2}{1728 \sqrt {3}}+\frac {7}{576} \left (i+3 \sqrt {3}\right )^6 x^2+\frac {5 \left (i+3 \sqrt {3}\right )^5 x^2}{144 \sqrt {3}}-\frac {25}{48} \left (i+3 \sqrt {3}\right )^4 x^2-\frac {4}{81} \left (540+143 i \sqrt {3}\right ) x^2-\frac {4}{81} \left (540-143 i \sqrt {3}\right ) x^2+\frac {14}{81} \left (117+71 i \sqrt {3}\right ) x^2+\frac {14}{81} \left (117-71 i \sqrt {3}\right ) x^2-\frac {25}{6} \left (71-39 i \sqrt {3}\right ) x^2+\frac {1}{243} \left (9+13 i \sqrt {3}\right ) x^2+\frac {1}{243} \left (9-13 i \sqrt {3}\right ) x^2-\frac {98}{81} \left (27+10 i \sqrt {3}\right ) x^2-\frac {98}{81} \left (27-10 i \sqrt {3}\right ) x^2-\frac {56}{9} \left (10+9 i \sqrt {3}\right ) x^2-\frac {56}{9} \left (10-9 i \sqrt {3}\right ) x^2+\frac {49}{6} \left (13+3 i \sqrt {3}\right ) x^2+\frac {1}{24} \left (1+3 i \sqrt {3}\right )^5 x^2-\frac {1}{27} \left (1+3 i \sqrt {3}\right ) x^2+\frac {49}{6} \left (13-3 i \sqrt {3}\right ) x^2+\frac {1}{24} \left (1-3 i \sqrt {3}\right )^5 x^2-\frac {1}{27} \left (1-3 i \sqrt {3}\right ) x^2-\frac {2}{243} \left (9+i \sqrt {3}\right ) x^2-\frac {2}{243} \left (9-i \sqrt {3}\right ) x^2+\frac {\left (i-3 \sqrt {3}\right )^7 x^2}{1728 \sqrt {3}}+\frac {7}{576} \left (i-3 \sqrt {3}\right )^6 x^2-\frac {5 \left (i-3 \sqrt {3}\right )^5 x^2}{144 \sqrt {3}}+\frac {4 x^2}{27}+\frac {i \left (i+3 \sqrt {3}\right )^8 x}{1728 \sqrt {3}}+\frac {\left (i+3 \sqrt {3}\right )^7 x}{432 \sqrt {3}}-\frac {7 \left (i+3 \sqrt {3}\right )^5 x}{108 \sqrt {3}}+\frac {35}{36} \left (i+3 \sqrt {3}\right )^4 x+\frac {8}{9} \left (1763+249 i \sqrt {3}\right ) x+\frac {8}{9} \left (1763-249 i \sqrt {3}\right ) x-\frac {2}{81} \left (8307+239 i \sqrt {3}\right ) x-\frac {28}{9} \left (143+180 i \sqrt {3}\right ) x-\frac {28}{9} \left (143-180 i \sqrt {3}\right ) x+\frac {20}{27} \left (540+143 i \sqrt {3}\right ) x+\frac {20}{27} \left (540-143 i \sqrt {3}\right ) x-10 \left (211+87 i \sqrt {3}\right ) x-\frac {98}{81} \left (117+71 i \sqrt {3}\right ) x-\frac {98}{81} \left (117-71 i \sqrt {3}\right ) x+\frac {70}{9} \left (71-39 i \sqrt {3}\right ) x-\frac {4}{243} \left (9+13 i \sqrt {3}\right ) x-\frac {4}{243} \left (9-13 i \sqrt {3}\right ) x-\frac {4}{243} \left (27+10 i \sqrt {3}\right ) x-\frac {4}{243} \left (27-10 i \sqrt {3}\right ) x+\frac {392}{9} \left (10+9 i \sqrt {3}\right ) x+\frac {392}{9} \left (10-9 i \sqrt {3}\right ) x+\frac {1}{9} \left (13+3 i \sqrt {3}\right ) x+\frac {4}{27} \left (1+3 i \sqrt {3}\right ) x+\frac {1}{9} \left (13-3 i \sqrt {3}\right ) x-\frac {5}{8} \left (1-3 i \sqrt {3}\right )^5 x+\frac {4}{27} \left (1-3 i \sqrt {3}\right ) x+\frac {10}{81} \left (9+i \sqrt {3}\right ) x+\frac {10}{81} \left (9-i \sqrt {3}\right ) x-\frac {\left (i-3 \sqrt {3}\right )^7 x}{432 \sqrt {3}}+\frac {7 \left (i-3 \sqrt {3}\right )^5 x}{108 \sqrt {3}}-\frac {20 x}{9}-\frac {4}{81} \left (1539+6290 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\left (239-2769 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {10}{27} \left (747-1763 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {16}{9} \left (1763+249 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {4}{81} \left (8307+239 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {98}{81} \left (261-211 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {70}{3} \left (143-180 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {56}{81} \left (540+143 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {28}{3} \left (211+87 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {2}{243} \left (117+71 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {245}{9} \left (71-39 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {10}{81} \left (9+13 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {8}{243} \left (27-10 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )+\frac {8}{27} \left (10+9 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {10}{9} \left (1+3 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {2}{9} \left (13-3 i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {28}{243} \left (9-i \sqrt {3}\right ) \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {196 i \log \left (-2 i x-3 \sqrt {3}+i\right )}{81 \sqrt {3}}+\frac {28}{27} \log \left (-2 i x-3 \sqrt {3}+i\right )-\frac {4}{81} \left (1539-6290 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\left (239+2769 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {10}{27} \left (747+1763 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {16}{9} \left (1763-249 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {4}{81} \left (8307-239 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {98}{81} \left (261+211 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {70}{3} \left (143+180 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {56}{81} \left (540-143 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {28}{3} \left (211-87 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {2}{243} \left (117-71 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {245}{9} \left (71+39 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {10}{81} \left (9-13 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {8}{243} \left (27+10 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {8}{27} \left (10-9 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {2}{9} \left (13+3 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {10}{9} \left (1-3 i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {28}{243} \left (9+i \sqrt {3}\right ) \log \left (-2 i x+3 \sqrt {3}+i\right )+\frac {196 i \log \left (-2 i x+3 \sqrt {3}+i\right )}{81 \sqrt {3}}+\frac {28}{27} \log \left (-2 i x+3 \sqrt {3}+i\right )-\frac {4 i \int \frac {e^{\frac {1}{x^2-x+7}}}{\left (-2 i x+3 \sqrt {3}+i\right )^2}dx}{3 \sqrt {3}}+\frac {4 i \int \frac {e^{\frac {1}{x^2-x+7}}}{\left (2 i x+3 \sqrt {3}-i\right )^2}dx}{3 \sqrt {3}}+\frac {4 \left (239 i+2769 \sqrt {3}\right )}{9 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {4 \left (6290 i+513 \sqrt {3}\right )}{9 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {56 \left (143 i+180 \sqrt {3}\right )}{9 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {2 \left (71 i+39 \sqrt {3}\right )}{27 \left (-2 i x-3 \sqrt {3}+i\right )}+\frac {10 \left (13 i+3 \sqrt {3}\right )}{9 \left (-2 i x-3 \sqrt {3}+i\right )}+\frac {28 \left (i-3 \sqrt {3}\right )}{27 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {8 \left (10 i-9 \sqrt {3}\right )}{27 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {98 \left (211 i-87 \sqrt {3}\right )}{9 \left (-2 i x-3 \sqrt {3}+i\right )}+\frac {10 \left (1763 i-249 \sqrt {3}\right )}{3 \left (-2 i x-3 \sqrt {3}+i\right )}-\frac {196 i}{27 \left (-2 i x-3 \sqrt {3}+i\right )}+\frac {10 \left (1763 i+249 \sqrt {3}\right )}{3 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {98 \left (211 i+87 \sqrt {3}\right )}{9 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {8 \left (10 i+9 \sqrt {3}\right )}{27 \left (-2 i x+3 \sqrt {3}+i\right )}+\frac {28 \left (i+3 \sqrt {3}\right )}{27 \left (-2 i x+3 \sqrt {3}+i\right )}+\frac {10 \left (13 i-3 \sqrt {3}\right )}{9 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {2 \left (71 i-39 \sqrt {3}\right )}{27 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {56 \left (143 i-180 \sqrt {3}\right )}{9 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {4 \left (6290 i-513 \sqrt {3}\right )}{9 \left (-2 i x+3 \sqrt {3}+i\right )}+\frac {4 \left (239 i-2769 \sqrt {3}\right )}{9 \left (-2 i x+3 \sqrt {3}+i\right )}-\frac {196 i}{27 \left (-2 i x+3 \sqrt {3}+i\right )}\) |
Input:
Int[(98 - 28*x + 30*x^2 - 4*x^3 + 2*x^4 + 294*x^5 - 84*x^6 + 90*x^7 - 12*x ^8 + 6*x^9 + E^(7 - x + x^2)^(-1)*(-1 + 2*x))/(49 - 14*x + 15*x^2 - 2*x^3 + x^4),x]
Output:
$Aborted
Time = 3.22 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95
| method | result | size |
| risch | \(x^{6}+2 x -{\mathrm e}^{\frac {1}{x^{2}-x +7}}\) | \(21\) |
| parts | \(x^{6}+2 x -{\mathrm e}^{\frac {1}{x^{2}-x +7}}\) | \(21\) |
| parallelrisch | \(x^{6}+2 x -{\mathrm e}^{\frac {1}{x^{2}-x +7}}-326\) | \(22\) |
| norman | \(\frac {x^{8}+12 x +{\mathrm e}^{\frac {1}{x^{2}-x +7}} x +2 x^{3}+7 x^{6}-x^{7}-{\mathrm e}^{\frac {1}{x^{2}-x +7}} x^{2}-7 \,{\mathrm e}^{\frac {1}{x^{2}-x +7}}+14}{x^{2}-x +7}\) | \(77\) |
| orering | \(-\frac {\left (30 x^{12}-120 x^{11}+1014 x^{10}-2628 x^{9}+11330 x^{8}-18446 x^{7}+50063 x^{6}-41172 x^{5}+71964 x^{4}+100 x^{3}-532 x^{2}+676 x +1245\right ) \left (\left (-1+2 x \right ) {\mathrm e}^{\frac {1}{x^{2}-x +7}}+6 x^{9}-12 x^{8}+90 x^{7}-84 x^{6}+294 x^{5}+2 x^{4}-4 x^{3}+30 x^{2}-28 x +98\right )}{2 \left (48 x^{9}-111 x^{8}+600 x^{7}-747 x^{6}+1431 x^{5}-729 x^{4}-12 x^{3}+40 x^{2}-34 x -83\right ) \left (x^{4}-2 x^{3}+15 x^{2}-14 x +49\right )}+\frac {\left (6 x^{9}-12 x^{8}+92 x^{7}-85 x^{6}+294 x^{5}+2 x^{4}-4 x^{3}+34 x^{2}+83\right ) \left (x^{2}-x +7\right )^{2} \left (\frac {2 \,{\mathrm e}^{\frac {1}{x^{2}-x +7}}-\frac {\left (-1+2 x \right )^{2} {\mathrm e}^{\frac {1}{x^{2}-x +7}}}{\left (x^{2}-x +7\right )^{2}}+54 x^{8}-96 x^{7}+630 x^{6}-504 x^{5}+1470 x^{4}+8 x^{3}-12 x^{2}+60 x -28}{x^{4}-2 x^{3}+15 x^{2}-14 x +49}-\frac {\left (\left (-1+2 x \right ) {\mathrm e}^{\frac {1}{x^{2}-x +7}}+6 x^{9}-12 x^{8}+90 x^{7}-84 x^{6}+294 x^{5}+2 x^{4}-4 x^{3}+30 x^{2}-28 x +98\right ) \left (4 x^{3}-6 x^{2}+30 x -14\right )}{\left (x^{4}-2 x^{3}+15 x^{2}-14 x +49\right )^{2}}\right )}{96 x^{9}-222 x^{8}+1200 x^{7}-1494 x^{6}+2862 x^{5}-1458 x^{4}-24 x^{3}+80 x^{2}-68 x -166}\) | \(498\) |
Input:
int(((-1+2*x)*exp(1/(x^2-x+7))+6*x^9-12*x^8+90*x^7-84*x^6+294*x^5+2*x^4-4* x^3+30*x^2-28*x+98)/(x^4-2*x^3+15*x^2-14*x+49),x,method=_RETURNVERBOSE)
Output:
x^6+2*x-exp(1/(x^2-x+7))
Time = 0.10 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=x^{6} + 2 \, x - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \] Input:
integrate(((-1+2*x)*exp(1/(x^2-x+7))+6*x^9-12*x^8+90*x^7-84*x^6+294*x^5+2* x^4-4*x^3+30*x^2-28*x+98)/(x^4-2*x^3+15*x^2-14*x+49),x, algorithm="fricas" )
Output:
x^6 + 2*x - e^(1/(x^2 - x + 7))
Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=x^{6} + 2 x - e^{\frac {1}{x^{2} - x + 7}} \] Input:
integrate(((-1+2*x)*exp(1/(x**2-x+7))+6*x**9-12*x**8+90*x**7-84*x**6+294*x **5+2*x**4-4*x**3+30*x**2-28*x+98)/(x**4-2*x**3+15*x**2-14*x+49),x)
Output:
x**6 + 2*x - exp(1/(x**2 - x + 7))
Leaf count of result is larger than twice the leaf count of optimal. 188 vs. \(2 (21) = 42\).
Time = 0.17 (sec) , antiderivative size = 188, normalized size of antiderivative = 8.55 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=x^{6} + 2 \, x + \frac {2 \, {\left (12580 \, x - 1673\right )}}{9 \, {\left (x^{2} - x + 7\right )}} - \frac {10 \, {\left (1763 \, x - 2002\right )}}{3 \, {\left (x^{2} - x + 7\right )}} + \frac {28 \, {\left (286 \, x + 1477\right )}}{9 \, {\left (x^{2} - x + 7\right )}} - \frac {4 \, {\left (239 \, x + 12341\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {98 \, {\left (211 \, x - 497\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {2 \, {\left (71 \, x + 140\right )}}{27 \, {\left (x^{2} - x + 7\right )}} + \frac {4 \, {\left (20 \, x - 91\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - \frac {10 \, {\left (13 \, x + 7\right )}}{9 \, {\left (x^{2} - x + 7\right )}} + \frac {98 \, {\left (2 \, x - 1\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - \frac {28 \, {\left (x - 14\right )}}{27 \, {\left (x^{2} - x + 7\right )}} - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \] Input:
integrate(((-1+2*x)*exp(1/(x^2-x+7))+6*x^9-12*x^8+90*x^7-84*x^6+294*x^5+2* x^4-4*x^3+30*x^2-28*x+98)/(x^4-2*x^3+15*x^2-14*x+49),x, algorithm="maxima" )
Output:
x^6 + 2*x + 2/9*(12580*x - 1673)/(x^2 - x + 7) - 10/3*(1763*x - 2002)/(x^2 - x + 7) + 28/9*(286*x + 1477)/(x^2 - x + 7) - 4/9*(239*x + 12341)/(x^2 - x + 7) + 98/9*(211*x - 497)/(x^2 - x + 7) + 2/27*(71*x + 140)/(x^2 - x + 7) + 4/27*(20*x - 91)/(x^2 - x + 7) - 10/9*(13*x + 7)/(x^2 - x + 7) + 98/2 7*(2*x - 1)/(x^2 - x + 7) - 28/27*(x - 14)/(x^2 - x + 7) - e^(1/(x^2 - x + 7))
Time = 0.12 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=x^{6} + 2 \, x - e^{\left (\frac {1}{x^{2} - x + 7}\right )} \] Input:
integrate(((-1+2*x)*exp(1/(x^2-x+7))+6*x^9-12*x^8+90*x^7-84*x^6+294*x^5+2* x^4-4*x^3+30*x^2-28*x+98)/(x^4-2*x^3+15*x^2-14*x+49),x, algorithm="giac")
Output:
x^6 + 2*x - e^(1/(x^2 - x + 7))
Time = 0.14 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=2\,x-{\mathrm {e}}^{\frac {1}{x^2-x+7}}+x^6 \] Input:
int((exp(1/(x^2 - x + 7))*(2*x - 1) - 28*x + 30*x^2 - 4*x^3 + 2*x^4 + 294* x^5 - 84*x^6 + 90*x^7 - 12*x^8 + 6*x^9 + 98)/(15*x^2 - 14*x - 2*x^3 + x^4 + 49),x)
Output:
2*x - exp(1/(x^2 - x + 7)) + x^6
Time = 0.17 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {98-28 x+30 x^2-4 x^3+2 x^4+294 x^5-84 x^6+90 x^7-12 x^8+6 x^9+e^{\frac {1}{7-x+x^2}} (-1+2 x)}{49-14 x+15 x^2-2 x^3+x^4} \, dx=-e^{\frac {1}{x^{2}-x +7}}+x^{6}+2 x \] Input:
int(((-1+2*x)*exp(1/(x^2-x+7))+6*x^9-12*x^8+90*x^7-84*x^6+294*x^5+2*x^4-4* x^3+30*x^2-28*x+98)/(x^4-2*x^3+15*x^2-14*x+49),x)
Output:
- e**(1/(x**2 - x + 7)) + x**6 + 2*x