Integrand size = 356, antiderivative size = 30 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=\frac {1}{16} x^3 \left (3-x+x \left (2-e^{2 x}+2 x\right )^4\right )^2 \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(468\) vs. \(2(30)=60\).
Time = 2.74 (sec) , antiderivative size = 468, normalized size of antiderivative = 15.60, number of steps used = 376, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {12, 1607, 2227, 2207, 2225, 1608} \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 x^{13}-64 e^{2 x} x^{12}+128 x^{12}-448 e^{2 x} x^{11}+112 e^{4 x} x^{11}+448 x^{11}-1344 e^{2 x} x^{10}+672 e^{4 x} x^{10}-112 e^{6 x} x^{10}+896 x^{10}-2240 e^{2 x} x^9+1680 e^{4 x} x^9-560 e^{6 x} x^9+70 e^{8 x} x^9+1118 x^9-2236 e^{2 x} x^8+2240 e^{4 x} x^8-1120 e^{6 x} x^8+280 e^{8 x} x^8-28 e^{10 x} x^8+894 x^8-1344 e^{2 x} x^7+1677 e^{4 x} x^7-1120 e^{6 x} x^7+420 e^{8 x} x^7-84 e^{10 x} x^7+7 e^{12 x} x^7+460 x^7-472 e^{2 x} x^6+675 e^{4 x} x^6-559 e^{6 x} x^6+280 e^{8 x} x^6-84 e^{10 x} x^6+14 e^{12 x} x^6-e^{14 x} x^6+156 x^6-96 e^{2 x} x^5+127 e^{4 x} x^5-114 e^{6 x} x^5+\frac {559}{8} e^{8 x} x^5-28 e^{10 x} x^5+7 e^{12 x} x^5-e^{14 x} x^5+\frac {1}{16} e^{16 x} x^5+\frac {609 x^5}{16}-12 e^{2 x} x^4+9 e^{4 x} x^4-3 e^{6 x} x^4+\frac {3}{8} e^{8 x} x^4+\frac {45 x^4}{8}+\frac {9 x^3}{16} \]
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Rule 12
Rule 1607
Rule 1608
Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = \frac {1}{16} \int \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx \\ & = \frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int e^{16 x} \left (5 x^4+16 x^5\right ) \, dx+\frac {1}{16} \int e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right ) \, dx+\frac {1}{16} \int e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right ) \, dx+\frac {1}{16} \int e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right ) \, dx+\frac {1}{16} \int e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right ) \, dx+\frac {1}{16} \int e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right ) \, dx+\frac {1}{16} \int e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right ) \, dx+\frac {1}{16} \int e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right ) \, dx \\ & = \frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int e^{16 x} x^4 (5+16 x) \, dx+\frac {1}{16} \int e^{14 x} x^4 \left (-80-320 x-224 x^2\right ) \, dx+\frac {1}{16} \int \left (560 e^{12 x} x^4+2688 e^{12 x} x^5+3472 e^{12 x} x^6+1344 e^{12 x} x^7\right ) \, dx+\frac {1}{16} \int \left (-2240 e^{10 x} x^4-12544 e^{10 x} x^5-22848 e^{10 x} x^6-17024 e^{10 x} x^7-4480 e^{10 x} x^8\right ) \, dx+\frac {1}{16} \int \left (24 e^{8 x} x^3+5638 e^{8 x} x^4+35824 e^{8 x} x^5+82880 e^{8 x} x^6+89600 e^{8 x} x^7+45920 e^{8 x} x^8+8960 e^{8 x} x^9\right ) \, dx+\frac {1}{16} \int \left (-192 e^{6 x} x^3-9408 e^{6 x} x^4-64608 e^{6 x} x^5-179104 e^{6 x} x^6-250880 e^{6 x} x^7-188160 e^{6 x} x^8-71680 e^{6 x} x^9-10752 e^{6 x} x^{10}\right ) \, dx+\frac {1}{16} \int \left (576 e^{4 x} x^3+10736 e^{4 x} x^4+72928 e^{4 x} x^5+231024 e^{4 x} x^6+394048 e^{4 x} x^7+385280 e^{4 x} x^8+215040 e^{4 x} x^9+62720 e^{4 x} x^{10}+7168 e^{4 x} x^{11}\right ) \, dx+\frac {1}{16} \int \left (-768 e^{2 x} x^3-8064 e^{2 x} x^4-48384 e^{2 x} x^5-165632 e^{2 x} x^6-329216 e^{2 x} x^7-394112 e^{2 x} x^8-286720 e^{2 x} x^9-121856 e^{2 x} x^{10}-26624 e^{2 x} x^{11}-2048 e^{2 x} x^{12}\right ) \, dx \\ & = \frac {9 x^3}{16}+\frac {45 x^4}{8}+\frac {609 x^5}{16}+156 x^6+460 x^7+894 x^8+1118 x^9+896 x^{10}+448 x^{11}+128 x^{12}+16 x^{13}+\frac {1}{16} \int \left (5 e^{16 x} x^4+16 e^{16 x} x^5\right ) \, dx+\frac {1}{16} \int \left (-80 e^{14 x} x^4-320 e^{14 x} x^5-224 e^{14 x} x^6\right ) \, dx+\frac {3}{2} \int e^{8 x} x^3 \, dx-12 \int e^{6 x} x^3 \, dx+35 \int e^{12 x} x^4 \, dx+36 \int e^{4 x} x^3 \, dx-48 \int e^{2 x} x^3 \, dx+84 \int e^{12 x} x^7 \, dx-128 \int e^{2 x} x^{12} \, dx-140 \int e^{10 x} x^4 \, dx+168 \int e^{12 x} x^5 \, dx+217 \int e^{12 x} x^6 \, dx-280 \int e^{10 x} x^8 \, dx+\frac {2819}{8} \int e^{8 x} x^4 \, dx+448 \int e^{4 x} x^{11} \, dx-504 \int e^{2 x} x^4 \, dx+560 \int e^{8 x} x^9 \, dx-588 \int e^{6 x} x^4 \, dx+671 \int e^{4 x} x^4 \, dx-672 \int e^{6 x} x^{10} \, dx-784 \int e^{10 x} x^5 \, dx-1064 \int e^{10 x} x^7 \, dx-1428 \int e^{10 x} x^6 \, dx-1664 \int e^{2 x} x^{11} \, dx+2239 \int e^{8 x} x^5 \, dx+2870 \int e^{8 x} x^8 \, dx-3024 \int e^{2 x} x^5 \, dx+3920 \int e^{4 x} x^{10} \, dx-4038 \int e^{6 x} x^5 \, dx-4480 \int e^{6 x} x^9 \, dx+4558 \int e^{4 x} x^5 \, dx+5180 \int e^{8 x} x^6 \, dx+5600 \int e^{8 x} x^7 \, dx-7616 \int e^{2 x} x^{10} \, dx-10352 \int e^{2 x} x^6 \, dx-11194 \int e^{6 x} x^6 \, dx-11760 \int e^{6 x} x^8 \, dx+13440 \int e^{4 x} x^9 \, dx+14439 \int e^{4 x} x^6 \, dx-15680 \int e^{6 x} x^7 \, dx-17920 \int e^{2 x} x^9 \, dx-20576 \int e^{2 x} x^7 \, dx+24080 \int e^{4 x} x^8 \, dx+24628 \int e^{4 x} x^7 \, dx-24632 \int e^{2 x} x^8 \, dx \\ & = \frac {9 x^3}{16}-24 e^{2 x} x^3+9 e^{4 x} x^3-2 e^{6 x} x^3+\frac {3}{16} e^{8 x} x^3+\frac {45 x^4}{8}-252 e^{2 x} x^4+\frac {671}{4} e^{4 x} x^4-98 e^{6 x} x^4+\frac {2819}{64} e^{8 x} x^4-14 e^{10 x} x^4+\frac {35}{12} e^{12 x} x^4+\frac {609 x^5}{16}-1512 e^{2 x} x^5+\frac {2279}{2} e^{4 x} x^5-673 e^{6 x} x^5+\frac {2239}{8} e^{8 x} x^5-\frac {392}{5} e^{10 x} x^5+14 e^{12 x} x^5+156 x^6-5176 e^{2 x} x^6+\frac {14439}{4} e^{4 x} x^6-\frac {5597}{3} e^{6 x} x^6+\frac {1295}{2} e^{8 x} x^6-\frac {714}{5} e^{10 x} x^6+\frac {217}{12} e^{12 x} x^6+460 x^7-10288 e^{2 x} x^7+6157 e^{4 x} x^7-\frac {7840}{3} e^{6 x} x^7+700 e^{8 x} x^7-\frac {532}{5} e^{10 x} x^7+7 e^{12 x} x^7+894 x^8-12316 e^{2 x} x^8+6020 e^{4 x} x^8-1960 e^{6 x} x^8+\frac {1435}{4} e^{8 x} x^8-28 e^{10 x} x^8+1118 x^9-8960 e^{2 x} x^9+3360 e^{4 x} x^9-\frac {2240}{3} e^{6 x} x^9+70 e^{8 x} x^9+896 x^{10}-3808 e^{2 x} x^{10}+980 e^{4 x} x^{10}-112 e^{6 x} x^{10}+448 x^{11}-832 e^{2 x} x^{11}+112 e^{4 x} x^{11}+128 x^{12}-64 e^{2 x} x^{12}+16 x^{13}+\frac {5}{16} \int e^{16 x} x^4 \, dx-\frac {9}{16} \int e^{8 x} x^2 \, dx-5 \int e^{14 x} x^4 \, dx+6 \int e^{6 x} x^2 \, dx-\frac {35}{3} \int e^{12 x} x^3 \, dx-14 \int e^{14 x} x^6 \, dx-20 \int e^{14 x} x^5 \, dx-27 \int e^{4 x} x^2 \, dx-49 \int e^{12 x} x^6 \, dx+56 \int e^{10 x} x^3 \, dx-70 \int e^{12 x} x^4 \, dx+72 \int e^{2 x} x^2 \, dx-\frac {217}{2} \int e^{12 x} x^5 \, dx-\frac {2819}{16} \int e^{8 x} x^3 \, dx+224 \int e^{10 x} x^7 \, dx+392 \int e^{6 x} x^3 \, dx+392 \int e^{10 x} x^4 \, dx-630 \int e^{8 x} x^8 \, dx-671 \int e^{4 x} x^3 \, dx+\frac {3724}{5} \int e^{10 x} x^6 \, dx+768 \int e^{2 x} x^{11} \, dx+\frac {4284}{5} \int e^{10 x} x^5 \, dx+1008 \int e^{2 x} x^3 \, dx+1120 \int e^{6 x} x^9 \, dx-1232 \int e^{4 x} x^{10} \, dx-\frac {11195}{8} \int e^{8 x} x^4 \, dx-2870 \int e^{8 x} x^7 \, dx+3365 \int e^{6 x} x^4 \, dx-3885 \int e^{8 x} x^5 \, dx-4900 \int e^{8 x} x^6 \, dx-\frac {11395}{2} \int e^{4 x} x^4 \, dx+6720 \int e^{6 x} x^8 \, dx+7560 \int e^{2 x} x^4 \, dx+9152 \int e^{2 x} x^{10} \, dx-9800 \int e^{4 x} x^9 \, dx+11194 \int e^{6 x} x^5 \, dx+15680 \int e^{6 x} x^7 \, dx+\frac {54880}{3} \int e^{6 x} x^6 \, dx-\frac {43317}{2} \int e^{4 x} x^5 \, dx-30240 \int e^{4 x} x^8 \, dx+31056 \int e^{2 x} x^5 \, dx+38080 \int e^{2 x} x^9 \, dx-43099 \int e^{4 x} x^6 \, dx-48160 \int e^{4 x} x^7 \, dx+72016 \int e^{2 x} x^6 \, dx+80640 \int e^{2 x} x^8 \, dx+98528 \int e^{2 x} x^7 \, dx+\int e^{16 x} x^5 \, dx \\ & = 36 e^{2 x} x^2-\frac {27}{4} e^{4 x} x^2+e^{6 x} x^2-\frac {9}{128} e^{8 x} x^2+\frac {9 x^3}{16}+480 e^{2 x} x^3-\frac {635}{4} e^{4 x} x^3+\frac {190}{3} e^{6 x} x^3-\frac {2795}{128} e^{8 x} x^3+\frac {28}{5} e^{10 x} x^3-\frac {35}{36} e^{12 x} x^3+\frac {45 x^4}{8}+3528 e^{2 x} x^4-\frac {10053}{8} e^{4 x} x^4+\frac {2777}{6} e^{6 x} x^4-\frac {1047}{8} e^{8 x} x^4+\frac {126}{5} e^{10 x} x^4-\frac {35}{12} e^{12 x} x^4-\frac {5}{14} e^{14 x} x^4+\frac {5}{256} e^{16 x} x^4+\frac {609 x^5}{16}+14016 e^{2 x} x^5-\frac {34201}{8} e^{4 x} x^5+\frac {3578}{3} e^{6 x} x^5-\frac {823}{4} e^{8 x} x^5+\frac {182}{25} e^{10 x} x^5+\frac {119}{24} e^{12 x} x^5-\frac {10}{7} e^{14 x} x^5+\frac {1}{16} e^{16 x} x^5+156 x^6+30832 e^{2 x} x^6-7165 e^{4 x} x^6+\frac {10649}{9} e^{6 x} x^6+35 e^{8 x} x^6-\frac {1708}{25} e^{10 x} x^6+14 e^{12 x} x^6-e^{14 x} x^6+460 x^7+38976 e^{2 x} x^7-5883 e^{4 x} x^7+\frac {1365}{4} e^{8 x} x^7-84 e^{10 x} x^7+7 e^{12 x} x^7+894 x^8+28004 e^{2 x} x^8-1540 e^{4 x} x^8-840 e^{6 x} x^8+280 e^{8 x} x^8-28 e^{10 x} x^8+1118 x^9+10080 e^{2 x} x^9+910 e^{4 x} x^9-560 e^{6 x} x^9+70 e^{8 x} x^9+896 x^{10}+768 e^{2 x} x^{10}+672 e^{4 x} x^{10}-112 e^{6 x} x^{10}+448 x^{11}-448 e^{2 x} x^{11}+112 e^{4 x} x^{11}+128 x^{12}-64 e^{2 x} x^{12}+16 x^{13}-\frac {5}{64} \int e^{16 x} x^3 \, dx+\frac {9}{64} \int e^{8 x} x \, dx-\frac {5}{16} \int e^{16 x} x^4 \, dx+\frac {10}{7} \int e^{14 x} x^3 \, dx-2 \int e^{6 x} x \, dx+\frac {35}{12} \int e^{12 x} x^2 \, dx+6 \int e^{14 x} x^5 \, dx+\frac {50}{7} \int e^{14 x} x^4 \, dx+\frac {27}{2} \int e^{4 x} x \, dx-\frac {84}{5} \int e^{10 x} x^2 \, dx+\frac {70}{3} \int e^{12 x} x^3 \, dx+\frac {49}{2} \int e^{12 x} x^5 \, dx+\frac {1085}{24} \int e^{12 x} x^4 \, dx+\frac {8457}{128} \int e^{8 x} x^2 \, dx-72 \int e^{2 x} x \, dx-\frac {784}{5} \int e^{10 x} x^3 \, dx-\frac {784}{5} \int e^{10 x} x^6 \, dx-196 \int e^{6 x} x^2 \, dx-\frac {2142}{5} \int e^{10 x} x^4 \, dx-\frac {11172}{25} \int e^{10 x} x^5 \, dx+\frac {2013}{4} \int e^{4 x} x^2 \, dx+630 \int e^{8 x} x^7 \, dx+\frac {11195}{16} \int e^{8 x} x^3 \, dx-1512 \int e^{2 x} x^2 \, dx-1680 \int e^{6 x} x^8 \, dx-\frac {6730}{3} \int e^{6 x} x^3 \, dx+\frac {19425}{8} \int e^{8 x} x^4 \, dx+\frac {10045}{4} \int e^{8 x} x^6 \, dx+3080 \int e^{4 x} x^9 \, dx+3675 \int e^{8 x} x^5 \, dx-4224 \int e^{2 x} x^{10} \, dx+\frac {11395}{2} \int e^{4 x} x^3 \, dx-8960 \int e^{6 x} x^7 \, dx-\frac {27985}{3} \int e^{6 x} x^4 \, dx-15120 \int e^{2 x} x^3 \, dx-\frac {54880}{3} \int e^{6 x} x^5 \, dx-\frac {54880}{3} \int e^{6 x} x^6 \, dx+22050 \int e^{4 x} x^8 \, dx+\frac {216585}{8} \int e^{4 x} x^4 \, dx-45760 \int e^{2 x} x^9 \, dx+60480 \int e^{4 x} x^7 \, dx+\frac {129297}{2} \int e^{4 x} x^5 \, dx-77640 \int e^{2 x} x^4 \, dx+84280 \int e^{4 x} x^6 \, dx-171360 \int e^{2 x} x^8 \, dx-216048 \int e^{2 x} x^5 \, dx-322560 \int e^{2 x} x^7 \, dx-344848 \int e^{2 x} x^6 \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(86\) vs. \(2(30)=60\).
Time = 13.35 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.87 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=\frac {1}{16} x^3 \left (3+\left (15-32 e^{2 x}+24 e^{4 x}-8 e^{6 x}+e^{8 x}\right ) x-8 \left (-2+e^{2 x}\right )^3 x^2+24 \left (-2+e^{2 x}\right )^2 x^3-32 \left (-2+e^{2 x}\right ) x^4+16 x^5\right )^2 \]
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[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(323\) vs. \(2(27)=54\).
Time = 0.19 (sec) , antiderivative size = 324, normalized size of antiderivative = 10.80
method | result | size |
risch | \(\frac {{\mathrm e}^{16 x} x^{5}}{16}+\frac {\left (-16 x^{6}-16 x^{5}\right ) {\mathrm e}^{14 x}}{16}+\frac {\left (112 x^{7}+224 x^{6}+112 x^{5}\right ) {\mathrm e}^{12 x}}{16}+\frac {\left (-448 x^{8}-1344 x^{7}-1344 x^{6}-448 x^{5}\right ) {\mathrm e}^{10 x}}{16}+\frac {\left (1120 x^{9}+4480 x^{8}+6720 x^{7}+4480 x^{6}+1118 x^{5}+6 x^{4}\right ) {\mathrm e}^{8 x}}{16}+\frac {\left (-1792 x^{10}-8960 x^{9}-17920 x^{8}-17920 x^{7}-8944 x^{6}-1824 x^{5}-48 x^{4}\right ) {\mathrm e}^{6 x}}{16}+\frac {\left (1792 x^{11}+10752 x^{10}+26880 x^{9}+35840 x^{8}+26832 x^{7}+10800 x^{6}+2032 x^{5}+144 x^{4}\right ) {\mathrm e}^{4 x}}{16}+\frac {\left (-1024 x^{12}-7168 x^{11}-21504 x^{10}-35840 x^{9}-35776 x^{8}-21504 x^{7}-7552 x^{6}-1536 x^{5}-192 x^{4}\right ) {\mathrm e}^{2 x}}{16}+16 x^{13}+128 x^{12}+448 x^{11}+896 x^{10}+1118 x^{9}+894 x^{8}+460 x^{7}+156 x^{6}+\frac {609 x^{5}}{16}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}\) | \(324\) |
derivativedivides | \(-96 x^{5} {\mathrm e}^{2 x}+448 x^{11}+128 x^{12}+16 x^{13}+896 x^{10}+1118 x^{9}+460 x^{7}+894 x^{8}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}+156 x^{6}+\frac {609 x^{5}}{16}+675 x^{6} {\mathrm e}^{4 x}-64 \,{\mathrm e}^{2 x} x^{12}-448 \,{\mathrm e}^{2 x} x^{11}-{\mathrm e}^{14 x} x^{6}-{\mathrm e}^{14 x} x^{5}+7 \,{\mathrm e}^{12 x} x^{7}+14 \,{\mathrm e}^{12 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{5}-28 \,{\mathrm e}^{10 x} x^{8}-84 \,{\mathrm e}^{10 x} x^{7}-84 \,{\mathrm e}^{10 x} x^{6}-28 \,{\mathrm e}^{10 x} x^{5}+70 \,{\mathrm e}^{8 x} x^{9}+280 \,{\mathrm e}^{8 x} x^{8}+420 \,{\mathrm e}^{8 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{6}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}+\frac {3 \,{\mathrm e}^{8 x} x^{4}}{8}-112 \,{\mathrm e}^{6 x} x^{10}-560 \,{\mathrm e}^{6 x} x^{9}-1120 \,{\mathrm e}^{6 x} x^{8}-1120 \,{\mathrm e}^{6 x} x^{7}-559 \,{\mathrm e}^{6 x} x^{6}-114 \,{\mathrm e}^{6 x} x^{5}-3 \,{\mathrm e}^{6 x} x^{4}+112 \,{\mathrm e}^{4 x} x^{11}+672 \,{\mathrm e}^{4 x} x^{10}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}+1680 \,{\mathrm e}^{4 x} x^{9}+1677 \,{\mathrm e}^{4 x} x^{7}+2240 x^{8} {\mathrm e}^{4 x}+127 x^{5} {\mathrm e}^{4 x}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}\) | \(479\) |
default | \(-96 x^{5} {\mathrm e}^{2 x}+448 x^{11}+128 x^{12}+16 x^{13}+896 x^{10}+1118 x^{9}+460 x^{7}+894 x^{8}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}+156 x^{6}+\frac {609 x^{5}}{16}+675 x^{6} {\mathrm e}^{4 x}-64 \,{\mathrm e}^{2 x} x^{12}-448 \,{\mathrm e}^{2 x} x^{11}-{\mathrm e}^{14 x} x^{6}-{\mathrm e}^{14 x} x^{5}+7 \,{\mathrm e}^{12 x} x^{7}+14 \,{\mathrm e}^{12 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{5}-28 \,{\mathrm e}^{10 x} x^{8}-84 \,{\mathrm e}^{10 x} x^{7}-84 \,{\mathrm e}^{10 x} x^{6}-28 \,{\mathrm e}^{10 x} x^{5}+70 \,{\mathrm e}^{8 x} x^{9}+280 \,{\mathrm e}^{8 x} x^{8}+420 \,{\mathrm e}^{8 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{6}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}+\frac {3 \,{\mathrm e}^{8 x} x^{4}}{8}-112 \,{\mathrm e}^{6 x} x^{10}-560 \,{\mathrm e}^{6 x} x^{9}-1120 \,{\mathrm e}^{6 x} x^{8}-1120 \,{\mathrm e}^{6 x} x^{7}-559 \,{\mathrm e}^{6 x} x^{6}-114 \,{\mathrm e}^{6 x} x^{5}-3 \,{\mathrm e}^{6 x} x^{4}+112 \,{\mathrm e}^{4 x} x^{11}+672 \,{\mathrm e}^{4 x} x^{10}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}+1680 \,{\mathrm e}^{4 x} x^{9}+1677 \,{\mathrm e}^{4 x} x^{7}+2240 x^{8} {\mathrm e}^{4 x}+127 x^{5} {\mathrm e}^{4 x}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}\) | \(479\) |
parallelrisch | \(-96 x^{5} {\mathrm e}^{2 x}+448 x^{11}+128 x^{12}+16 x^{13}+896 x^{10}+1118 x^{9}+460 x^{7}+894 x^{8}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}+156 x^{6}+\frac {609 x^{5}}{16}+675 x^{6} {\mathrm e}^{4 x}-64 \,{\mathrm e}^{2 x} x^{12}-448 \,{\mathrm e}^{2 x} x^{11}-{\mathrm e}^{14 x} x^{6}-{\mathrm e}^{14 x} x^{5}+7 \,{\mathrm e}^{12 x} x^{7}+14 \,{\mathrm e}^{12 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{5}-28 \,{\mathrm e}^{10 x} x^{8}-84 \,{\mathrm e}^{10 x} x^{7}-84 \,{\mathrm e}^{10 x} x^{6}-28 \,{\mathrm e}^{10 x} x^{5}+70 \,{\mathrm e}^{8 x} x^{9}+280 \,{\mathrm e}^{8 x} x^{8}+420 \,{\mathrm e}^{8 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{6}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}+\frac {3 \,{\mathrm e}^{8 x} x^{4}}{8}-112 \,{\mathrm e}^{6 x} x^{10}-560 \,{\mathrm e}^{6 x} x^{9}-1120 \,{\mathrm e}^{6 x} x^{8}-1120 \,{\mathrm e}^{6 x} x^{7}-559 \,{\mathrm e}^{6 x} x^{6}-114 \,{\mathrm e}^{6 x} x^{5}-3 \,{\mathrm e}^{6 x} x^{4}+112 \,{\mathrm e}^{4 x} x^{11}+672 \,{\mathrm e}^{4 x} x^{10}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}+1680 \,{\mathrm e}^{4 x} x^{9}+1677 \,{\mathrm e}^{4 x} x^{7}+2240 x^{8} {\mathrm e}^{4 x}+127 x^{5} {\mathrm e}^{4 x}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}\) | \(479\) |
parts | \(-96 x^{5} {\mathrm e}^{2 x}+448 x^{11}+128 x^{12}+16 x^{13}+896 x^{10}+1118 x^{9}+460 x^{7}+894 x^{8}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}+156 x^{6}+\frac {609 x^{5}}{16}+675 x^{6} {\mathrm e}^{4 x}-64 \,{\mathrm e}^{2 x} x^{12}-448 \,{\mathrm e}^{2 x} x^{11}-{\mathrm e}^{14 x} x^{6}-{\mathrm e}^{14 x} x^{5}+7 \,{\mathrm e}^{12 x} x^{7}+14 \,{\mathrm e}^{12 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{5}-28 \,{\mathrm e}^{10 x} x^{8}-84 \,{\mathrm e}^{10 x} x^{7}-84 \,{\mathrm e}^{10 x} x^{6}-28 \,{\mathrm e}^{10 x} x^{5}+70 \,{\mathrm e}^{8 x} x^{9}+280 \,{\mathrm e}^{8 x} x^{8}+420 \,{\mathrm e}^{8 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{6}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}+\frac {3 \,{\mathrm e}^{8 x} x^{4}}{8}-112 \,{\mathrm e}^{6 x} x^{10}-560 \,{\mathrm e}^{6 x} x^{9}-1120 \,{\mathrm e}^{6 x} x^{8}-1120 \,{\mathrm e}^{6 x} x^{7}-559 \,{\mathrm e}^{6 x} x^{6}-114 \,{\mathrm e}^{6 x} x^{5}-3 \,{\mathrm e}^{6 x} x^{4}+112 \,{\mathrm e}^{4 x} x^{11}+672 \,{\mathrm e}^{4 x} x^{10}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}+1680 \,{\mathrm e}^{4 x} x^{9}+1677 \,{\mathrm e}^{4 x} x^{7}+2240 x^{8} {\mathrm e}^{4 x}+127 x^{5} {\mathrm e}^{4 x}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}\) | \(479\) |
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Leaf count of result is larger than twice the leaf count of optimal. 296 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 296, normalized size of antiderivative = 9.87 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 323 vs. \(2 (22) = 44\).
Time = 0.24 (sec) , antiderivative size = 323, normalized size of antiderivative = 10.77 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 x^{13} + 128 x^{12} + 448 x^{11} + 896 x^{10} + 1118 x^{9} + 894 x^{8} + 460 x^{7} + 156 x^{6} + \frac {x^{5} e^{16 x}}{16} + \frac {609 x^{5}}{16} + \frac {45 x^{4}}{8} + \frac {9 x^{3}}{16} + \frac {\left (- 128 x^{6} - 128 x^{5}\right ) e^{14 x}}{128} + \frac {\left (896 x^{7} + 1792 x^{6} + 896 x^{5}\right ) e^{12 x}}{128} + \frac {\left (- 3584 x^{8} - 10752 x^{7} - 10752 x^{6} - 3584 x^{5}\right ) e^{10 x}}{128} + \frac {\left (8960 x^{9} + 35840 x^{8} + 53760 x^{7} + 35840 x^{6} + 8944 x^{5} + 48 x^{4}\right ) e^{8 x}}{128} + \frac {\left (- 14336 x^{10} - 71680 x^{9} - 143360 x^{8} - 143360 x^{7} - 71552 x^{6} - 14592 x^{5} - 384 x^{4}\right ) e^{6 x}}{128} + \frac {\left (14336 x^{11} + 86016 x^{10} + 215040 x^{9} + 286720 x^{8} + 214656 x^{7} + 86400 x^{6} + 16256 x^{5} + 1152 x^{4}\right ) e^{4 x}}{128} + \frac {\left (- 8192 x^{12} - 57344 x^{11} - 172032 x^{10} - 286720 x^{9} - 286208 x^{8} - 172032 x^{7} - 60416 x^{6} - 12288 x^{5} - 1536 x^{4}\right ) e^{2 x}}{128} \]
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Leaf count of result is larger than twice the leaf count of optimal. 296 vs. \(2 (27) = 54\).
Time = 0.22 (sec) , antiderivative size = 296, normalized size of antiderivative = 9.87 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 296 vs. \(2 (27) = 54\).
Time = 0.29 (sec) , antiderivative size = 296, normalized size of antiderivative = 9.87 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
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Time = 13.75 (sec) , antiderivative size = 416, normalized size of antiderivative = 13.87 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=9\,x^4\,{\mathrm {e}}^{4\,x}-96\,x^5\,{\mathrm {e}}^{2\,x}-12\,x^4\,{\mathrm {e}}^{2\,x}-472\,x^6\,{\mathrm {e}}^{2\,x}+127\,x^5\,{\mathrm {e}}^{4\,x}-1344\,x^7\,{\mathrm {e}}^{2\,x}-3\,x^4\,{\mathrm {e}}^{6\,x}+675\,x^6\,{\mathrm {e}}^{4\,x}-2236\,x^8\,{\mathrm {e}}^{2\,x}-114\,x^5\,{\mathrm {e}}^{6\,x}+1677\,x^7\,{\mathrm {e}}^{4\,x}-2240\,x^9\,{\mathrm {e}}^{2\,x}+\frac {3\,x^4\,{\mathrm {e}}^{8\,x}}{8}-559\,x^6\,{\mathrm {e}}^{6\,x}+2240\,x^8\,{\mathrm {e}}^{4\,x}-1344\,x^{10}\,{\mathrm {e}}^{2\,x}+\frac {559\,x^5\,{\mathrm {e}}^{8\,x}}{8}-1120\,x^7\,{\mathrm {e}}^{6\,x}+1680\,x^9\,{\mathrm {e}}^{4\,x}-448\,x^{11}\,{\mathrm {e}}^{2\,x}+280\,x^6\,{\mathrm {e}}^{8\,x}-1120\,x^8\,{\mathrm {e}}^{6\,x}+672\,x^{10}\,{\mathrm {e}}^{4\,x}-64\,x^{12}\,{\mathrm {e}}^{2\,x}-28\,x^5\,{\mathrm {e}}^{10\,x}+420\,x^7\,{\mathrm {e}}^{8\,x}-560\,x^9\,{\mathrm {e}}^{6\,x}+112\,x^{11}\,{\mathrm {e}}^{4\,x}-84\,x^6\,{\mathrm {e}}^{10\,x}+280\,x^8\,{\mathrm {e}}^{8\,x}-112\,x^{10}\,{\mathrm {e}}^{6\,x}+7\,x^5\,{\mathrm {e}}^{12\,x}-84\,x^7\,{\mathrm {e}}^{10\,x}+70\,x^9\,{\mathrm {e}}^{8\,x}+14\,x^6\,{\mathrm {e}}^{12\,x}-28\,x^8\,{\mathrm {e}}^{10\,x}-x^5\,{\mathrm {e}}^{14\,x}+7\,x^7\,{\mathrm {e}}^{12\,x}-x^6\,{\mathrm {e}}^{14\,x}+\frac {x^5\,{\mathrm {e}}^{16\,x}}{16}+\frac {9\,x^3}{16}+\frac {45\,x^4}{8}+\frac {609\,x^5}{16}+156\,x^6+460\,x^7+894\,x^8+1118\,x^9+896\,x^{10}+448\,x^{11}+128\,x^{12}+16\,x^{13} \]
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