Integrand size = 356, antiderivative size = 30 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=\frac {1}{16} x^3 \left (3-x+x \left (2-e^{2 x}+2 x\right )^4\right )^2 \]
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 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=\frac {1}{16} x^3 \left (3+\left (15-32 e^{2 x}+24 e^{4 x}-8 e^{6 x}+e^{8 x}\right ) x-8 \left (-2+e^{2 x}\right )^3 x^2+24 \left (-2+e^{2 x}\right )^2 x^3-32 \left (-2+e^{2 x}\right ) x^4+16 x^5\right )^2 \]
Integrate[(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)*(5*x^4 + 16*x^5) + E^(14*x)*(-80*x^4 - 320*x^5 - 224*x^6) + E^(12*x)*(5 60*x^4 + 2688*x^5 + 3472*x^6 + 1344*x^7) + E^(10*x)*(-2240*x^4 - 12544*x^5 - 22848*x^6 - 17024*x^7 - 4480*x^8) + E^(8*x)*(24*x^3 + 5638*x^4 + 35824* x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8 + 8960*x^9) + E^(6*x)*(-192*x^3 - 9408*x^4 - 64608*x^5 - 179104*x^6 - 250880*x^7 - 188160*x^8 - 71680*x^9 - 10752*x^10) + E^(4*x)*(576*x^3 + 10736*x^4 + 72928*x^5 + 231024*x^6 + 3940 48*x^7 + 385280*x^8 + 215040*x^9 + 62720*x^10 + 7168*x^11) + E^(2*x)*(-768 *x^3 - 8064*x^4 - 48384*x^5 - 165632*x^6 - 329216*x^7 - 394112*x^8 - 28672 0*x^9 - 121856*x^10 - 26624*x^11 - 2048*x^12))/16,x]
(x^3*(3 + (15 - 32*E^(2*x) + 24*E^(4*x) - 8*E^(6*x) + E^(8*x))*x - 8*(-2 + E^(2*x))^3*x^2 + 24*(-2 + E^(2*x))^2*x^3 - 32*(-2 + E^(2*x))*x^4 + 16*x^5 )^2)/16
Leaf count is larger than twice the leaf count of optimal. \(459\) vs. \(2(30)=60\).
Time = 3.72 (sec) , antiderivative size = 459, normalized size of antiderivative = 15.30, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {27, 2009}
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.
| \(\displaystyle \int \frac {1}{16} \left (3328 x^{12}+24576 x^{11}+78848 x^{10}+143360 x^9+160992 x^8+114432 x^7+51520 x^6+14976 x^5+3045 x^4+360 x^3+27 x^2+e^{16 x} \left (16 x^5+5 x^4\right )+e^{14 x} \left (-224 x^6-320 x^5-80 x^4\right )+e^{12 x} \left (1344 x^7+3472 x^6+2688 x^5+560 x^4\right )+e^{10 x} \left (-4480 x^8-17024 x^7-22848 x^6-12544 x^5-2240 x^4\right )+e^{8 x} \left (8960 x^9+45920 x^8+89600 x^7+82880 x^6+35824 x^5+5638 x^4+24 x^3\right )+e^{6 x} \left (-10752 x^{10}-71680 x^9-188160 x^8-250880 x^7-179104 x^6-64608 x^5-9408 x^4-192 x^3\right )+e^{4 x} \left (7168 x^{11}+62720 x^{10}+215040 x^9+385280 x^8+394048 x^7+231024 x^6+72928 x^5+10736 x^4+576 x^3\right )+e^{2 x} \left (-2048 x^{12}-26624 x^{11}-121856 x^{10}-286720 x^9-394112 x^8-329216 x^7-165632 x^6-48384 x^5-8064 x^4-768 x^3\right )\right ) \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{16} \int \left (3328 x^{12}+24576 x^{11}+78848 x^{10}+143360 x^9+160992 x^8+114432 x^7+51520 x^6+14976 x^5+3045 x^4+360 x^3+27 x^2+e^{16 x} \left (16 x^5+5 x^4\right )-16 e^{14 x} \left (14 x^6+20 x^5+5 x^4\right )+112 e^{12 x} \left (12 x^7+31 x^6+24 x^5+5 x^4\right )-448 e^{10 x} \left (10 x^8+38 x^7+51 x^6+28 x^5+5 x^4\right )+2 e^{8 x} \left (4480 x^9+22960 x^8+44800 x^7+41440 x^6+17912 x^5+2819 x^4+12 x^3\right )-32 e^{6 x} \left (336 x^{10}+2240 x^9+5880 x^8+7840 x^7+5597 x^6+2019 x^5+294 x^4+6 x^3\right )+16 e^{4 x} \left (448 x^{11}+3920 x^{10}+13440 x^9+24080 x^8+24628 x^7+14439 x^6+4558 x^5+671 x^4+36 x^3\right )-128 e^{2 x} \left (16 x^{12}+208 x^{11}+952 x^{10}+2240 x^9+3079 x^8+2572 x^7+1294 x^6+378 x^5+63 x^4+6 x^3\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{16} \left (256 x^{13}-1024 e^{2 x} x^{12}+2048 x^{12}-7168 e^{2 x} x^{11}+1792 e^{4 x} x^{11}+7168 x^{11}-21504 e^{2 x} x^{10}+10752 e^{4 x} x^{10}-1792 e^{6 x} x^{10}+14336 x^{10}-35840 e^{2 x} x^9+26880 e^{4 x} x^9-8960 e^{6 x} x^9+1120 e^{8 x} x^9+17888 x^9-35776 e^{2 x} x^8+35840 e^{4 x} x^8-17920 e^{6 x} x^8+4480 e^{8 x} x^8-448 e^{10 x} x^8+14304 x^8-21504 e^{2 x} x^7+26832 e^{4 x} x^7-17920 e^{6 x} x^7+6720 e^{8 x} x^7-1344 e^{10 x} x^7+112 e^{12 x} x^7+7360 x^7-7552 e^{2 x} x^6+10800 e^{4 x} x^6-8944 e^{6 x} x^6+4480 e^{8 x} x^6-1344 e^{10 x} x^6+224 e^{12 x} x^6-16 e^{14 x} x^6+2496 x^6-1536 e^{2 x} x^5+2032 e^{4 x} x^5-1824 e^{6 x} x^5+1118 e^{8 x} x^5-448 e^{10 x} x^5+112 e^{12 x} x^5-16 e^{14 x} x^5+e^{16 x} x^5+609 x^5-192 e^{2 x} x^4+144 e^{4 x} x^4-48 e^{6 x} x^4+6 e^{8 x} x^4+90 x^4+9 x^3\right )\) |
Int[(27*x^2 + 360*x^3 + 3045*x^4 + 14976*x^5 + 51520*x^6 + 114432*x^7 + 16 0992*x^8 + 143360*x^9 + 78848*x^10 + 24576*x^11 + 3328*x^12 + E^(16*x)*(5* x^4 + 16*x^5) + E^(14*x)*(-80*x^4 - 320*x^5 - 224*x^6) + E^(12*x)*(560*x^4 + 2688*x^5 + 3472*x^6 + 1344*x^7) + E^(10*x)*(-2240*x^4 - 12544*x^5 - 228 48*x^6 - 17024*x^7 - 4480*x^8) + E^(8*x)*(24*x^3 + 5638*x^4 + 35824*x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8 + 8960*x^9) + E^(6*x)*(-192*x^3 - 9408*x ^4 - 64608*x^5 - 179104*x^6 - 250880*x^7 - 188160*x^8 - 71680*x^9 - 10752* x^10) + E^(4*x)*(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) + E^(2*x)*(-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))/16,x]
(9*x^3 + 90*x^4 - 192*E^(2*x)*x^4 + 144*E^(4*x)*x^4 - 48*E^(6*x)*x^4 + 6*E ^(8*x)*x^4 + 609*x^5 - 1536*E^(2*x)*x^5 + 2032*E^(4*x)*x^5 - 1824*E^(6*x)* x^5 + 1118*E^(8*x)*x^5 - 448*E^(10*x)*x^5 + 112*E^(12*x)*x^5 - 16*E^(14*x) *x^5 + E^(16*x)*x^5 + 2496*x^6 - 7552*E^(2*x)*x^6 + 10800*E^(4*x)*x^6 - 89 44*E^(6*x)*x^6 + 4480*E^(8*x)*x^6 - 1344*E^(10*x)*x^6 + 224*E^(12*x)*x^6 - 16*E^(14*x)*x^6 + 7360*x^7 - 21504*E^(2*x)*x^7 + 26832*E^(4*x)*x^7 - 1792 0*E^(6*x)*x^7 + 6720*E^(8*x)*x^7 - 1344*E^(10*x)*x^7 + 112*E^(12*x)*x^7 + 14304*x^8 - 35776*E^(2*x)*x^8 + 35840*E^(4*x)*x^8 - 17920*E^(6*x)*x^8 + 44 80*E^(8*x)*x^8 - 448*E^(10*x)*x^8 + 17888*x^9 - 35840*E^(2*x)*x^9 + 26880* E^(4*x)*x^9 - 8960*E^(6*x)*x^9 + 1120*E^(8*x)*x^9 + 14336*x^10 - 21504*E^( 2*x)*x^10 + 10752*E^(4*x)*x^10 - 1792*E^(6*x)*x^10 + 7168*x^11 - 7168*E^(2 *x)*x^11 + 1792*E^(4*x)*x^11 + 2048*x^12 - 1024*E^(2*x)*x^12 + 256*x^13)/1 6
3.9.28.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
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 | \(-96 x^{5} {\mathrm e}^{2 x}+448 x^{11}+128 x^{12}+16 x^{13}+896 x^{10}+1118 x^{9}+460 x^{7}+894 x^{8}+\frac {45 x^{4}}{8}+\frac {9 x^{3}}{16}+156 x^{6}+\frac {609 x^{5}}{16}+675 x^{6} {\mathrm e}^{4 x}-64 \,{\mathrm e}^{2 x} x^{12}-448 \,{\mathrm e}^{2 x} x^{11}-{\mathrm e}^{14 x} x^{6}-{\mathrm e}^{14 x} x^{5}+7 \,{\mathrm e}^{12 x} x^{7}+14 \,{\mathrm e}^{12 x} x^{6}+7 \,{\mathrm e}^{12 x} x^{5}-28 \,{\mathrm e}^{10 x} x^{8}-84 \,{\mathrm e}^{10 x} x^{7}-84 \,{\mathrm e}^{10 x} x^{6}-28 \,{\mathrm e}^{10 x} x^{5}+70 \,{\mathrm e}^{8 x} x^{9}+280 \,{\mathrm e}^{8 x} x^{8}+420 \,{\mathrm e}^{8 x} x^{7}+280 \,{\mathrm e}^{8 x} x^{6}+\frac {559 \,{\mathrm e}^{8 x} x^{5}}{8}+\frac {3 \,{\mathrm e}^{8 x} x^{4}}{8}-112 \,{\mathrm e}^{6 x} x^{10}-560 \,{\mathrm e}^{6 x} x^{9}-1120 \,{\mathrm e}^{6 x} x^{8}-1120 \,{\mathrm e}^{6 x} x^{7}-559 \,{\mathrm e}^{6 x} x^{6}-114 \,{\mathrm e}^{6 x} x^{5}-3 \,{\mathrm e}^{6 x} x^{4}+112 \,{\mathrm e}^{4 x} x^{11}+672 \,{\mathrm e}^{4 x} x^{10}-1344 \,{\mathrm e}^{2 x} x^{10}-2240 \,{\mathrm e}^{2 x} x^{9}+1680 \,{\mathrm e}^{4 x} x^{9}+1677 \,{\mathrm e}^{4 x} x^{7}+2240 x^{8} {\mathrm e}^{4 x}+127 x^{5} {\mathrm e}^{4 x}-2236 \,{\mathrm e}^{2 x} x^{8}-1344 \,{\mathrm e}^{2 x} x^{7}-472 \,{\mathrm e}^{2 x} x^{6}-12 \,{\mathrm e}^{2 x} x^{4}+9 x^{4} {\mathrm e}^{4 x}+\frac {{\mathrm e}^{16 x} x^{5}}{16}\) | \(479\) |
int(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*exp(2*x) ^7+1/16*(1344*x^7+3472*x^6+2688*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480*x^8-17 024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+45920*x^8+ 89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-10752*x^1 0-71680*x^9-188160*x^8-250880*x^7-179104*x^6-64608*x^5-9408*x^4-192*x^3)*e xp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+394048*x^7+2310 24*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-26624*x^11 -121856*x^10-286720*x^9-394112*x^8-329216*x^7-165632*x^6-48384*x^5-8064*x^ 4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+10062*x^8+7152*x ^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x,method=_RETURNVERBOSE )
1/16*exp(2*x)^8*x^5+1/16*(-16*x^6-16*x^5)*exp(2*x)^7+1/16*(112*x^7+224*x^6 +112*x^5)*exp(2*x)^6+1/16*(-448*x^8-1344*x^7-1344*x^6-448*x^5)*exp(2*x)^5+ 1/16*(1120*x^9+4480*x^8+6720*x^7+4480*x^6+1118*x^5+6*x^4)*exp(2*x)^4+1/16* (-1792*x^10-8960*x^9-17920*x^8-17920*x^7-8944*x^6-1824*x^5-48*x^4)*exp(2*x )^3+1/16*(1792*x^11+10752*x^10+26880*x^9+35840*x^8+26832*x^7+10800*x^6+203 2*x^5+144*x^4)*exp(2*x)^2+1/16*(-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)*exp(2*x)+16*x^13+128*x^12+4 48*x^11+896*x^10+1118*x^9+894*x^8+460*x^7+156*x^6+609/16*x^5+45/8*x^4+9/16 *x^3
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 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*ex p(2*x)^7+1/16*(1344*x^7+3472*x^6+2688*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480* x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+4592 0*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-107 52*x^10-71680*x^9-188160*x^8-250880*x^7-179104*x^6-64608*x^5-9408*x^4-192* x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+394048*x^ 7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-2662 4*x^11-121856*x^10-286720*x^9-394112*x^8-329216*x^7-165632*x^6-48384*x^5-8 064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+10062*x^8+ 7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm=\
16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^ 5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 + x ^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3 *x^4)*e^(8*x) - (112*x^10 + 560*x^9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114* x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 1677*x ^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(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)*e^(2*x)
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 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 x^{13} + 128 x^{12} + 448 x^{11} + 896 x^{10} + 1118 x^{9} + 894 x^{8} + 460 x^{7} + 156 x^{6} + \frac {x^{5} e^{16 x}}{16} + \frac {609 x^{5}}{16} + \frac {45 x^{4}}{8} + \frac {9 x^{3}}{16} + \frac {\left (- 128 x^{6} - 128 x^{5}\right ) e^{14 x}}{128} + \frac {\left (896 x^{7} + 1792 x^{6} + 896 x^{5}\right ) e^{12 x}}{128} + \frac {\left (- 3584 x^{8} - 10752 x^{7} - 10752 x^{6} - 3584 x^{5}\right ) e^{10 x}}{128} + \frac {\left (8960 x^{9} + 35840 x^{8} + 53760 x^{7} + 35840 x^{6} + 8944 x^{5} + 48 x^{4}\right ) e^{8 x}}{128} + \frac {\left (- 14336 x^{10} - 71680 x^{9} - 143360 x^{8} - 143360 x^{7} - 71552 x^{6} - 14592 x^{5} - 384 x^{4}\right ) e^{6 x}}{128} + \frac {\left (14336 x^{11} + 86016 x^{10} + 215040 x^{9} + 286720 x^{8} + 214656 x^{7} + 86400 x^{6} + 16256 x^{5} + 1152 x^{4}\right ) e^{4 x}}{128} + \frac {\left (- 8192 x^{12} - 57344 x^{11} - 172032 x^{10} - 286720 x^{9} - 286208 x^{8} - 172032 x^{7} - 60416 x^{6} - 12288 x^{5} - 1536 x^{4}\right ) e^{2 x}}{128} \]
integrate(1/16*(16*x**5+5*x**4)*exp(2*x)**8+1/16*(-224*x**6-320*x**5-80*x* *4)*exp(2*x)**7+1/16*(1344*x**7+3472*x**6+2688*x**5+560*x**4)*exp(2*x)**6+ 1/16*(-4480*x**8-17024*x**7-22848*x**6-12544*x**5-2240*x**4)*exp(2*x)**5+1 /16*(8960*x**9+45920*x**8+89600*x**7+82880*x**6+35824*x**5+5638*x**4+24*x* *3)*exp(2*x)**4+1/16*(-10752*x**10-71680*x**9-188160*x**8-250880*x**7-1791 04*x**6-64608*x**5-9408*x**4-192*x**3)*exp(2*x)**3+1/16*(7168*x**11+62720* x**10+215040*x**9+385280*x**8+394048*x**7+231024*x**6+72928*x**5+10736*x** 4+576*x**3)*exp(2*x)**2+1/16*(-2048*x**12-26624*x**11-121856*x**10-286720* x**9-394112*x**8-329216*x**7-165632*x**6-48384*x**5-8064*x**4-768*x**3)*ex p(2*x)+208*x**12+1536*x**11+4928*x**10+8960*x**9+10062*x**8+7152*x**7+3220 *x**6+936*x**5+3045/16*x**4+45/2*x**3+27/16*x**2,x)
16*x**13 + 128*x**12 + 448*x**11 + 896*x**10 + 1118*x**9 + 894*x**8 + 460* x**7 + 156*x**6 + x**5*exp(16*x)/16 + 609*x**5/16 + 45*x**4/8 + 9*x**3/16 + (-128*x**6 - 128*x**5)*exp(14*x)/128 + (896*x**7 + 1792*x**6 + 896*x**5) *exp(12*x)/128 + (-3584*x**8 - 10752*x**7 - 10752*x**6 - 3584*x**5)*exp(10 *x)/128 + (8960*x**9 + 35840*x**8 + 53760*x**7 + 35840*x**6 + 8944*x**5 + 48*x**4)*exp(8*x)/128 + (-14336*x**10 - 71680*x**9 - 143360*x**8 - 143360* x**7 - 71552*x**6 - 14592*x**5 - 384*x**4)*exp(6*x)/128 + (14336*x**11 + 8 6016*x**10 + 215040*x**9 + 286720*x**8 + 214656*x**7 + 86400*x**6 + 16256* x**5 + 1152*x**4)*exp(4*x)/128 + (-8192*x**12 - 57344*x**11 - 172032*x**10 - 286720*x**9 - 286208*x**8 - 172032*x**7 - 60416*x**6 - 12288*x**5 - 153 6*x**4)*exp(2*x)/128
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 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*ex p(2*x)^7+1/16*(1344*x^7+3472*x^6+2688*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480* x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+4592 0*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-107 52*x^10-71680*x^9-188160*x^8-250880*x^7-179104*x^6-64608*x^5-9408*x^4-192* x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+394048*x^ 7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-2662 4*x^11-121856*x^10-286720*x^9-394112*x^8-329216*x^7-165632*x^6-48384*x^5-8 064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+10062*x^8+ 7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm=\
16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^ 5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 + x ^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3 *x^4)*e^(8*x) - (112*x^10 + 560*x^9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114* x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 1677*x ^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(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)*e^(2*x)
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 \[ \int \frac {1}{16} \left (27 x^2+360 x^3+3045 x^4+14976 x^5+51520 x^6+114432 x^7+160992 x^8+143360 x^9+78848 x^{10}+24576 x^{11}+3328 x^{12}+e^{16 x} \left (5 x^4+16 x^5\right )+e^{14 x} \left (-80 x^4-320 x^5-224 x^6\right )+e^{12 x} \left (560 x^4+2688 x^5+3472 x^6+1344 x^7\right )+e^{10 x} \left (-2240 x^4-12544 x^5-22848 x^6-17024 x^7-4480 x^8\right )+e^{8 x} \left (24 x^3+5638 x^4+35824 x^5+82880 x^6+89600 x^7+45920 x^8+8960 x^9\right )+e^{6 x} \left (-192 x^3-9408 x^4-64608 x^5-179104 x^6-250880 x^7-188160 x^8-71680 x^9-10752 x^{10}\right )+e^{4 x} \left (576 x^3+10736 x^4+72928 x^5+231024 x^6+394048 x^7+385280 x^8+215040 x^9+62720 x^{10}+7168 x^{11}\right )+e^{2 x} \left (-768 x^3-8064 x^4-48384 x^5-165632 x^6-329216 x^7-394112 x^8-286720 x^9-121856 x^{10}-26624 x^{11}-2048 x^{12}\right )\right ) \, dx=16 \, x^{13} + 128 \, x^{12} + 448 \, x^{11} + 896 \, x^{10} + 1118 \, x^{9} + 894 \, x^{8} + 460 \, x^{7} + 156 \, x^{6} + \frac {1}{16} \, x^{5} e^{\left (16 \, x\right )} + \frac {609}{16} \, x^{5} + \frac {45}{8} \, x^{4} + \frac {9}{16} \, x^{3} - {\left (x^{6} + x^{5}\right )} e^{\left (14 \, x\right )} + 7 \, {\left (x^{7} + 2 \, x^{6} + x^{5}\right )} e^{\left (12 \, x\right )} - 28 \, {\left (x^{8} + 3 \, x^{7} + 3 \, x^{6} + x^{5}\right )} e^{\left (10 \, x\right )} + \frac {1}{8} \, {\left (560 \, x^{9} + 2240 \, x^{8} + 3360 \, x^{7} + 2240 \, x^{6} + 559 \, x^{5} + 3 \, x^{4}\right )} e^{\left (8 \, x\right )} - {\left (112 \, x^{10} + 560 \, x^{9} + 1120 \, x^{8} + 1120 \, x^{7} + 559 \, x^{6} + 114 \, x^{5} + 3 \, x^{4}\right )} e^{\left (6 \, x\right )} + {\left (112 \, x^{11} + 672 \, x^{10} + 1680 \, x^{9} + 2240 \, x^{8} + 1677 \, x^{7} + 675 \, x^{6} + 127 \, x^{5} + 9 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (16 \, x^{12} + 112 \, x^{11} + 336 \, x^{10} + 560 \, x^{9} + 559 \, x^{8} + 336 \, x^{7} + 118 \, x^{6} + 24 \, x^{5} + 3 \, x^{4}\right )} e^{\left (2 \, x\right )} \]
integrate(1/16*(16*x^5+5*x^4)*exp(2*x)^8+1/16*(-224*x^6-320*x^5-80*x^4)*ex p(2*x)^7+1/16*(1344*x^7+3472*x^6+2688*x^5+560*x^4)*exp(2*x)^6+1/16*(-4480* x^8-17024*x^7-22848*x^6-12544*x^5-2240*x^4)*exp(2*x)^5+1/16*(8960*x^9+4592 0*x^8+89600*x^7+82880*x^6+35824*x^5+5638*x^4+24*x^3)*exp(2*x)^4+1/16*(-107 52*x^10-71680*x^9-188160*x^8-250880*x^7-179104*x^6-64608*x^5-9408*x^4-192* x^3)*exp(2*x)^3+1/16*(7168*x^11+62720*x^10+215040*x^9+385280*x^8+394048*x^ 7+231024*x^6+72928*x^5+10736*x^4+576*x^3)*exp(2*x)^2+1/16*(-2048*x^12-2662 4*x^11-121856*x^10-286720*x^9-394112*x^8-329216*x^7-165632*x^6-48384*x^5-8 064*x^4-768*x^3)*exp(2*x)+208*x^12+1536*x^11+4928*x^10+8960*x^9+10062*x^8+ 7152*x^7+3220*x^6+936*x^5+3045/16*x^4+45/2*x^3+27/16*x^2,x, algorithm=\
16*x^13 + 128*x^12 + 448*x^11 + 896*x^10 + 1118*x^9 + 894*x^8 + 460*x^7 + 156*x^6 + 1/16*x^5*e^(16*x) + 609/16*x^5 + 45/8*x^4 + 9/16*x^3 - (x^6 + x^ 5)*e^(14*x) + 7*(x^7 + 2*x^6 + x^5)*e^(12*x) - 28*(x^8 + 3*x^7 + 3*x^6 + x ^5)*e^(10*x) + 1/8*(560*x^9 + 2240*x^8 + 3360*x^7 + 2240*x^6 + 559*x^5 + 3 *x^4)*e^(8*x) - (112*x^10 + 560*x^9 + 1120*x^8 + 1120*x^7 + 559*x^6 + 114* x^5 + 3*x^4)*e^(6*x) + (112*x^11 + 672*x^10 + 1680*x^9 + 2240*x^8 + 1677*x ^7 + 675*x^6 + 127*x^5 + 9*x^4)*e^(4*x) - 4*(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)*e^(2*x)
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} \]
int((exp(16*x)*(5*x^4 + 16*x^5))/16 - (exp(2*x)*(768*x^3 + 8064*x^4 + 4838 4*x^5 + 165632*x^6 + 329216*x^7 + 394112*x^8 + 286720*x^9 + 121856*x^10 + 26624*x^11 + 2048*x^12))/16 - (exp(10*x)*(2240*x^4 + 12544*x^5 + 22848*x^6 + 17024*x^7 + 4480*x^8))/16 + (exp(8*x)*(24*x^3 + 5638*x^4 + 35824*x^5 + 82880*x^6 + 89600*x^7 + 45920*x^8 + 8960*x^9))/16 - (exp(14*x)*(80*x^4 + 3 20*x^5 + 224*x^6))/16 - (exp(6*x)*(192*x^3 + 9408*x^4 + 64608*x^5 + 179104 *x^6 + 250880*x^7 + 188160*x^8 + 71680*x^9 + 10752*x^10))/16 + (exp(12*x)* (560*x^4 + 2688*x^5 + 3472*x^6 + 1344*x^7))/16 + (27*x^2)/16 + (45*x^3)/2 + (3045*x^4)/16 + 936*x^5 + 3220*x^6 + 7152*x^7 + 10062*x^8 + 8960*x^9 + 4 928*x^10 + 1536*x^11 + 208*x^12 + (exp(4*x)*(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))/16,x)
9*x^4*exp(4*x) - 96*x^5*exp(2*x) - 12*x^4*exp(2*x) - 472*x^6*exp(2*x) + 12 7*x^5*exp(4*x) - 1344*x^7*exp(2*x) - 3*x^4*exp(6*x) + 675*x^6*exp(4*x) - 2 236*x^8*exp(2*x) - 114*x^5*exp(6*x) + 1677*x^7*exp(4*x) - 2240*x^9*exp(2*x ) + (3*x^4*exp(8*x))/8 - 559*x^6*exp(6*x) + 2240*x^8*exp(4*x) - 1344*x^10* exp(2*x) + (559*x^5*exp(8*x))/8 - 1120*x^7*exp(6*x) + 1680*x^9*exp(4*x) - 448*x^11*exp(2*x) + 280*x^6*exp(8*x) - 1120*x^8*exp(6*x) + 672*x^10*exp(4* x) - 64*x^12*exp(2*x) - 28*x^5*exp(10*x) + 420*x^7*exp(8*x) - 560*x^9*exp( 6*x) + 112*x^11*exp(4*x) - 84*x^6*exp(10*x) + 280*x^8*exp(8*x) - 112*x^10* exp(6*x) + 7*x^5*exp(12*x) - 84*x^7*exp(10*x) + 70*x^9*exp(8*x) + 14*x^6*e xp(12*x) - 28*x^8*exp(10*x) - x^5*exp(14*x) + 7*x^7*exp(12*x) - x^6*exp(14 *x) + (x^5*exp(16*x))/16 + (9*x^3)/16 + (45*x^4)/8 + (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^1 3