Integrand size = 698, antiderivative size = 30 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=e^x \left (-e^{3 x}+x+\frac {2 x}{\left (e^x-x+x^2\right )^2}\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(83\) vs. \(2(30)=60\).
Time = 10.26 (sec) , antiderivative size = 83, normalized size of antiderivative = 2.77 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=\frac {e^x \left (e^{5 x}-e^{2 x} x+2 e^{4 x} (-1+x) x-2 e^x (-1+x) x^2+e^{3 x} (-1+x)^2 x^2-x \left (2+x^2-2 x^3+x^4\right )\right )^2}{\left (e^x+(-1+x) x\right )^4} \]
Integrate[(E^(6*x)*(2*x + x^2) + E^(5*x)*(-10*x^2 + 5*x^3 + 5*x^4) + E^(4* x)*(8*x - 4*x^2 + 20*x^3 - 30*x^4 + 10*x^6) + E^(3*x)*(-16*x^2 + 12*x^3 - 24*x^4 + 50*x^5 - 30*x^6 - 10*x^7 + 10*x^8) + E^(2*x)*(8*x - 12*x^2 + 8*x^ 3 + 4*x^4 - 6*x^5 - 31*x^6 + 40*x^7 - 10*x^8 - 10*x^9 + 5*x^10) + E^x*(8*x ^2 - 28*x^3 + 4*x^4 - 12*x^5 + 26*x^6 - 11*x^7 - 11*x^8 + 10*x^9 - 3*x^11 + x^12) + E^(6*x)*(7*E^(6*x) + E^(5*x)*(-35*x + 35*x^2) + E^(4*x)*(70*x^2 - 140*x^3 + 70*x^4) + E^(3*x)*(-70*x^3 + 210*x^4 - 210*x^5 + 70*x^6) + E^( 2*x)*(35*x^4 - 140*x^5 + 210*x^6 - 140*x^7 + 35*x^8) + E^x*(-7*x^5 + 35*x^ 6 - 70*x^7 + 70*x^8 - 35*x^9 + 7*x^10)) + E^(3*x)*(E^(6*x)*(-2 - 8*x) + E^ (5*x)*(10*x + 30*x^2 - 40*x^3) + E^(4*x)*(-4 - 8*x - 20*x^2 - 40*x^3 + 140 *x^4 - 80*x^5) + E^(3*x)*(4*x + 36*x^2 - 12*x^3 + 20*x^4 - 180*x^5 + 220*x ^6 - 80*x^7) + E^(2*x)*(4*x^2 - 64*x^3 + 90*x^4 - 40*x^5 + 100*x^6 - 200*x ^7 + 150*x^8 - 40*x^9) + E^x*(-4*x^3 + 36*x^4 - 74*x^5 + 58*x^6 - 36*x^7 + 60*x^8 - 70*x^9 + 38*x^10 - 8*x^11)))/(E^(5*x) - x^5 + 5*x^6 - 10*x^7 + 1 0*x^8 - 5*x^9 + x^10 + E^(4*x)*(-5*x + 5*x^2) + E^(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + E^(2*x)*(-10*x^3 + 30*x^4 - 30*x^5 + 10*x^6) + E^x*(5*x^4 - 20* x^5 + 30*x^6 - 20*x^7 + 5*x^8)),x]
(E^x*(E^(5*x) - E^(2*x)*x + 2*E^(4*x)*(-1 + x)*x - 2*E^x*(-1 + x)*x^2 + E^ (3*x)*(-1 + x)^2*x^2 - x*(2 + x^2 - 2*x^3 + x^4))^2)/(E^x + (-1 + x)*x)^4
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.
| \(\displaystyle \int \frac {e^{6 x} \left (x^2+2 x\right )+e^{5 x} \left (5 x^4+5 x^3-10 x^2\right )+e^{4 x} \left (10 x^6-30 x^4+20 x^3-4 x^2+8 x\right )+e^{3 x} \left (10 x^8-10 x^7-30 x^6+50 x^5-24 x^4+12 x^3-16 x^2\right )+e^{2 x} \left (5 x^{10}-10 x^9-10 x^8+40 x^7-31 x^6-6 x^5+4 x^4+8 x^3-12 x^2+8 x\right )+e^{6 x} \left (e^{5 x} \left (35 x^2-35 x\right )+e^{4 x} \left (70 x^4-140 x^3+70 x^2\right )+e^{3 x} \left (70 x^6-210 x^5+210 x^4-70 x^3\right )+e^{2 x} \left (35 x^8-140 x^7+210 x^6-140 x^5+35 x^4\right )+e^x \left (7 x^{10}-35 x^9+70 x^8-70 x^7+35 x^6-7 x^5\right )+7 e^{6 x}\right )+e^x \left (x^{12}-3 x^{11}+10 x^9-11 x^8-11 x^7+26 x^6-12 x^5+4 x^4-28 x^3+8 x^2\right )+e^{3 x} \left (e^{5 x} \left (-40 x^3+30 x^2+10 x\right )+e^{4 x} \left (-80 x^5+140 x^4-40 x^3-20 x^2-8 x-4\right )+e^{3 x} \left (-80 x^7+220 x^6-180 x^5+20 x^4-12 x^3+36 x^2+4 x\right )+e^{2 x} \left (-40 x^9+150 x^8-200 x^7+100 x^6-40 x^5+90 x^4-64 x^3+4 x^2\right )+e^x \left (-8 x^{11}+38 x^{10}-70 x^9+60 x^8-36 x^7+58 x^6-74 x^5+36 x^4-4 x^3\right )+e^{6 x} (-8 x-2)\right )}{x^{10}-5 x^9+10 x^8-10 x^7+5 x^6-x^5+e^{4 x} \left (5 x^2-5 x\right )+e^{3 x} \left (10 x^4-20 x^3+10 x^2\right )+e^{2 x} \left (10 x^6-30 x^5+30 x^4-10 x^3\right )+e^x \left (5 x^8-20 x^7+30 x^6-20 x^5+5 x^4\right )+e^{5 x}} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^{6 x} \left (x^2+2 x\right )+e^{5 x} \left (5 x^4+5 x^3-10 x^2\right )+e^{4 x} \left (10 x^6-30 x^4+20 x^3-4 x^2+8 x\right )+e^{3 x} \left (10 x^8-10 x^7-30 x^6+50 x^5-24 x^4+12 x^3-16 x^2\right )+e^{2 x} \left (5 x^{10}-10 x^9-10 x^8+40 x^7-31 x^6-6 x^5+4 x^4+8 x^3-12 x^2+8 x\right )+e^{6 x} \left (e^{5 x} \left (35 x^2-35 x\right )+e^{4 x} \left (70 x^4-140 x^3+70 x^2\right )+e^{3 x} \left (70 x^6-210 x^5+210 x^4-70 x^3\right )+e^{2 x} \left (35 x^8-140 x^7+210 x^6-140 x^5+35 x^4\right )+e^x \left (7 x^{10}-35 x^9+70 x^8-70 x^7+35 x^6-7 x^5\right )+7 e^{6 x}\right )+e^x \left (x^{12}-3 x^{11}+10 x^9-11 x^8-11 x^7+26 x^6-12 x^5+4 x^4-28 x^3+8 x^2\right )+e^{3 x} \left (e^{5 x} \left (-40 x^3+30 x^2+10 x\right )+e^{4 x} \left (-80 x^5+140 x^4-40 x^3-20 x^2-8 x-4\right )+e^{3 x} \left (-80 x^7+220 x^6-180 x^5+20 x^4-12 x^3+36 x^2+4 x\right )+e^{2 x} \left (-40 x^9+150 x^8-200 x^7+100 x^6-40 x^5+90 x^4-64 x^3+4 x^2\right )+e^x \left (-8 x^{11}+38 x^{10}-70 x^9+60 x^8-36 x^7+58 x^6-74 x^5+36 x^4-4 x^3\right )+e^{6 x} (-8 x-2)\right )}{\left (x^2-x+e^x\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-12 \left (5 x^2-8 x+3\right ) x^2+\frac {4 \left (7 x^2-17 x+6\right ) x^2}{\left (x^2-x+e^x\right )^4}+e^x \left (8 x^2+17 x-14\right ) x-\frac {16 \left (x^3-4 x^2+4 x-1\right ) x^3}{\left (x^2-x+e^x\right )^5}-\frac {4 \left (4 x^6-40 x^5+84 x^4-64 x^3+16 x^2+x-2\right ) x}{x^2-x+e^x}+\frac {4 \left (6 x^7-41 x^6+96 x^5-102 x^4+50 x^3-6 x^2-9 x+4\right ) x^2}{\left (x^2-x+e^x\right )^2}-\frac {4 \left (2 x^{10}-14 x^9+38 x^8-52 x^7+38 x^6-12 x^5-6 x^4+8 x^3-2 x^2+3 x-2\right ) x}{\left (x^2-x+e^x\right )^3}+7 e^{7 x}-4 e^{2 x} (2 x+1)-2 e^{4 x} (4 x+1)\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 24 \int \frac {x^2}{\left (x^2-x+e^x\right )^4}dx+8 \int \frac {x}{\left (x^2-x+e^x\right )^3}dx-12 \int \frac {x^2}{\left (x^2-x+e^x\right )^3}dx+16 \int \frac {x^2}{\left (x^2-x+e^x\right )^2}dx+8 \int \frac {x}{x^2-x+e^x}dx-4 \int \frac {x^2}{x^2-x+e^x}dx-8 \int \frac {x^{11}}{\left (x^2-x+e^x\right )^3}dx+56 \int \frac {x^{10}}{\left (x^2-x+e^x\right )^3}dx-152 \int \frac {x^9}{\left (x^2-x+e^x\right )^3}dx+24 \int \frac {x^9}{\left (x^2-x+e^x\right )^2}dx+208 \int \frac {x^8}{\left (x^2-x+e^x\right )^3}dx-164 \int \frac {x^8}{\left (x^2-x+e^x\right )^2}dx-152 \int \frac {x^7}{\left (x^2-x+e^x\right )^3}dx+384 \int \frac {x^7}{\left (x^2-x+e^x\right )^2}dx-16 \int \frac {x^7}{x^2-x+e^x}dx-16 \int \frac {x^6}{\left (x^2-x+e^x\right )^5}dx+48 \int \frac {x^6}{\left (x^2-x+e^x\right )^3}dx-408 \int \frac {x^6}{\left (x^2-x+e^x\right )^2}dx+160 \int \frac {x^6}{x^2-x+e^x}dx+64 \int \frac {x^5}{\left (x^2-x+e^x\right )^5}dx+24 \int \frac {x^5}{\left (x^2-x+e^x\right )^3}dx+200 \int \frac {x^5}{\left (x^2-x+e^x\right )^2}dx-336 \int \frac {x^5}{x^2-x+e^x}dx-64 \int \frac {x^4}{\left (x^2-x+e^x\right )^5}dx+28 \int \frac {x^4}{\left (x^2-x+e^x\right )^4}dx-32 \int \frac {x^4}{\left (x^2-x+e^x\right )^3}dx-24 \int \frac {x^4}{\left (x^2-x+e^x\right )^2}dx+256 \int \frac {x^4}{x^2-x+e^x}dx+16 \int \frac {x^3}{\left (x^2-x+e^x\right )^5}dx-68 \int \frac {x^3}{\left (x^2-x+e^x\right )^4}dx+8 \int \frac {x^3}{\left (x^2-x+e^x\right )^3}dx-36 \int \frac {x^3}{\left (x^2-x+e^x\right )^2}dx-64 \int \frac {x^3}{x^2-x+e^x}dx-12 x^5+24 x^4+8 e^x x^3-12 x^3-7 e^x x^2+2 e^{2 x}+\frac {e^{4 x}}{2}+e^{7 x}-2 e^{2 x} (2 x+1)-\frac {1}{2} e^{4 x} (4 x+1)\) |
Int[(E^(6*x)*(2*x + x^2) + E^(5*x)*(-10*x^2 + 5*x^3 + 5*x^4) + E^(4*x)*(8* x - 4*x^2 + 20*x^3 - 30*x^4 + 10*x^6) + E^(3*x)*(-16*x^2 + 12*x^3 - 24*x^4 + 50*x^5 - 30*x^6 - 10*x^7 + 10*x^8) + E^(2*x)*(8*x - 12*x^2 + 8*x^3 + 4* x^4 - 6*x^5 - 31*x^6 + 40*x^7 - 10*x^8 - 10*x^9 + 5*x^10) + E^x*(8*x^2 - 2 8*x^3 + 4*x^4 - 12*x^5 + 26*x^6 - 11*x^7 - 11*x^8 + 10*x^9 - 3*x^11 + x^12 ) + E^(6*x)*(7*E^(6*x) + E^(5*x)*(-35*x + 35*x^2) + E^(4*x)*(70*x^2 - 140* x^3 + 70*x^4) + E^(3*x)*(-70*x^3 + 210*x^4 - 210*x^5 + 70*x^6) + E^(2*x)*( 35*x^4 - 140*x^5 + 210*x^6 - 140*x^7 + 35*x^8) + E^x*(-7*x^5 + 35*x^6 - 70 *x^7 + 70*x^8 - 35*x^9 + 7*x^10)) + E^(3*x)*(E^(6*x)*(-2 - 8*x) + E^(5*x)* (10*x + 30*x^2 - 40*x^3) + E^(4*x)*(-4 - 8*x - 20*x^2 - 40*x^3 + 140*x^4 - 80*x^5) + E^(3*x)*(4*x + 36*x^2 - 12*x^3 + 20*x^4 - 180*x^5 + 220*x^6 - 8 0*x^7) + E^(2*x)*(4*x^2 - 64*x^3 + 90*x^4 - 40*x^5 + 100*x^6 - 200*x^7 + 1 50*x^8 - 40*x^9) + E^x*(-4*x^3 + 36*x^4 - 74*x^5 + 58*x^6 - 36*x^7 + 60*x^ 8 - 70*x^9 + 38*x^10 - 8*x^11)))/(E^(5*x) - x^5 + 5*x^6 - 10*x^7 + 10*x^8 - 5*x^9 + x^10 + E^(4*x)*(-5*x + 5*x^2) + E^(3*x)*(10*x^2 - 20*x^3 + 10*x^ 4) + E^(2*x)*(-10*x^3 + 30*x^4 - 30*x^5 + 10*x^6) + E^x*(5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8)),x]
3.12.14.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(258\) vs. \(2(27)=54\).
Time = 22.00 (sec) , antiderivative size = 259, normalized size of antiderivative = 8.63
| method | result | size |
| risch | \({\mathrm e}^{7 x}-12 x^{5}-2 x \,{\mathrm e}^{4 x}+24 x^{4}-12 x^{3}-4 x \,{\mathrm e}^{2 x}+\left (8 x^{3}-7 x^{2}\right ) {\mathrm e}^{x}+\frac {4 \left (11 \,{\mathrm e}^{2 x} x^{7}-44 \,{\mathrm e}^{2 x} x^{4}+100 x^{7} {\mathrm e}^{x}+10 x^{9} {\mathrm e}^{x}-50 x^{8} {\mathrm e}^{x}-4 x^{2} {\mathrm e}^{3 x}+11 \,{\mathrm e}^{2 x} x^{3}+66 x^{5} {\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} x^{2}-2 x \,{\mathrm e}^{2 x}-100 x^{6} {\mathrm e}^{x}-9 \,{\mathrm e}^{x} x^{4}+{\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x^{3}+50 x^{5} {\mathrm e}^{x}+3 x^{11}+12 x^{3} {\mathrm e}^{3 x}+{\mathrm e}^{3 x}+45 x^{7}-60 x^{8}-18 x^{10}+45 x^{9}-18 x^{6}+3 x^{5}+{\mathrm e}^{x}-12 x^{4} {\mathrm e}^{3 x}-44 \,{\mathrm e}^{2 x} x^{6}+4 \,{\mathrm e}^{3 x} x^{5}\right ) x^{2}}{\left (x^{2}+{\mathrm e}^{x}-x \right )^{4}}\) | \(259\) |
| parallelrisch | \(\frac {-16 \,{\mathrm e}^{x} {\mathrm e}^{6 x} x^{5}-48 \,{\mathrm e}^{6 x} {\mathrm e}^{2 x} x^{5}+24 \,{\mathrm e}^{3 x} {\mathrm e}^{6 x} x^{4}+48 \,{\mathrm e}^{6 x} {\mathrm e}^{2 x} x^{4}-48 \,{\mathrm e}^{3 x} {\mathrm e}^{6 x} x^{3}+4 \,{\mathrm e}^{x} x^{10}+16 \,{\mathrm e}^{6 x} {\mathrm e}^{4 x} x^{2}-16 \,{\mathrm e}^{x} {\mathrm e}^{6 x} x^{7}+24 \,{\mathrm e}^{x} {\mathrm e}^{6 x} x^{6}+4 \,{\mathrm e}^{x} {\mathrm e}^{6 x} x^{8}-48 \,{\mathrm e}^{2 x} x^{7}+24 \,{\mathrm e}^{3 x} x^{6}+16 x^{4} {\mathrm e}^{4 x}-32 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{7}+96 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{6}-48 \left ({\mathrm e}^{3 x}\right )^{2} x^{5}+96 \left ({\mathrm e}^{3 x}\right )^{2} x^{4}+16 \,{\mathrm e}^{6 x} {\mathrm e}^{2 x} x^{6}+32 \,{\mathrm e}^{2 x} x^{4}-16 x^{7} {\mathrm e}^{x}-16 x^{9} {\mathrm e}^{x}+24 x^{8} {\mathrm e}^{x}+16 x^{2} {\mathrm e}^{3 x}-32 \,{\mathrm e}^{2 x} x^{3}-16 x^{3} {\mathrm e}^{4 x}-16 x^{5} {\mathrm e}^{2 x}+20 x^{6} {\mathrm e}^{x}+16 \,{\mathrm e}^{x} x^{4}-16 x \left ({\mathrm e}^{3 x}\right )^{2}+16 \,{\mathrm e}^{x} x^{2}+4 x^{2} {\mathrm e}^{5 x}-48 x^{3} \left ({\mathrm e}^{3 x}\right )^{2}-32 x^{5} {\mathrm e}^{x}+24 x^{4} {\mathrm e}^{3 x}-48 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{7}+32 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{4}-8 \,{\mathrm e}^{5 x} {\mathrm e}^{3 x} x -32 \,{\mathrm e}^{4 x} {\mathrm e}^{3 x} x^{3}-32 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{3}+16 \,{\mathrm e}^{2 x} x^{8}+32 \,{\mathrm e}^{4 x} {\mathrm e}^{3 x} x^{2}+32 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{2}+32 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{6}+32 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{4}-16 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{3}-24 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{5}+48 \,{\mathrm e}^{2 x} x^{6}-48 \,{\mathrm e}^{3 x} x^{5}-8 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{9}+32 \,{\mathrm e}^{3 x} {\mathrm e}^{x} x^{8}-96 \,{\mathrm e}^{3 x} {\mathrm e}^{2 x} x^{5}-16 \,{\mathrm e}^{6 x} {\mathrm e}^{4 x} x +24 \,{\mathrm e}^{6 x} {\mathrm e}^{3 x} x^{2}-16 \,{\mathrm e}^{6 x} {\mathrm e}^{2 x} x^{3}+4 \,{\mathrm e}^{6 x} {\mathrm e}^{x} x^{4}+4 \,{\mathrm e}^{6 x} {\mathrm e}^{5 x}}{4 x^{8}-16 x^{7}+16 x^{6} {\mathrm e}^{x}+24 x^{6}-48 x^{5} {\mathrm e}^{x}+24 \,{\mathrm e}^{2 x} x^{4}-16 x^{5}+48 \,{\mathrm e}^{x} x^{4}-48 \,{\mathrm e}^{2 x} x^{3}+16 x^{2} {\mathrm e}^{3 x}+4 x^{4}-16 \,{\mathrm e}^{x} x^{3}+24 \,{\mathrm e}^{2 x} x^{2}-16 x \,{\mathrm e}^{3 x}+4 \,{\mathrm e}^{4 x}}\) | \(728\) |
int(((7*exp(x)^6+(35*x^2-35*x)*exp(x)^5+(70*x^4-140*x^3+70*x^2)*exp(x)^4+( 70*x^6-210*x^5+210*x^4-70*x^3)*exp(x)^3+(35*x^8-140*x^7+210*x^6-140*x^5+35 *x^4)*exp(x)^2+(7*x^10-35*x^9+70*x^8-70*x^7+35*x^6-7*x^5)*exp(x))*exp(3*x) ^2+((-8*x-2)*exp(x)^6+(-40*x^3+30*x^2+10*x)*exp(x)^5+(-80*x^5+140*x^4-40*x ^3-20*x^2-8*x-4)*exp(x)^4+(-80*x^7+220*x^6-180*x^5+20*x^4-12*x^3+36*x^2+4* x)*exp(x)^3+(-40*x^9+150*x^8-200*x^7+100*x^6-40*x^5+90*x^4-64*x^3+4*x^2)*e xp(x)^2+(-8*x^11+38*x^10-70*x^9+60*x^8-36*x^7+58*x^6-74*x^5+36*x^4-4*x^3)* exp(x))*exp(3*x)+(x^2+2*x)*exp(x)^6+(5*x^4+5*x^3-10*x^2)*exp(x)^5+(10*x^6- 30*x^4+20*x^3-4*x^2+8*x)*exp(x)^4+(10*x^8-10*x^7-30*x^6+50*x^5-24*x^4+12*x ^3-16*x^2)*exp(x)^3+(5*x^10-10*x^9-10*x^8+40*x^7-31*x^6-6*x^5+4*x^4+8*x^3- 12*x^2+8*x)*exp(x)^2+(x^12-3*x^11+10*x^9-11*x^8-11*x^7+26*x^6-12*x^5+4*x^4 -28*x^3+8*x^2)*exp(x))/(exp(x)^5+(5*x^2-5*x)*exp(x)^4+(10*x^4-20*x^3+10*x^ 2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(5*x^8-20*x^7+30*x^6-20 *x^5+5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x,method=_RETURNVER BOSE)
exp(x)^7-12*x^5-2*x*exp(x)^4+24*x^4-12*x^3-4*x*exp(x)^2+(8*x^3-7*x^2)*exp( x)+4*(100*x^7*exp(x)+10*x^9*exp(x)-50*x^8*exp(x)+4*x^5*exp(x)^3-44*x^6*exp (x)^2-12*x^4*exp(x)^3-4*x^2*exp(x)^3-100*x^6*exp(x)-44*exp(x)^2*x^4+66*x^5 *exp(x)^2-9*exp(x)*x^4+2*exp(x)^2*x^2+exp(x)*x^2-2*x*exp(x)^2-2*exp(x)*x^3 +12*x^3*exp(x)^3+50*x^5*exp(x)+3*x^11+11*exp(x)^2*x^3+45*x^7+exp(x)^3-60*x ^8-18*x^10+45*x^9-18*x^6+3*x^5+exp(x)+11*exp(x)^2*x^7)*x^2/(x^2+exp(x)-x)^ 4
Leaf count of result is larger than twice the leaf count of optimal. 390 vs. \(2 (27) = 54\).
Time = 0.27 (sec) , antiderivative size = 390, normalized size of antiderivative = 13.00 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=\frac {4 \, {\left (x^{2} - x\right )} e^{\left (10 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (9 \, x\right )} + 2 \, {\left (2 \, x^{6} - 6 \, x^{5} + 6 \, x^{4} - 2 \, x^{3} - x\right )} e^{\left (8 \, x\right )} + {\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} - 8 \, x^{3} + 8 \, x^{2}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (3 \, x^{5} - 6 \, x^{4} + 3 \, x^{3} + x\right )} e^{\left (6 \, x\right )} - {\left (8 \, x^{7} - 24 \, x^{6} + 24 \, x^{5} - 8 \, x^{4} + 8 \, x^{3} - 9 \, x^{2}\right )} e^{\left (5 \, x\right )} - 2 \, {\left (x^{9} - 4 \, x^{8} + 6 \, x^{7} - 4 \, x^{6} + 3 \, x^{5} - 6 \, x^{4} + 4 \, x^{3}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (3 \, x^{6} - 6 \, x^{5} + 3 \, x^{4} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 4 \, {\left (x^{8} - 3 \, x^{7} + 3 \, x^{6} - x^{5} + 2 \, x^{4} - 2 \, x^{3}\right )} e^{\left (2 \, x\right )} + {\left (x^{10} - 4 \, x^{9} + 6 \, x^{8} - 4 \, x^{7} + 5 \, x^{6} - 8 \, x^{5} + 4 \, x^{4} + 4 \, x^{2}\right )} e^{x} + e^{\left (11 \, x\right )}}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} + 4 \, {\left (x^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}} \]
integrate(((7*exp(x)^6+(35*x^2-35*x)*exp(x)^5+(70*x^4-140*x^3+70*x^2)*exp( x)^4+(70*x^6-210*x^5+210*x^4-70*x^3)*exp(x)^3+(35*x^8-140*x^7+210*x^6-140* x^5+35*x^4)*exp(x)^2+(7*x^10-35*x^9+70*x^8-70*x^7+35*x^6-7*x^5)*exp(x))*ex p(3*x)^2+((-8*x-2)*exp(x)^6+(-40*x^3+30*x^2+10*x)*exp(x)^5+(-80*x^5+140*x^ 4-40*x^3-20*x^2-8*x-4)*exp(x)^4+(-80*x^7+220*x^6-180*x^5+20*x^4-12*x^3+36* x^2+4*x)*exp(x)^3+(-40*x^9+150*x^8-200*x^7+100*x^6-40*x^5+90*x^4-64*x^3+4* x^2)*exp(x)^2+(-8*x^11+38*x^10-70*x^9+60*x^8-36*x^7+58*x^6-74*x^5+36*x^4-4 *x^3)*exp(x))*exp(3*x)+(x^2+2*x)*exp(x)^6+(5*x^4+5*x^3-10*x^2)*exp(x)^5+(1 0*x^6-30*x^4+20*x^3-4*x^2+8*x)*exp(x)^4+(10*x^8-10*x^7-30*x^6+50*x^5-24*x^ 4+12*x^3-16*x^2)*exp(x)^3+(5*x^10-10*x^9-10*x^8+40*x^7-31*x^6-6*x^5+4*x^4+ 8*x^3-12*x^2+8*x)*exp(x)^2+(x^12-3*x^11+10*x^9-11*x^8-11*x^7+26*x^6-12*x^5 +4*x^4-28*x^3+8*x^2)*exp(x))/(exp(x)^5+(5*x^2-5*x)*exp(x)^4+(10*x^4-20*x^3 +10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(5*x^8-20*x^7+30* x^6-20*x^5+5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm= \
(4*(x^2 - x)*e^(10*x) + 6*(x^4 - 2*x^3 + x^2)*e^(9*x) + 2*(2*x^6 - 6*x^5 + 6*x^4 - 2*x^3 - x)*e^(8*x) + (x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4 - 8*x^3 + 8*x^2)*e^(7*x) - 4*(3*x^5 - 6*x^4 + 3*x^3 + x)*e^(6*x) - (8*x^7 - 24*x^6 + 24*x^5 - 8*x^4 + 8*x^3 - 9*x^2)*e^(5*x) - 2*(x^9 - 4*x^8 + 6*x^7 - 4*x^6 + 3*x^5 - 6*x^4 + 4*x^3)*e^(4*x) + 2*(3*x^6 - 6*x^5 + 3*x^4 + 2*x^2)*e^(3 *x) + 4*(x^8 - 3*x^7 + 3*x^6 - x^5 + 2*x^4 - 2*x^3)*e^(2*x) + (x^10 - 4*x^ 9 + 6*x^8 - 4*x^7 + 5*x^6 - 8*x^5 + 4*x^4 + 4*x^2)*e^x + e^(11*x))/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4 + 4*(x^2 - x)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)* e^(2*x) + 4*(x^6 - 3*x^5 + 3*x^4 - x^3)*e^x + e^(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 291 vs. \(2 (24) = 48\).
Time = 0.37 (sec) , antiderivative size = 291, normalized size of antiderivative = 9.70 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=- 12 x^{5} + 24 x^{4} - 12 x^{3} - 2 x e^{4 x} - 4 x e^{2 x} + \left (8 x^{3} - 7 x^{2}\right ) e^{x} + e^{7 x} + \frac {12 x^{13} - 72 x^{12} + 180 x^{11} - 240 x^{10} + 180 x^{9} - 72 x^{8} + 12 x^{7} + \left (16 x^{7} - 48 x^{6} + 48 x^{5} - 16 x^{4} + 4 x^{2}\right ) e^{3 x} + \left (44 x^{9} - 176 x^{8} + 264 x^{7} - 176 x^{6} + 44 x^{5} + 8 x^{4} - 8 x^{3}\right ) e^{2 x} + \left (40 x^{11} - 200 x^{10} + 400 x^{9} - 400 x^{8} + 200 x^{7} - 36 x^{6} - 8 x^{5} + 4 x^{4} + 4 x^{2}\right ) e^{x}}{x^{8} - 4 x^{7} + 6 x^{6} - 4 x^{5} + x^{4} + \left (4 x^{2} - 4 x\right ) e^{3 x} + \left (6 x^{4} - 12 x^{3} + 6 x^{2}\right ) e^{2 x} + \left (4 x^{6} - 12 x^{5} + 12 x^{4} - 4 x^{3}\right ) e^{x} + e^{4 x}} \]
integrate(((7*exp(x)**6+(35*x**2-35*x)*exp(x)**5+(70*x**4-140*x**3+70*x**2 )*exp(x)**4+(70*x**6-210*x**5+210*x**4-70*x**3)*exp(x)**3+(35*x**8-140*x** 7+210*x**6-140*x**5+35*x**4)*exp(x)**2+(7*x**10-35*x**9+70*x**8-70*x**7+35 *x**6-7*x**5)*exp(x))*exp(3*x)**2+((-8*x-2)*exp(x)**6+(-40*x**3+30*x**2+10 *x)*exp(x)**5+(-80*x**5+140*x**4-40*x**3-20*x**2-8*x-4)*exp(x)**4+(-80*x** 7+220*x**6-180*x**5+20*x**4-12*x**3+36*x**2+4*x)*exp(x)**3+(-40*x**9+150*x **8-200*x**7+100*x**6-40*x**5+90*x**4-64*x**3+4*x**2)*exp(x)**2+(-8*x**11+ 38*x**10-70*x**9+60*x**8-36*x**7+58*x**6-74*x**5+36*x**4-4*x**3)*exp(x))*e xp(3*x)+(x**2+2*x)*exp(x)**6+(5*x**4+5*x**3-10*x**2)*exp(x)**5+(10*x**6-30 *x**4+20*x**3-4*x**2+8*x)*exp(x)**4+(10*x**8-10*x**7-30*x**6+50*x**5-24*x* *4+12*x**3-16*x**2)*exp(x)**3+(5*x**10-10*x**9-10*x**8+40*x**7-31*x**6-6*x **5+4*x**4+8*x**3-12*x**2+8*x)*exp(x)**2+(x**12-3*x**11+10*x**9-11*x**8-11 *x**7+26*x**6-12*x**5+4*x**4-28*x**3+8*x**2)*exp(x))/(exp(x)**5+(5*x**2-5* x)*exp(x)**4+(10*x**4-20*x**3+10*x**2)*exp(x)**3+(10*x**6-30*x**5+30*x**4- 10*x**3)*exp(x)**2+(5*x**8-20*x**7+30*x**6-20*x**5+5*x**4)*exp(x)+x**10-5* x**9+10*x**8-10*x**7+5*x**6-x**5),x)
-12*x**5 + 24*x**4 - 12*x**3 - 2*x*exp(4*x) - 4*x*exp(2*x) + (8*x**3 - 7*x **2)*exp(x) + exp(7*x) + (12*x**13 - 72*x**12 + 180*x**11 - 240*x**10 + 18 0*x**9 - 72*x**8 + 12*x**7 + (16*x**7 - 48*x**6 + 48*x**5 - 16*x**4 + 4*x* *2)*exp(3*x) + (44*x**9 - 176*x**8 + 264*x**7 - 176*x**6 + 44*x**5 + 8*x** 4 - 8*x**3)*exp(2*x) + (40*x**11 - 200*x**10 + 400*x**9 - 400*x**8 + 200*x **7 - 36*x**6 - 8*x**5 + 4*x**4 + 4*x**2)*exp(x))/(x**8 - 4*x**7 + 6*x**6 - 4*x**5 + x**4 + (4*x**2 - 4*x)*exp(3*x) + (6*x**4 - 12*x**3 + 6*x**2)*ex p(2*x) + (4*x**6 - 12*x**5 + 12*x**4 - 4*x**3)*exp(x) + exp(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 390 vs. \(2 (27) = 54\).
Time = 0.37 (sec) , antiderivative size = 390, normalized size of antiderivative = 13.00 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=\frac {4 \, {\left (x^{2} - x\right )} e^{\left (10 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (9 \, x\right )} + 2 \, {\left (2 \, x^{6} - 6 \, x^{5} + 6 \, x^{4} - 2 \, x^{3} - x\right )} e^{\left (8 \, x\right )} + {\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} - 8 \, x^{3} + 8 \, x^{2}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (3 \, x^{5} - 6 \, x^{4} + 3 \, x^{3} + x\right )} e^{\left (6 \, x\right )} - {\left (8 \, x^{7} - 24 \, x^{6} + 24 \, x^{5} - 8 \, x^{4} + 8 \, x^{3} - 9 \, x^{2}\right )} e^{\left (5 \, x\right )} - 2 \, {\left (x^{9} - 4 \, x^{8} + 6 \, x^{7} - 4 \, x^{6} + 3 \, x^{5} - 6 \, x^{4} + 4 \, x^{3}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (3 \, x^{6} - 6 \, x^{5} + 3 \, x^{4} + 2 \, x^{2}\right )} e^{\left (3 \, x\right )} + 4 \, {\left (x^{8} - 3 \, x^{7} + 3 \, x^{6} - x^{5} + 2 \, x^{4} - 2 \, x^{3}\right )} e^{\left (2 \, x\right )} + {\left (x^{10} - 4 \, x^{9} + 6 \, x^{8} - 4 \, x^{7} + 5 \, x^{6} - 8 \, x^{5} + 4 \, x^{4} + 4 \, x^{2}\right )} e^{x} + e^{\left (11 \, x\right )}}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4} + 4 \, {\left (x^{2} - x\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} + 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{x} + e^{\left (4 \, x\right )}} \]
integrate(((7*exp(x)^6+(35*x^2-35*x)*exp(x)^5+(70*x^4-140*x^3+70*x^2)*exp( x)^4+(70*x^6-210*x^5+210*x^4-70*x^3)*exp(x)^3+(35*x^8-140*x^7+210*x^6-140* x^5+35*x^4)*exp(x)^2+(7*x^10-35*x^9+70*x^8-70*x^7+35*x^6-7*x^5)*exp(x))*ex p(3*x)^2+((-8*x-2)*exp(x)^6+(-40*x^3+30*x^2+10*x)*exp(x)^5+(-80*x^5+140*x^ 4-40*x^3-20*x^2-8*x-4)*exp(x)^4+(-80*x^7+220*x^6-180*x^5+20*x^4-12*x^3+36* x^2+4*x)*exp(x)^3+(-40*x^9+150*x^8-200*x^7+100*x^6-40*x^5+90*x^4-64*x^3+4* x^2)*exp(x)^2+(-8*x^11+38*x^10-70*x^9+60*x^8-36*x^7+58*x^6-74*x^5+36*x^4-4 *x^3)*exp(x))*exp(3*x)+(x^2+2*x)*exp(x)^6+(5*x^4+5*x^3-10*x^2)*exp(x)^5+(1 0*x^6-30*x^4+20*x^3-4*x^2+8*x)*exp(x)^4+(10*x^8-10*x^7-30*x^6+50*x^5-24*x^ 4+12*x^3-16*x^2)*exp(x)^3+(5*x^10-10*x^9-10*x^8+40*x^7-31*x^6-6*x^5+4*x^4+ 8*x^3-12*x^2+8*x)*exp(x)^2+(x^12-3*x^11+10*x^9-11*x^8-11*x^7+26*x^6-12*x^5 +4*x^4-28*x^3+8*x^2)*exp(x))/(exp(x)^5+(5*x^2-5*x)*exp(x)^4+(10*x^4-20*x^3 +10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(5*x^8-20*x^7+30* x^6-20*x^5+5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm= \
(4*(x^2 - x)*e^(10*x) + 6*(x^4 - 2*x^3 + x^2)*e^(9*x) + 2*(2*x^6 - 6*x^5 + 6*x^4 - 2*x^3 - x)*e^(8*x) + (x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4 - 8*x^3 + 8*x^2)*e^(7*x) - 4*(3*x^5 - 6*x^4 + 3*x^3 + x)*e^(6*x) - (8*x^7 - 24*x^6 + 24*x^5 - 8*x^4 + 8*x^3 - 9*x^2)*e^(5*x) - 2*(x^9 - 4*x^8 + 6*x^7 - 4*x^6 + 3*x^5 - 6*x^4 + 4*x^3)*e^(4*x) + 2*(3*x^6 - 6*x^5 + 3*x^4 + 2*x^2)*e^(3 *x) + 4*(x^8 - 3*x^7 + 3*x^6 - x^5 + 2*x^4 - 2*x^3)*e^(2*x) + (x^10 - 4*x^ 9 + 6*x^8 - 4*x^7 + 5*x^6 - 8*x^5 + 4*x^4 + 4*x^2)*e^x + e^(11*x))/(x^8 - 4*x^7 + 6*x^6 - 4*x^5 + x^4 + 4*(x^2 - x)*e^(3*x) + 6*(x^4 - 2*x^3 + x^2)* e^(2*x) + 4*(x^6 - 3*x^5 + 3*x^4 - x^3)*e^x + e^(4*x))
Leaf count of result is larger than twice the leaf count of optimal. 548 vs. \(2 (27) = 54\).
Time = 0.55 (sec) , antiderivative size = 548, normalized size of antiderivative = 18.27 \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx =\text {Too large to display} \]
integrate(((7*exp(x)^6+(35*x^2-35*x)*exp(x)^5+(70*x^4-140*x^3+70*x^2)*exp( x)^4+(70*x^6-210*x^5+210*x^4-70*x^3)*exp(x)^3+(35*x^8-140*x^7+210*x^6-140* x^5+35*x^4)*exp(x)^2+(7*x^10-35*x^9+70*x^8-70*x^7+35*x^6-7*x^5)*exp(x))*ex p(3*x)^2+((-8*x-2)*exp(x)^6+(-40*x^3+30*x^2+10*x)*exp(x)^5+(-80*x^5+140*x^ 4-40*x^3-20*x^2-8*x-4)*exp(x)^4+(-80*x^7+220*x^6-180*x^5+20*x^4-12*x^3+36* x^2+4*x)*exp(x)^3+(-40*x^9+150*x^8-200*x^7+100*x^6-40*x^5+90*x^4-64*x^3+4* x^2)*exp(x)^2+(-8*x^11+38*x^10-70*x^9+60*x^8-36*x^7+58*x^6-74*x^5+36*x^4-4 *x^3)*exp(x))*exp(3*x)+(x^2+2*x)*exp(x)^6+(5*x^4+5*x^3-10*x^2)*exp(x)^5+(1 0*x^6-30*x^4+20*x^3-4*x^2+8*x)*exp(x)^4+(10*x^8-10*x^7-30*x^6+50*x^5-24*x^ 4+12*x^3-16*x^2)*exp(x)^3+(5*x^10-10*x^9-10*x^8+40*x^7-31*x^6-6*x^5+4*x^4+ 8*x^3-12*x^2+8*x)*exp(x)^2+(x^12-3*x^11+10*x^9-11*x^8-11*x^7+26*x^6-12*x^5 +4*x^4-28*x^3+8*x^2)*exp(x))/(exp(x)^5+(5*x^2-5*x)*exp(x)^4+(10*x^4-20*x^3 +10*x^2)*exp(x)^3+(10*x^6-30*x^5+30*x^4-10*x^3)*exp(x)^2+(5*x^8-20*x^7+30* x^6-20*x^5+5*x^4)*exp(x)+x^10-5*x^9+10*x^8-10*x^7+5*x^6-x^5),x, algorithm= \
(x^10*e^x - 2*x^9*e^(4*x) - 4*x^9*e^x + x^8*e^(7*x) + 8*x^8*e^(4*x) + 4*x^ 8*e^(2*x) + 6*x^8*e^x - 4*x^7*e^(7*x) - 8*x^7*e^(5*x) - 12*x^7*e^(4*x) - 1 2*x^7*e^(2*x) - 4*x^7*e^x + 4*x^6*e^(8*x) + 6*x^6*e^(7*x) + 24*x^6*e^(5*x) + 8*x^6*e^(4*x) + 6*x^6*e^(3*x) + 12*x^6*e^(2*x) + 5*x^6*e^x - 12*x^5*e^( 8*x) - 4*x^5*e^(7*x) - 12*x^5*e^(6*x) - 24*x^5*e^(5*x) - 6*x^5*e^(4*x) - 1 2*x^5*e^(3*x) - 4*x^5*e^(2*x) - 8*x^5*e^x + 6*x^4*e^(9*x) + 12*x^4*e^(8*x) + x^4*e^(7*x) + 24*x^4*e^(6*x) + 8*x^4*e^(5*x) + 12*x^4*e^(4*x) + 6*x^4*e ^(3*x) + 8*x^4*e^(2*x) + 4*x^4*e^x - 12*x^3*e^(9*x) - 4*x^3*e^(8*x) - 8*x^ 3*e^(7*x) - 12*x^3*e^(6*x) - 8*x^3*e^(5*x) - 8*x^3*e^(4*x) - 8*x^3*e^(2*x) + 4*x^2*e^(10*x) + 6*x^2*e^(9*x) + 8*x^2*e^(7*x) + 9*x^2*e^(5*x) + 4*x^2* e^(3*x) + 4*x^2*e^x - 4*x*e^(10*x) - 2*x*e^(8*x) - 4*x*e^(6*x) + e^(11*x)) /(x^8 - 4*x^7 + 4*x^6*e^x + 6*x^6 - 12*x^5*e^x - 4*x^5 + 6*x^4*e^(2*x) + 1 2*x^4*e^x + x^4 - 12*x^3*e^(2*x) - 4*x^3*e^x + 4*x^2*e^(3*x) + 6*x^2*e^(2* x) - 4*x*e^(3*x) + e^(4*x))
Timed out. \[ \int \frac {e^{6 x} \left (2 x+x^2\right )+e^{5 x} \left (-10 x^2+5 x^3+5 x^4\right )+e^{4 x} \left (8 x-4 x^2+20 x^3-30 x^4+10 x^6\right )+e^{3 x} \left (-16 x^2+12 x^3-24 x^4+50 x^5-30 x^6-10 x^7+10 x^8\right )+e^{2 x} \left (8 x-12 x^2+8 x^3+4 x^4-6 x^5-31 x^6+40 x^7-10 x^8-10 x^9+5 x^{10}\right )+e^x \left (8 x^2-28 x^3+4 x^4-12 x^5+26 x^6-11 x^7-11 x^8+10 x^9-3 x^{11}+x^{12}\right )+e^{6 x} \left (7 e^{6 x}+e^{5 x} \left (-35 x+35 x^2\right )+e^{4 x} \left (70 x^2-140 x^3+70 x^4\right )+e^{3 x} \left (-70 x^3+210 x^4-210 x^5+70 x^6\right )+e^{2 x} \left (35 x^4-140 x^5+210 x^6-140 x^7+35 x^8\right )+e^x \left (-7 x^5+35 x^6-70 x^7+70 x^8-35 x^9+7 x^{10}\right )\right )+e^{3 x} \left (e^{6 x} (-2-8 x)+e^{5 x} \left (10 x+30 x^2-40 x^3\right )+e^{4 x} \left (-4-8 x-20 x^2-40 x^3+140 x^4-80 x^5\right )+e^{3 x} \left (4 x+36 x^2-12 x^3+20 x^4-180 x^5+220 x^6-80 x^7\right )+e^{2 x} \left (4 x^2-64 x^3+90 x^4-40 x^5+100 x^6-200 x^7+150 x^8-40 x^9\right )+e^x \left (-4 x^3+36 x^4-74 x^5+58 x^6-36 x^7+60 x^8-70 x^9+38 x^{10}-8 x^{11}\right )\right )}{e^{5 x}-x^5+5 x^6-10 x^7+10 x^8-5 x^9+x^{10}+e^{4 x} \left (-5 x+5 x^2\right )+e^{3 x} \left (10 x^2-20 x^3+10 x^4\right )+e^{2 x} \left (-10 x^3+30 x^4-30 x^5+10 x^6\right )+e^x \left (5 x^4-20 x^5+30 x^6-20 x^7+5 x^8\right )} \, dx=\int \frac {{\mathrm {e}}^{6\,x}\,\left (7\,{\mathrm {e}}^{6\,x}-{\mathrm {e}}^{5\,x}\,\left (35\,x-35\,x^2\right )+{\mathrm {e}}^{2\,x}\,\left (35\,x^8-140\,x^7+210\,x^6-140\,x^5+35\,x^4\right )+{\mathrm {e}}^{4\,x}\,\left (70\,x^4-140\,x^3+70\,x^2\right )-{\mathrm {e}}^{3\,x}\,\left (-70\,x^6+210\,x^5-210\,x^4+70\,x^3\right )-{\mathrm {e}}^x\,\left (-7\,x^{10}+35\,x^9-70\,x^8+70\,x^7-35\,x^6+7\,x^5\right )\right )+{\mathrm {e}}^{3\,x}\,\left ({\mathrm {e}}^{3\,x}\,\left (-80\,x^7+220\,x^6-180\,x^5+20\,x^4-12\,x^3+36\,x^2+4\,x\right )+{\mathrm {e}}^{5\,x}\,\left (-40\,x^3+30\,x^2+10\,x\right )-{\mathrm {e}}^x\,\left (8\,x^{11}-38\,x^{10}+70\,x^9-60\,x^8+36\,x^7-58\,x^6+74\,x^5-36\,x^4+4\,x^3\right )-{\mathrm {e}}^{4\,x}\,\left (80\,x^5-140\,x^4+40\,x^3+20\,x^2+8\,x+4\right )+{\mathrm {e}}^{2\,x}\,\left (-40\,x^9+150\,x^8-200\,x^7+100\,x^6-40\,x^5+90\,x^4-64\,x^3+4\,x^2\right )-{\mathrm {e}}^{6\,x}\,\left (8\,x+2\right )\right )+{\mathrm {e}}^x\,\left (x^{12}-3\,x^{11}+10\,x^9-11\,x^8-11\,x^7+26\,x^6-12\,x^5+4\,x^4-28\,x^3+8\,x^2\right )-{\mathrm {e}}^{3\,x}\,\left (-10\,x^8+10\,x^7+30\,x^6-50\,x^5+24\,x^4-12\,x^3+16\,x^2\right )+{\mathrm {e}}^{5\,x}\,\left (5\,x^4+5\,x^3-10\,x^2\right )+{\mathrm {e}}^{6\,x}\,\left (x^2+2\,x\right )+{\mathrm {e}}^{4\,x}\,\left (10\,x^6-30\,x^4+20\,x^3-4\,x^2+8\,x\right )+{\mathrm {e}}^{2\,x}\,\left (5\,x^{10}-10\,x^9-10\,x^8+40\,x^7-31\,x^6-6\,x^5+4\,x^4+8\,x^3-12\,x^2+8\,x\right )}{{\mathrm {e}}^{5\,x}-{\mathrm {e}}^{4\,x}\,\left (5\,x-5\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (10\,x^4-20\,x^3+10\,x^2\right )+{\mathrm {e}}^x\,\left (5\,x^8-20\,x^7+30\,x^6-20\,x^5+5\,x^4\right )-{\mathrm {e}}^{2\,x}\,\left (-10\,x^6+30\,x^5-30\,x^4+10\,x^3\right )-x^5+5\,x^6-10\,x^7+10\,x^8-5\,x^9+x^{10}} \,d x \]
int((exp(6*x)*(7*exp(6*x) - exp(5*x)*(35*x - 35*x^2) + exp(2*x)*(35*x^4 - 140*x^5 + 210*x^6 - 140*x^7 + 35*x^8) + exp(4*x)*(70*x^2 - 140*x^3 + 70*x^ 4) - exp(3*x)*(70*x^3 - 210*x^4 + 210*x^5 - 70*x^6) - exp(x)*(7*x^5 - 35*x ^6 + 70*x^7 - 70*x^8 + 35*x^9 - 7*x^10)) + exp(3*x)*(exp(3*x)*(4*x + 36*x^ 2 - 12*x^3 + 20*x^4 - 180*x^5 + 220*x^6 - 80*x^7) + exp(5*x)*(10*x + 30*x^ 2 - 40*x^3) - exp(x)*(4*x^3 - 36*x^4 + 74*x^5 - 58*x^6 + 36*x^7 - 60*x^8 + 70*x^9 - 38*x^10 + 8*x^11) - exp(4*x)*(8*x + 20*x^2 + 40*x^3 - 140*x^4 + 80*x^5 + 4) + exp(2*x)*(4*x^2 - 64*x^3 + 90*x^4 - 40*x^5 + 100*x^6 - 200*x ^7 + 150*x^8 - 40*x^9) - exp(6*x)*(8*x + 2)) + exp(x)*(8*x^2 - 28*x^3 + 4* x^4 - 12*x^5 + 26*x^6 - 11*x^7 - 11*x^8 + 10*x^9 - 3*x^11 + x^12) - exp(3* x)*(16*x^2 - 12*x^3 + 24*x^4 - 50*x^5 + 30*x^6 + 10*x^7 - 10*x^8) + exp(5* x)*(5*x^3 - 10*x^2 + 5*x^4) + exp(6*x)*(2*x + x^2) + exp(4*x)*(8*x - 4*x^2 + 20*x^3 - 30*x^4 + 10*x^6) + exp(2*x)*(8*x - 12*x^2 + 8*x^3 + 4*x^4 - 6* x^5 - 31*x^6 + 40*x^7 - 10*x^8 - 10*x^9 + 5*x^10))/(exp(5*x) - exp(4*x)*(5 *x - 5*x^2) + exp(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + exp(x)*(5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8) - exp(2*x)*(10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) - x^5 + 5*x^6 - 10*x^7 + 10*x^8 - 5*x^9 + x^10),x)
int((exp(6*x)*(7*exp(6*x) - exp(5*x)*(35*x - 35*x^2) + exp(2*x)*(35*x^4 - 140*x^5 + 210*x^6 - 140*x^7 + 35*x^8) + exp(4*x)*(70*x^2 - 140*x^3 + 70*x^ 4) - exp(3*x)*(70*x^3 - 210*x^4 + 210*x^5 - 70*x^6) - exp(x)*(7*x^5 - 35*x ^6 + 70*x^7 - 70*x^8 + 35*x^9 - 7*x^10)) + exp(3*x)*(exp(3*x)*(4*x + 36*x^ 2 - 12*x^3 + 20*x^4 - 180*x^5 + 220*x^6 - 80*x^7) + exp(5*x)*(10*x + 30*x^ 2 - 40*x^3) - exp(x)*(4*x^3 - 36*x^4 + 74*x^5 - 58*x^6 + 36*x^7 - 60*x^8 + 70*x^9 - 38*x^10 + 8*x^11) - exp(4*x)*(8*x + 20*x^2 + 40*x^3 - 140*x^4 + 80*x^5 + 4) + exp(2*x)*(4*x^2 - 64*x^3 + 90*x^4 - 40*x^5 + 100*x^6 - 200*x ^7 + 150*x^8 - 40*x^9) - exp(6*x)*(8*x + 2)) + exp(x)*(8*x^2 - 28*x^3 + 4* x^4 - 12*x^5 + 26*x^6 - 11*x^7 - 11*x^8 + 10*x^9 - 3*x^11 + x^12) - exp(3* x)*(16*x^2 - 12*x^3 + 24*x^4 - 50*x^5 + 30*x^6 + 10*x^7 - 10*x^8) + exp(5* x)*(5*x^3 - 10*x^2 + 5*x^4) + exp(6*x)*(2*x + x^2) + exp(4*x)*(8*x - 4*x^2 + 20*x^3 - 30*x^4 + 10*x^6) + exp(2*x)*(8*x - 12*x^2 + 8*x^3 + 4*x^4 - 6* x^5 - 31*x^6 + 40*x^7 - 10*x^8 - 10*x^9 + 5*x^10))/(exp(5*x) - exp(4*x)*(5 *x - 5*x^2) + exp(3*x)*(10*x^2 - 20*x^3 + 10*x^4) + exp(x)*(5*x^4 - 20*x^5 + 30*x^6 - 20*x^7 + 5*x^8) - exp(2*x)*(10*x^3 - 30*x^4 + 30*x^5 - 10*x^6) - x^5 + 5*x^6 - 10*x^7 + 10*x^8 - 5*x^9 + x^10), x)