Integrand size = 564, antiderivative size = 36 \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=x^2 \left (-\frac {x}{80}+\frac {3}{e^x+x}+\frac {4}{-e^{5 (2+x)}+x}\right )^2 \]
Time = 10.58 (sec) , antiderivative size = 70, normalized size of antiderivative = 1.94 \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\frac {x^2 \left (e^{10+6 x} x-x \left (-560+x^2\right )-e^x \left (-320+x^2\right )+e^{5 (2+x)} \left (-240+x^2\right )\right )^2}{6400 \left (e^{5 (2+x)}-x\right )^2 \left (e^x+x\right )^2} \]
Integrate[(560*x^7 - x^9 + E^(3*x)*(320*x^4 - x^6) + E^(2*x)*(-38400*x^3 + 38400*x^4 + 1320*x^5 - 120*x^6 - 3*x^7) + E^x*(-67200*x^4 + 67200*x^5 + 1 560*x^6 - 120*x^7 - 3*x^8) + E^(30 + 15*x)*(E^(3*x)*x^3 - 240*x^4 + x^6 + E^(2*x)*(-360*x^2 + 120*x^3 + 3*x^4) + E^x*(28800*x - 28800*x^2 - 600*x^3 + 120*x^4 + 3*x^5)) + E^(20 + 10*x)*(-38400*x^3 + 192000*x^4 + 1200*x^5 - 800*x^6 - 3*x^7 + E^(3*x)*(480*x^2 - 800*x^3 - 3*x^4) + E^(2*x)*(-76800*x + 230400*x^2 + 2520*x^3 - 2760*x^4 - 9*x^5) + E^x*(-201600*x^2 + 508800*x^ 3 + 3240*x^4 - 2760*x^5 - 9*x^6)) + E^(10 + 5*x)*(89600*x^4 - 448000*x^5 - 1520*x^6 + 800*x^7 + 3*x^8 + E^(3*x)*(51200*x - 256000*x^2 - 800*x^3 + 80 0*x^4 + 3*x^5) + E^(2*x)*(268800*x^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6) + E^x*(393600*x^3 - 1315200*x^4 - 4200*x^5 + 2760*x^6 + 9*x^7)))/( -1600*E^(3*x)*x^3 - 4800*E^(2*x)*x^4 - 4800*E^x*x^5 - 1600*x^6 + E^(30 + 1 5*x)*(1600*E^(3*x) + 4800*E^(2*x)*x + 4800*E^x*x^2 + 1600*x^3) + E^(20 + 1 0*x)*(-4800*E^(3*x)*x - 14400*E^(2*x)*x^2 - 14400*E^x*x^3 - 4800*x^4) + E^ (10 + 5*x)*(4800*E^(3*x)*x^2 + 14400*E^(2*x)*x^3 + 14400*E^x*x^4 + 4800*x^ 5)),x]
(x^2*(E^(10 + 6*x)*x - x*(-560 + x^2) - E^x*(-320 + x^2) + E^(5*(2 + x))*( -240 + x^2))^2)/(6400*(E^(5*(2 + x)) - x)^2*(E^x + x)^2)
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.
| \(\displaystyle \int \frac {-x^9+560 x^7+e^{3 x} \left (320 x^4-x^6\right )+e^x \left (-3 x^8-120 x^7+1560 x^6+67200 x^5-67200 x^4\right )+e^{2 x} \left (-3 x^7-120 x^6+1320 x^5+38400 x^4-38400 x^3\right )+e^{15 x+30} \left (x^6-240 x^4+e^{3 x} x^3+e^{2 x} \left (3 x^4+120 x^3-360 x^2\right )+e^x \left (3 x^5+120 x^4-600 x^3-28800 x^2+28800 x\right )\right )+e^{10 x+20} \left (-3 x^7-800 x^6+1200 x^5+192000 x^4-38400 x^3+e^{3 x} \left (-3 x^4-800 x^3+480 x^2\right )+e^{2 x} \left (-9 x^5-2760 x^4+2520 x^3+230400 x^2-76800 x\right )+e^x \left (-9 x^6-2760 x^5+3240 x^4+508800 x^3-201600 x^2\right )\right )+e^{5 x+10} \left (3 x^8+800 x^7-1520 x^6-448000 x^5+89600 x^4+e^{3 x} \left (3 x^5+800 x^4-800 x^3-256000 x^2+51200 x\right )+e^x \left (9 x^7+2760 x^6-4200 x^5-1315200 x^4+393600 x^3\right )+e^{2 x} \left (9 x^6+2760 x^5-3480 x^4-1036800 x^3+268800 x^2\right )\right )}{-1600 x^6-4800 e^x x^5-4800 e^{2 x} x^4-1600 e^{3 x} x^3+e^{15 x+30} \left (1600 x^3+4800 e^x x^2+4800 e^{2 x} x+1600 e^{3 x}\right )+e^{10 x+20} \left (-4800 x^4-14400 e^x x^3-14400 e^{2 x} x^2-4800 e^{3 x} x\right )+e^{5 x+10} \left (4800 x^5+14400 e^x x^4+14400 e^{2 x} x^3+4800 e^{3 x} x^2\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-x^9+560 x^7+e^{3 x} \left (320 x^4-x^6\right )+e^x \left (-3 x^8-120 x^7+1560 x^6+67200 x^5-67200 x^4\right )+e^{2 x} \left (-3 x^7-120 x^6+1320 x^5+38400 x^4-38400 x^3\right )+e^{15 x+30} \left (x^6-240 x^4+e^{3 x} x^3+e^{2 x} \left (3 x^4+120 x^3-360 x^2\right )+e^x \left (3 x^5+120 x^4-600 x^3-28800 x^2+28800 x\right )\right )+e^{10 x+20} \left (-3 x^7-800 x^6+1200 x^5+192000 x^4-38400 x^3+e^{3 x} \left (-3 x^4-800 x^3+480 x^2\right )+e^{2 x} \left (-9 x^5-2760 x^4+2520 x^3+230400 x^2-76800 x\right )+e^x \left (-9 x^6-2760 x^5+3240 x^4+508800 x^3-201600 x^2\right )\right )+e^{5 x+10} \left (3 x^8+800 x^7-1520 x^6-448000 x^5+89600 x^4+e^{3 x} \left (3 x^5+800 x^4-800 x^3-256000 x^2+51200 x\right )+e^x \left (9 x^7+2760 x^6-4200 x^5-1315200 x^4+393600 x^3\right )+e^{2 x} \left (9 x^6+2760 x^5-3480 x^4-1036800 x^3+268800 x^2\right )\right )}{1600 \left (e^{5 x+10}-x\right )^3 \left (x+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {-x^9+560 x^7+e^{3 x} \left (320 x^4-x^6\right )-3 e^{2 x} \left (x^7+40 x^6-440 x^5-12800 x^4+12800 x^3\right )-3 e^x \left (x^8+40 x^7-520 x^6-22400 x^5+22400 x^4\right )+e^{15 x+30} \left (x^6-240 x^4+e^{3 x} x^3-3 e^{2 x} \left (-x^4-40 x^3+120 x^2\right )+3 e^x \left (x^5+40 x^4-200 x^3-9600 x^2+9600 x\right )\right )-e^{10 x+20} \left (3 x^7+800 x^6-1200 x^5-192000 x^4+38400 x^3-e^{3 x} \left (-3 x^4-800 x^3+480 x^2\right )+3 e^{2 x} \left (3 x^5+920 x^4-840 x^3-76800 x^2+25600 x\right )+3 e^x \left (3 x^6+920 x^5-1080 x^4-169600 x^3+67200 x^2\right )\right )+e^{5 x+10} \left (3 x^8+800 x^7-1520 x^6-448000 x^5+89600 x^4+e^{3 x} \left (3 x^5+800 x^4-800 x^3-256000 x^2+51200 x\right )+3 e^{2 x} \left (3 x^6+920 x^5-1160 x^4-345600 x^3+89600 x^2\right )+3 e^x \left (3 x^7+920 x^6-1400 x^5-438400 x^4+131200 x^3\right )\right )}{\left (e^{5 x+10}-x\right )^3 \left (x+e^x\right )^3}dx}{1600}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {\int \left (x^3-\frac {51200 (5 x-1) x^2}{\left (e^{5 x+10}-x\right )^3}+\frac {28800 (x-1) x^2}{\left (x+e^x\right )^3}+\frac {160 (5 x-1) \left (-e^{10} x^6-80 e^{10} x^4-240 e^{x+10} x^3+240 e^{2 x+10} x^2-x^2-240 e^{3 x+10} x+240 e^{4 x+10}-320\right ) x}{\left (e^{5 x+10}-x\right )^2 \left (e^{10} x^4+1\right )}-\frac {120 (x-1) \left (e^{10} x^6+240 e^{10} x^4+x^2-80\right ) x}{\left (x+e^x\right )^2 \left (e^{10} x^4+1\right )}+\frac {160 \left (-5 e^{20} x^{11}+3 e^{20} x^{10}+1200 e^{20} x^9-960 e^{x+20} x^8-240 e^{20} x^8+720 e^{2 x+20} x^7-10 e^{10} x^7+240 e^{2 x+20} x^6-480 e^{3 x+20} x^6+6 e^{10} x^6-480 e^{3 x+20} x^5+240 e^{4 x+20} x^5+1200 e^{10} x^5-960 e^{x+10} x^4+720 e^{4 x+20} x^4-1200 e^{10} x^4+960 e^{x+10} x^3+720 e^{2 x+10} x^3-5 x^3-720 e^{2 x+10} x^2-480 e^{3 x+10} x^2+3 x^2+480 e^{3 x+10} x+240 e^{4 x+10} x-240 e^{4 x+10}\right )}{\left (e^{5 x+10}-x\right ) \left (e^{10} x^4+1\right )^2}+\frac {120 \left (e^{20} x^{11}-3 e^{20} x^{10}+2 e^{10} x^7-6 e^{10} x^6-320 e^{10} x^5-960 e^{10} x^4+x^3-3 x^2-320 x+320\right )}{\left (x+e^x\right ) \left (e^{10} x^4+1\right )^2}\right )dx}{1600}\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \frac {\int \left (x^3-\frac {51200 (5 x-1) x^2}{\left (e^{5 x+10}-x\right )^3}+\frac {28800 (x-1) x^2}{\left (x+e^x\right )^3}+\frac {160 (5 x-1) \left (-e^{10} x^6-80 e^{10} x^4-240 e^{x+10} x^3+240 e^{2 x+10} x^2-x^2-240 e^{3 x+10} x+240 e^{4 x+10}-320\right ) x}{\left (e^{5 x+10}-x\right )^2 \left (e^{10} x^4+1\right )}-\frac {120 (x-1) \left (e^{10} x^6+240 e^{10} x^4+x^2-80\right ) x}{\left (x+e^x\right )^2 \left (e^{10} x^4+1\right )}+\frac {160 \left (-5 e^{20} x^{11}+3 e^{20} x^{10}+1200 e^{20} x^9-960 e^{x+20} x^8-240 e^{20} x^8+720 e^{2 x+20} x^7-10 e^{10} x^7+240 e^{2 x+20} x^6-480 e^{3 x+20} x^6+6 e^{10} x^6-480 e^{3 x+20} x^5+240 e^{4 x+20} x^5+1200 e^{10} x^5-960 e^{x+10} x^4+720 e^{4 x+20} x^4-1200 e^{10} x^4+960 e^{x+10} x^3+720 e^{2 x+10} x^3-5 x^3-720 e^{2 x+10} x^2-480 e^{3 x+10} x^2+3 x^2+480 e^{3 x+10} x+240 e^{4 x+10} x-240 e^{4 x+10}\right )}{\left (e^{5 x+10}-x\right ) \left (e^{10} x^4+1\right )^2}+\frac {120 \left (e^{20} x^{11}-3 e^{20} x^{10}+2 e^{10} x^7-6 e^{10} x^6-320 e^{10} x^5-960 e^{10} x^4+x^3-3 x^2-320 x+320\right )}{\left (x+e^x\right ) \left (e^{10} x^4+1\right )^2}\right )dx}{1600}\) |
Int[(560*x^7 - x^9 + E^(3*x)*(320*x^4 - x^6) + E^(2*x)*(-38400*x^3 + 38400 *x^4 + 1320*x^5 - 120*x^6 - 3*x^7) + E^x*(-67200*x^4 + 67200*x^5 + 1560*x^ 6 - 120*x^7 - 3*x^8) + E^(30 + 15*x)*(E^(3*x)*x^3 - 240*x^4 + x^6 + E^(2*x )*(-360*x^2 + 120*x^3 + 3*x^4) + E^x*(28800*x - 28800*x^2 - 600*x^3 + 120* x^4 + 3*x^5)) + E^(20 + 10*x)*(-38400*x^3 + 192000*x^4 + 1200*x^5 - 800*x^ 6 - 3*x^7 + E^(3*x)*(480*x^2 - 800*x^3 - 3*x^4) + E^(2*x)*(-76800*x + 2304 00*x^2 + 2520*x^3 - 2760*x^4 - 9*x^5) + E^x*(-201600*x^2 + 508800*x^3 + 32 40*x^4 - 2760*x^5 - 9*x^6)) + E^(10 + 5*x)*(89600*x^4 - 448000*x^5 - 1520* x^6 + 800*x^7 + 3*x^8 + E^(3*x)*(51200*x - 256000*x^2 - 800*x^3 + 800*x^4 + 3*x^5) + E^(2*x)*(268800*x^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6 ) + E^x*(393600*x^3 - 1315200*x^4 - 4200*x^5 + 2760*x^6 + 9*x^7)))/(-1600* E^(3*x)*x^3 - 4800*E^(2*x)*x^4 - 4800*E^x*x^5 - 1600*x^6 + E^(30 + 15*x)*( 1600*E^(3*x) + 4800*E^(2*x)*x + 4800*E^x*x^2 + 1600*x^3) + E^(20 + 10*x)*( -4800*E^(3*x)*x - 14400*E^(2*x)*x^2 - 14400*E^x*x^3 - 4800*x^4) + E^(10 + 5*x)*(4800*E^(3*x)*x^2 + 14400*E^(2*x)*x^3 + 14400*E^x*x^4 + 4800*x^5)),x]
3.22.16.3.1 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. \(152\) vs. \(2(32)=64\).
Time = 1.42 (sec) , antiderivative size = 153, normalized size of antiderivative = 4.25
| method | result | size |
| risch | \(\frac {x^{4}}{6400}-\frac {x^{2} \left (3 \,{\mathrm e}^{10 x +20} x^{2}+3 x \,{\mathrm e}^{11 x +20}-360 \,{\mathrm e}^{10 x +20}-10 \,{\mathrm e}^{5 x +10} x^{3}-14 x^{2} {\mathrm e}^{6 x +10}-4 x \,{\mathrm e}^{7 x +10}+1680 \,{\mathrm e}^{5 x +10} x +960 \,{\mathrm e}^{6 x +10}+7 x^{4}+11 \,{\mathrm e}^{x} x^{3}+4 \,{\mathrm e}^{2 x} x^{2}-1960 x^{2}-2240 \,{\mathrm e}^{x} x -640 \,{\mathrm e}^{2 x}\right )}{40 \left ({\mathrm e}^{5 x +10} x +{\mathrm e}^{6 x +10}-x^{2}-{\mathrm e}^{x} x \right )^{2}}\) | \(153\) |
| parallelrisch | \(\frac {2 x^{7} {\mathrm e}^{x}-4 \,{\mathrm e}^{x} {\mathrm e}^{5 x +10} x^{6}-76800 \,{\mathrm e}^{2 x} x^{2}-1760 x^{5} {\mathrm e}^{x}+x^{8}+134400 x^{4}-1120 x^{6}+1600 \,{\mathrm e}^{5 x +10} x^{5}+89600 \,{\mathrm e}^{5 x +10} x^{3}-2 \,{\mathrm e}^{5 x +10} x^{7}+2240 \,{\mathrm e}^{x} {\mathrm e}^{5 x +10} x^{4}+563200 \,{\mathrm e}^{x} x^{2} {\mathrm e}^{5 x +10}+2 \,{\mathrm e}^{x} {\mathrm e}^{10 x +20} x^{5}+{\mathrm e}^{10 x +20} x^{6}-480 \,{\mathrm e}^{10 x +20} x^{4}-121600 \,{\mathrm e}^{10 x +20} x^{2}-179200 \,{\mathrm e}^{2 x} {\mathrm e}^{10 x +20}-2 \,{\mathrm e}^{5 x +10} {\mathrm e}^{2 x} x^{5}+{\mathrm e}^{2 x} {\mathrm e}^{10 x +20} x^{4}-480 \,{\mathrm e}^{x} {\mathrm e}^{10 x +20} x^{3}+640 \,{\mathrm e}^{5 x +10} {\mathrm e}^{2 x} x^{3}-358400 \,{\mathrm e}^{x} {\mathrm e}^{10 x +20} x +358400 \,{\mathrm e}^{5 x +10} {\mathrm e}^{2 x} x +{\mathrm e}^{2 x} x^{6}-640 \,{\mathrm e}^{2 x} x^{4}}{6400 x^{4}+12800 \,{\mathrm e}^{x} x^{3}-12800 \,{\mathrm e}^{5 x +10} x^{3}+6400 \,{\mathrm e}^{2 x} x^{2}-25600 \,{\mathrm e}^{x} x^{2} {\mathrm e}^{5 x +10}+6400 \,{\mathrm e}^{10 x +20} x^{2}-12800 \,{\mathrm e}^{5 x +10} {\mathrm e}^{2 x} x +12800 \,{\mathrm e}^{x} {\mathrm e}^{10 x +20} x +6400 \,{\mathrm e}^{2 x} {\mathrm e}^{10 x +20}}\) | \(379\) |
int(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-600*x^3 -28800*x^2+28800*x)*exp(x)+x^6-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x^3+480 *x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x)^2+(-9* x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+1200*x^5 +192000*x^4-38400*x^3)*exp(5*x+10)^2+((3*x^5+800*x^4-800*x^3-256000*x^2+51 200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)*exp(x)^2+ (9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^7-1520 *x^6-448000*x^5+89600*x^4)*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x^7-120 *x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+1560*x^6+67200 *x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+4800*e xp(x)*x^2+1600*x^3)*exp(5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x^2-144 00*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+14400*exp(x)^2*x^ 3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp(x)^2*x ^4-4800*x^5*exp(x)-1600*x^6),x,method=_RETURNVERBOSE)
1/6400*x^4-1/40*x^2*(3*exp(10*x+20)*x^2+3*x*exp(11*x+20)-360*exp(10*x+20)- 10*exp(5*x+10)*x^3-14*x^2*exp(6*x+10)-4*x*exp(7*x+10)+1680*exp(5*x+10)*x+9 60*exp(6*x+10)+7*x^4+11*exp(x)*x^3+4*exp(2*x)*x^2-1960*x^2-2240*exp(x)*x-6 40*exp(2*x))/(exp(5*x+10)*x+exp(6*x+10)-x^2-exp(x)*x)^2
Leaf count of result is larger than twice the leaf count of optimal. 239 vs. \(2 (31) = 62\).
Time = 0.33 (sec) , antiderivative size = 239, normalized size of antiderivative = 6.64 \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\frac {x^{8} - 1120 \, x^{6} + x^{4} e^{\left (12 \, x + 20\right )} + 313600 \, x^{4} + {\left (x^{6} - 640 \, x^{4} + 102400 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{5} - 240 \, x^{3}\right )} e^{\left (11 \, x + 20\right )} + {\left (x^{6} - 480 \, x^{4} + 57600 \, x^{2}\right )} e^{\left (10 \, x + 20\right )} - 2 \, {\left (x^{5} - 320 \, x^{3}\right )} e^{\left (7 \, x + 10\right )} - 4 \, {\left (x^{6} - 560 \, x^{4} + 38400 \, x^{2}\right )} e^{\left (6 \, x + 10\right )} - 2 \, {\left (x^{7} - 800 \, x^{5} + 134400 \, x^{3}\right )} e^{\left (5 \, x + 10\right )} + 2 \, {\left (x^{7} - 880 \, x^{5} + 179200 \, x^{3}\right )} e^{x}}{6400 \, {\left (x^{4} - 2 \, x^{3} e^{\left (5 \, x + 10\right )} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (10 \, x + 20\right )} - 4 \, x^{2} e^{\left (6 \, x + 10\right )} + 2 \, x e^{\left (11 \, x + 20\right )} - 2 \, x e^{\left (7 \, x + 10\right )} + e^{\left (12 \, x + 20\right )}\right )}} \]
integrate(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-6 00*x^3-28800*x^2+28800*x)*exp(x)+x^6-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x ^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x)^ 2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+12 00*x^5+192000*x^4-38400*x^3)*exp(5*x+10)^2+((3*x^5+800*x^4-800*x^3-256000* x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)*exp (x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^ 7-1520*x^6-448000*x^5+89600*x^4)*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x ^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+1560*x^6 +67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+ 4800*exp(x)*x^2+1600*x^3)*exp(5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x ^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+14400*exp(x )^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp( x)^2*x^4-4800*x^5*exp(x)-1600*x^6),x, algorithm=\
1/6400*(x^8 - 1120*x^6 + x^4*e^(12*x + 20) + 313600*x^4 + (x^6 - 640*x^4 + 102400*x^2)*e^(2*x) + 2*(x^5 - 240*x^3)*e^(11*x + 20) + (x^6 - 480*x^4 + 57600*x^2)*e^(10*x + 20) - 2*(x^5 - 320*x^3)*e^(7*x + 10) - 4*(x^6 - 560*x ^4 + 38400*x^2)*e^(6*x + 10) - 2*(x^7 - 800*x^5 + 134400*x^3)*e^(5*x + 10) + 2*(x^7 - 880*x^5 + 179200*x^3)*e^x)/(x^4 - 2*x^3*e^(5*x + 10) + 2*x^3*e ^x + x^2*e^(2*x) + x^2*e^(10*x + 20) - 4*x^2*e^(6*x + 10) + 2*x*e^(11*x + 20) - 2*x*e^(7*x + 10) + e^(12*x + 20))
Timed out. \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\text {Timed out} \]
integrate(((x**3*exp(x)**3+(3*x**4+120*x**3-360*x**2)*exp(x)**2+(3*x**5+12 0*x**4-600*x**3-28800*x**2+28800*x)*exp(x)+x**6-240*x**4)*exp(5*x+10)**3+( (-3*x**4-800*x**3+480*x**2)*exp(x)**3+(-9*x**5-2760*x**4+2520*x**3+230400* x**2-76800*x)*exp(x)**2+(-9*x**6-2760*x**5+3240*x**4+508800*x**3-201600*x* *2)*exp(x)-3*x**7-800*x**6+1200*x**5+192000*x**4-38400*x**3)*exp(5*x+10)** 2+((3*x**5+800*x**4-800*x**3-256000*x**2+51200*x)*exp(x)**3+(9*x**6+2760*x **5-3480*x**4-1036800*x**3+268800*x**2)*exp(x)**2+(9*x**7+2760*x**6-4200*x **5-1315200*x**4+393600*x**3)*exp(x)+3*x**8+800*x**7-1520*x**6-448000*x**5 +89600*x**4)*exp(5*x+10)+(-x**6+320*x**4)*exp(x)**3+(-3*x**7-120*x**6+1320 *x**5+38400*x**4-38400*x**3)*exp(x)**2+(-3*x**8-120*x**7+1560*x**6+67200*x **5-67200*x**4)*exp(x)-x**9+560*x**7)/((1600*exp(x)**3+4800*x*exp(x)**2+48 00*exp(x)*x**2+1600*x**3)*exp(5*x+10)**3+(-4800*x*exp(x)**3-14400*exp(x)** 2*x**2-14400*exp(x)*x**3-4800*x**4)*exp(5*x+10)**2+(4800*x**2*exp(x)**3+14 400*exp(x)**2*x**3+14400*exp(x)*x**4+4800*x**5)*exp(5*x+10)-1600*x**3*exp( x)**3-4800*exp(x)**2*x**4-4800*x**5*exp(x)-1600*x**6),x)
Leaf count of result is larger than twice the leaf count of optimal. 260 vs. \(2 (31) = 62\).
Time = 2.77 (sec) , antiderivative size = 260, normalized size of antiderivative = 7.22 \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\frac {x^{8} - 1120 \, x^{6} + x^{4} e^{\left (12 \, x + 20\right )} + 313600 \, x^{4} + 2 \, {\left (x^{5} e^{20} - 240 \, x^{3} e^{20}\right )} e^{\left (11 \, x\right )} + {\left (x^{6} e^{20} - 480 \, x^{4} e^{20} + 57600 \, x^{2} e^{20}\right )} e^{\left (10 \, x\right )} - 2 \, {\left (x^{5} e^{10} - 320 \, x^{3} e^{10}\right )} e^{\left (7 \, x\right )} - 4 \, {\left (x^{6} e^{10} - 560 \, x^{4} e^{10} + 38400 \, x^{2} e^{10}\right )} e^{\left (6 \, x\right )} - 2 \, {\left (x^{7} e^{10} - 800 \, x^{5} e^{10} + 134400 \, x^{3} e^{10}\right )} e^{\left (5 \, x\right )} + {\left (x^{6} - 640 \, x^{4} + 102400 \, x^{2}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{7} - 880 \, x^{5} + 179200 \, x^{3}\right )} e^{x}}{6400 \, {\left (x^{4} - 2 \, x^{3} e^{\left (5 \, x + 10\right )} + 2 \, x^{3} e^{x} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (10 \, x + 20\right )} - 4 \, x^{2} e^{\left (6 \, x + 10\right )} + 2 \, x e^{\left (11 \, x + 20\right )} - 2 \, x e^{\left (7 \, x + 10\right )} + e^{\left (12 \, x + 20\right )}\right )}} \]
integrate(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-6 00*x^3-28800*x^2+28800*x)*exp(x)+x^6-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x ^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x)^ 2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+12 00*x^5+192000*x^4-38400*x^3)*exp(5*x+10)^2+((3*x^5+800*x^4-800*x^3-256000* x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)*exp (x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^ 7-1520*x^6-448000*x^5+89600*x^4)*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x ^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+1560*x^6 +67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+ 4800*exp(x)*x^2+1600*x^3)*exp(5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x ^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+14400*exp(x )^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp( x)^2*x^4-4800*x^5*exp(x)-1600*x^6),x, algorithm=\
1/6400*(x^8 - 1120*x^6 + x^4*e^(12*x + 20) + 313600*x^4 + 2*(x^5*e^20 - 24 0*x^3*e^20)*e^(11*x) + (x^6*e^20 - 480*x^4*e^20 + 57600*x^2*e^20)*e^(10*x) - 2*(x^5*e^10 - 320*x^3*e^10)*e^(7*x) - 4*(x^6*e^10 - 560*x^4*e^10 + 3840 0*x^2*e^10)*e^(6*x) - 2*(x^7*e^10 - 800*x^5*e^10 + 134400*x^3*e^10)*e^(5*x ) + (x^6 - 640*x^4 + 102400*x^2)*e^(2*x) + 2*(x^7 - 880*x^5 + 179200*x^3)* e^x)/(x^4 - 2*x^3*e^(5*x + 10) + 2*x^3*e^x + x^2*e^(2*x) + x^2*e^(10*x + 2 0) - 4*x^2*e^(6*x + 10) + 2*x*e^(11*x + 20) - 2*x*e^(7*x + 10) + e^(12*x + 20))
Timed out. \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\text {Timed out} \]
integrate(((x^3*exp(x)^3+(3*x^4+120*x^3-360*x^2)*exp(x)^2+(3*x^5+120*x^4-6 00*x^3-28800*x^2+28800*x)*exp(x)+x^6-240*x^4)*exp(5*x+10)^3+((-3*x^4-800*x ^3+480*x^2)*exp(x)^3+(-9*x^5-2760*x^4+2520*x^3+230400*x^2-76800*x)*exp(x)^ 2+(-9*x^6-2760*x^5+3240*x^4+508800*x^3-201600*x^2)*exp(x)-3*x^7-800*x^6+12 00*x^5+192000*x^4-38400*x^3)*exp(5*x+10)^2+((3*x^5+800*x^4-800*x^3-256000* x^2+51200*x)*exp(x)^3+(9*x^6+2760*x^5-3480*x^4-1036800*x^3+268800*x^2)*exp (x)^2+(9*x^7+2760*x^6-4200*x^5-1315200*x^4+393600*x^3)*exp(x)+3*x^8+800*x^ 7-1520*x^6-448000*x^5+89600*x^4)*exp(5*x+10)+(-x^6+320*x^4)*exp(x)^3+(-3*x ^7-120*x^6+1320*x^5+38400*x^4-38400*x^3)*exp(x)^2+(-3*x^8-120*x^7+1560*x^6 +67200*x^5-67200*x^4)*exp(x)-x^9+560*x^7)/((1600*exp(x)^3+4800*x*exp(x)^2+ 4800*exp(x)*x^2+1600*x^3)*exp(5*x+10)^3+(-4800*x*exp(x)^3-14400*exp(x)^2*x ^2-14400*exp(x)*x^3-4800*x^4)*exp(5*x+10)^2+(4800*x^2*exp(x)^3+14400*exp(x )^2*x^3+14400*exp(x)*x^4+4800*x^5)*exp(5*x+10)-1600*x^3*exp(x)^3-4800*exp( x)^2*x^4-4800*x^5*exp(x)-1600*x^6),x, algorithm=\
Time = 14.47 (sec) , antiderivative size = 2084, normalized size of antiderivative = 57.89 \[ \int \frac {560 x^7-x^9+e^{3 x} \left (320 x^4-x^6\right )+e^{2 x} \left (-38400 x^3+38400 x^4+1320 x^5-120 x^6-3 x^7\right )+e^x \left (-67200 x^4+67200 x^5+1560 x^6-120 x^7-3 x^8\right )+e^{30+15 x} \left (e^{3 x} x^3-240 x^4+x^6+e^{2 x} \left (-360 x^2+120 x^3+3 x^4\right )+e^x \left (28800 x-28800 x^2-600 x^3+120 x^4+3 x^5\right )\right )+e^{20+10 x} \left (-38400 x^3+192000 x^4+1200 x^5-800 x^6-3 x^7+e^{3 x} \left (480 x^2-800 x^3-3 x^4\right )+e^{2 x} \left (-76800 x+230400 x^2+2520 x^3-2760 x^4-9 x^5\right )+e^x \left (-201600 x^2+508800 x^3+3240 x^4-2760 x^5-9 x^6\right )\right )+e^{10+5 x} \left (89600 x^4-448000 x^5-1520 x^6+800 x^7+3 x^8+e^{3 x} \left (51200 x-256000 x^2-800 x^3+800 x^4+3 x^5\right )+e^{2 x} \left (268800 x^2-1036800 x^3-3480 x^4+2760 x^5+9 x^6\right )+e^x \left (393600 x^3-1315200 x^4-4200 x^5+2760 x^6+9 x^7\right )\right )}{-1600 e^{3 x} x^3-4800 e^{2 x} x^4-4800 e^x x^5-1600 x^6+e^{30+15 x} \left (1600 e^{3 x}+4800 e^{2 x} x+4800 e^x x^2+1600 x^3\right )+e^{20+10 x} \left (-4800 e^{3 x} x-14400 e^{2 x} x^2-14400 e^x x^3-4800 x^4\right )+e^{10+5 x} \left (4800 e^{3 x} x^2+14400 e^{2 x} x^3+14400 e^x x^4+4800 x^5\right )} \, dx=\text {Too large to display} \]
int((exp(2*x)*(38400*x^3 - 38400*x^4 - 1320*x^5 + 120*x^6 + 3*x^7) - exp(3 *x)*(320*x^4 - x^6) + exp(10*x + 20)*(exp(3*x)*(800*x^3 - 480*x^2 + 3*x^4) + exp(2*x)*(76800*x - 230400*x^2 - 2520*x^3 + 2760*x^4 + 9*x^5) + exp(x)* (201600*x^2 - 508800*x^3 - 3240*x^4 + 2760*x^5 + 9*x^6) + 38400*x^3 - 1920 00*x^4 - 1200*x^5 + 800*x^6 + 3*x^7) + exp(x)*(67200*x^4 - 67200*x^5 - 156 0*x^6 + 120*x^7 + 3*x^8) - exp(15*x + 30)*(exp(x)*(28800*x - 28800*x^2 - 6 00*x^3 + 120*x^4 + 3*x^5) + x^3*exp(3*x) + exp(2*x)*(120*x^3 - 360*x^2 + 3 *x^4) - 240*x^4 + x^6) - 560*x^7 + x^9 - exp(5*x + 10)*(exp(2*x)*(268800*x ^2 - 1036800*x^3 - 3480*x^4 + 2760*x^5 + 9*x^6) + exp(3*x)*(51200*x - 2560 00*x^2 - 800*x^3 + 800*x^4 + 3*x^5) + exp(x)*(393600*x^3 - 1315200*x^4 - 4 200*x^5 + 2760*x^6 + 9*x^7) + 89600*x^4 - 448000*x^5 - 1520*x^6 + 800*x^7 + 3*x^8))/(4800*x^5*exp(x) + exp(10*x + 20)*(4800*x*exp(3*x) + 14400*x^3*e xp(x) + 14400*x^2*exp(2*x) + 4800*x^4) - exp(15*x + 30)*(1600*exp(3*x) + 4 800*x*exp(2*x) + 4800*x^2*exp(x) + 1600*x^3) + 1600*x^3*exp(3*x) + 4800*x^ 4*exp(2*x) - exp(5*x + 10)*(14400*x^4*exp(x) + 4800*x^2*exp(3*x) + 14400*x ^3*exp(2*x) + 4800*x^5) + 1600*x^6),x)
(x^2*((7*x^6)/40 - 49*x^4 - 24*exp(12*x)*exp(20) - x^8/6400 + 96*x^2*exp(2 0)*exp(6*x - 10) + 48*x^3*exp(20)*exp(5*x - 10) - (7*x^3*exp(20)*exp(7*x - 10))/20 - (7*x^4*exp(20)*exp(6*x - 10))/10 - (7*x^5*exp(20)*exp(5*x - 10) )/20 + (x^5*exp(20)*exp(7*x - 10))/3200 + (x^6*exp(20)*exp(6*x - 10))/1600 + (x^7*exp(20)*exp(5*x - 10))/3200 - 24*x^2*exp(20)*exp(2*x - 20) + (7*x^ 4*exp(20)*exp(2*x - 20))/40 - (x^6*exp(20)*exp(2*x - 20))/6400 - 18*x^5*ex p(30)*exp(7*x - 10) - 36*x^6*exp(30)*exp(6*x - 10) - 18*x^7*exp(30)*exp(5* x - 10) + 9*x^4*exp(30)*exp(4*x - 20) - 9*x^5*exp(30)*exp(3*x - 20) + 9*x^ 6*exp(30)*exp(2*x - 20) - (3*x^5*exp(30)*exp(5*x - 20))/40 - (x^5*exp(30)* exp(3*x - 30))/6400 + 9*x^3*exp(40)*exp(5*x - 30) + 9*x^6*exp(40)*exp(2*x - 30) - 16*x^2*exp(40)*exp(2*x - 40) + 9*x^7*exp(50)*exp(5*x - 30) - 48*x* exp(11*x)*exp(20) + 9*exp(12*x)*exp(50)*exp(4*x - 20) + 16*exp(6*x)*exp(50 )*exp(2*x - 40) + 48*x*exp(20)*exp(7*x - 10) + 25*x^2*exp(6*x)*exp(10) + 2 5*x^3*exp(5*x)*exp(10) + (x^6*exp(6*x)*exp(10))/6400 + (x^7*exp(5*x)*exp(1 0))/6400 - 24*x^2*exp(10*x)*exp(20) + 9*x^6*exp(6*x)*exp(20) + 9*x^7*exp(5 *x)*exp(20) + (7*x^2*exp(12*x)*exp(20))/40 + (7*x^3*exp(11*x)*exp(20))/20 + (7*x^4*exp(10*x)*exp(20))/40 - (x^4*exp(12*x)*exp(20))/6400 - (x^5*exp(1 1*x)*exp(20))/3200 - (x^6*exp(10*x)*exp(20))/6400 + 9*x^4*exp(12*x)*exp(30 ) + 18*x^5*exp(11*x)*exp(30) + 9*x^6*exp(10*x)*exp(30) + (x^2*exp(18*x)*ex p(30))/6400 + (3*x^3*exp(17*x)*exp(30))/6400 + (3*x^4*exp(16*x)*exp(30)...