\(\int \frac {-4-1152 x-904 x^2-216 x^3-16 x^4+e^5 (-7040 x-5824 x^2-1536 x^3-128 x^4)+e^{15} (-80352 x-92160 x^2-38976 x^3-7168 x^4-480 x^5)+e^{10} (-30048 x-30176 x^2-10800 x^3-1600 x^4-80 x^5)+e^{25} (-230688 x-354240 x^2-216000 x^3-65280 x^4-9760 x^5-576 x^6)+e^{20} (-163080 x-219888 x^2-115056 x^3-28864 x^4-3400 x^5-144 x^6)+e^{35} (-163296 x-326592 x^2-272160 x^3-120960 x^4-30240 x^5-4032 x^6-224 x^7)+e^{30} (-244944 x-435456 x^2-317520 x^3-120960 x^4-25200 x^5-2688 x^6-112 x^7)+e^{40} (-69984 x-163296 x^2-163296 x^3-90720 x^4-30240 x^5-6048 x^6-672 x^7-32 x^8)}{63001 x+144576 x^2+139670 x^3+74124 x^4+23639 x^5+4644 x^6+550 x^7+36 x^8+x^9+e^5 (771072 x+1768256 x^2+1726352 x^3+936640 x^4+308704 x^5+63264 x^6+7872 x^7+544 x^8+16 x^9)+e^{10} (5250816 x+12495504 x^2+12856232 x^3+7485320 x^4+2708144 x^5+628352 x^6+92880 x^7+8352 x^8+408 x^9+8 x^{10})+e^{15} (24634368 x+61398864 x^2+66894336 x^3+41757840 x^4+16432544 x^5+4219552 x^6+705472 x^7+73872 x^8+4384 x^9+112 x^{10})+e^{20} (88006176 x+231559020 x^2+268957044 x^3+181099452 x^4+78004732 x^5+22350752 x^6+4285848 x^7+537772 x^8+41596 x^9+1740 x^{10}+28 x^{11})+e^{25} (250511616 x+697894704 x^2+865077840 x^3+627485328 x^4+294493200 x^5+93268000 x^6+20140928 x^7+2920080 x^8+271056 x^9+14480 x^{10}+336 x^{11})+e^{30} (584961264 x+1729205496 x^2+2290471344 x^3+1790543232 x^4+915313392 x^5+320091912 x^6+77750400 x^7+13024328 x^8+1458624 x^9+102144 x^{10}+3888 x^{11}+56 x^{12})+e^{35} (1137484944 x+3569522256 x^2+5049648864 x^3+4246618752 x^4+2356128432 x^5+904257648 x^6+244526352 x^7+46486928 x^8+6071424 x^9+516864 x^{10}+25680 x^{11}+560 x^{12})+e^{40} (1859269302 x+6195088656 x^2+9357185934 x^3+8457998940 x^4+5085305874 x^5+2136903552 x^6+641272212 x^7+137808408 x^8+20901410 x^9+2158608 x^{10}+141486 x^{11}+5100 x^{12}+70 x^{13})+e^{45} (2559734784 x+9051030720 x^2+14579591760 x^3+14137467840 x^4+9183475440 x^5+4205851776 x^6+1390828320 x^7+334108800 x^8+57754080 x^9+6988480 x^{10}+560016 x^{11}+26560 x^{12}+560 x^{13})+e^{50} (2962842624 x+11112864336 x^2+19076921064 x^3+19822775544 x^4+13890511800 x^5+6918985656 x^6+2514459024 x^7+672897456 x^8+132024816 x^9+18638400 x^{10}+1822216 x^{11}+114904 x^{12}+4056 x^{13}+56 x^{14})+e^{55} (2857026816 x+11357248464 x^2+20751235776 x^3+23064696864 x^4+17390324160 x^5+9386848944 x^6+3729027456 x^7+1102901184 x^8+242580096 x^9+39132720 x^{10}+4492224 x^{11}+346656 x^{12}+16064 x^{13}+336 x^{14})+e^{60} (2261812896 x+9525548484 x^2+18514695852 x^3+21996618552 x^4+17828546472 x^5+10416007404 x^6+4516653636 x^7+1473828048 x^8+362715408 x^9+66754908 x^{10}+8996724 x^{11}+854136 x^{12}+53288 x^{13}+1908 x^{14}+28 x^{15})+e^{65} (1428513408 x+6368788944 x^2+13154227632 x^3+16679216736 x^4+14501174688 x^5+9142044912 x^6+4308320016 x^7+1541187648 x^8+420323904 x^9+86918832 x^{10}[phone] x^{11}+1493856 x^{12}+113568 x^{13}+5264 x^{14}+112 x^{15})+e^{70} (688747536 x+3252418920 x^2+7142567040 x^3+9672226200 x^4+9027411120 x^5+6147237096 x^6+3152429280 x^7+1238454360 x^8+375289200 x^9+87567480 x^{10}[phone] x^{11}+2063880 x^{12}+196560 x^{13}+12600 x^{14}+480 x^{15}+8 x^{16})+e^{75} (229582512 x+1147912560 x^2+2678462640 x^3+3868890480 x^4+3868890480 x^5+2837186352 x^6+1576214640 x^7+675520560 x^8+225173520 x^9+58378320 x^{10}[phone] x^{11}+1769040 x^{12}+196560 x^{13}+15120 x^{14}+720 x^{15}+16 x^{16})+e^{80} (43046721 x+229582512 x^2+573956280 x^3+892820880 x^4+967222620 x^5+773778096 x^6+472864392 x^7+225173520 x^8+84440070 x^9+25019280 x^{10}+5837832 x^{11}+1061424 x^{12}+147420 x^{13}+15120 x^{14}+1080 x^{15}+48 x^{16}+x^{17})+(502 x+576 x^2+226 x^3+36 x^4+2 x^5+e^5 (3072 x+3520 x^2+1456 x^3+256 x^4+16 x^5)+e^{10} (11520 x+15024 x^2+7544 x^3+1800 x^4+200 x^5+8 x^6)+e^{15} (27648 x+40176 x^2+23040 x^3+6496 x^4+896 x^5+48 x^6)+e^{20} (49248 x+81540 x^2+54972 x^3+19176 x^4+3608 x^5+340 x^6+12 x^7)+e^{25} (62208 x+115344 x^2+88560 x^3+36000 x^4+8160 x^5+976 x^6+48 x^7)+e^{30} (58320 x+122472 x^2+108864 x^3+52920 x^4+15120 x^5+2520 x^6+224 x^7+8 x^8)+e^{35} (34992 x+81648 x^2+81648 x^3+45360 x^4+15120 x^5+3024 x^6+336 x^7+16 x^8)+e^{40} (13122 x+34992 x^2+40824 x^3+27216 x^4+11340 x^5+3024 x^6+504 x^7+48 x^8+2 x^9)) \log (x)+x \log ^2(x)} \, dx\) [2936]

Optimal result

Integrand size = 1752, antiderivative size = 28 \[ \text {the integral} =\frac {4}{-5+\left (x+\left (3+x+\left (1+e^5 (3+x)\right )^2\right )^2\right )^2+\log (x)} \] Output:

4/((x+(x+(1+(3+x)*exp(5))^2+3)^2)^2+ln(x)-5)
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(157\) vs. \(2(28)=56\).

Time = 0.44 (sec) , antiderivative size = 157, normalized size of antiderivative = 5.61 \[ \text {the integral} =\frac {4}{251+288 x+113 x^2+18 x^3+x^4+8 e^{35} (3+x)^7+e^{40} (3+x)^8+4 e^{30} (3+x)^6 (10+x)+8 e^{25} (3+x)^5 (16+3 x)+8 e^{15} (3+x)^3 \left (64+29 x+3 x^2\right )+2 e^{20} (3+x)^4 \left (152+49 x+3 x^2\right )+4 e^{10} (3+x)^2 \left (160+102 x+19 x^2+x^3\right )+8 e^5 \left (192+220 x+91 x^2+16 x^3+x^4\right )+\log (x)} \] Input:

Integrate[(-4 - 1152*x - 904*x^2 - 216*x^3 - 16*x^4 + E^5*(-7040*x - 5824* 
x^2 - 1536*x^3 - 128*x^4) + E^15*(-80352*x - 92160*x^2 - 38976*x^3 - 7168* 
x^4 - 480*x^5) + E^10*(-30048*x - 30176*x^2 - 10800*x^3 - 1600*x^4 - 80*x^ 
5) + E^25*(-230688*x - 354240*x^2 - 216000*x^3 - 65280*x^4 - 9760*x^5 - 57 
6*x^6) + E^20*(-163080*x - 219888*x^2 - 115056*x^3 - 28864*x^4 - 3400*x^5 
- 144*x^6) + E^35*(-163296*x - 326592*x^2 - 272160*x^3 - 120960*x^4 - 3024 
0*x^5 - 4032*x^6 - 224*x^7) + E^30*(-244944*x - 435456*x^2 - 317520*x^3 - 
120960*x^4 - 25200*x^5 - 2688*x^6 - 112*x^7) + E^40*(-69984*x - 163296*x^2 
 - 163296*x^3 - 90720*x^4 - 30240*x^5 - 6048*x^6 - 672*x^7 - 32*x^8))/(630 
01*x + 144576*x^2 + 139670*x^3 + 74124*x^4 + 23639*x^5 + 4644*x^6 + 550*x^ 
7 + 36*x^8 + x^9 + E^5*(771072*x + 1768256*x^2 + 1726352*x^3 + 936640*x^4 
+ 308704*x^5 + 63264*x^6 + 7872*x^7 + 544*x^8 + 16*x^9) + E^10*(5250816*x 
+ 12495504*x^2 + 12856232*x^3 + 7485320*x^4 + 2708144*x^5 + 628352*x^6 + 9 
2880*x^7 + 8352*x^8 + 408*x^9 + 8*x^10) + E^15*(24634368*x + 61398864*x^2 
+ 66894336*x^3 + 41757840*x^4 + 16432544*x^5 + 4219552*x^6 + 705472*x^7 + 
73872*x^8 + 4384*x^9 + 112*x^10) + E^20*(88006176*x + 231559020*x^2 + 2689 
57044*x^3 + 181099452*x^4 + 78004732*x^5 + 22350752*x^6 + 4285848*x^7 + 53 
7772*x^8 + 41596*x^9 + 1740*x^10 + 28*x^11) + E^25*(250511616*x + 69789470 
4*x^2 + 865077840*x^3 + 627485328*x^4 + 294493200*x^5 + 93268000*x^6 + 201 
40928*x^7 + 2920080*x^8 + 271056*x^9 + 14480*x^10 + 336*x^11) + E^30*(5849 
61264*x + 1729205496*x^2 + 2290471344*x^3 + 1790543232*x^4 + 915313392*x^5 
 + 320091912*x^6 + 77750400*x^7 + 13024328*x^8 + 1458624*x^9 + 102144*x^10 
 + 3888*x^11 + 56*x^12) + E^35*(1137484944*x + 3569522256*x^2 + 5049648864 
*x^3 + 4246618752*x^4 + 2356128432*x^5 + 904257648*x^6 + 244526352*x^7 + 4 
6486928*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^12) + E^40*(1 
859269302*x + 6195088656*x^2 + 9357185934*x^3 + 8457998940*x^4 + 508530587 
4*x^5 + 2136903552*x^6 + 641272212*x^7 + 137808408*x^8 + 20901410*x^9 + 21 
58608*x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + E^45*(2559734784*x + 905 
1030720*x^2 + 14579591760*x^3 + 14137467840*x^4 + 9183475440*x^5 + 4205851 
776*x^6 + 1390828320*x^7 + 334108800*x^8 + 57754080*x^9 + 6988480*x^10 + 5 
60016*x^11 + 26560*x^12 + 560*x^13) + E^50*(2962842624*x + 11112864336*x^2 
 + 19076921064*x^3 + 19822775544*x^4 + 13890511800*x^5 + 6918985656*x^6 + 
2514459024*x^7 + 672897456*x^8 + 132024816*x^9 + 18638400*x^10 + 1822216*x 
^11 + 114904*x^12 + 4056*x^13 + 56*x^14) + E^55*(2857026816*x + 1135724846 
4*x^2 + 20751235776*x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x 
^6 + 3729027456*x^7 + 1102901184*x^8 + 242580096*x^9 + 39132720*x^10 + 449 
2224*x^11 + 346656*x^12 + 16064*x^13 + 336*x^14) + E^60*(2261812896*x + 95 
25548484*x^2 + 18514695852*x^3 + 21996618552*x^4 + 17828546472*x^5 + 10416 
007404*x^6 + 4516653636*x^7 + 1473828048*x^8 + 362715408*x^9 + 66754908*x^ 
10 + 8996724*x^11 + 854136*x^12 + 53288*x^13 + 1908*x^14 + 28*x^15) + E^65 
*(1428513408*x + 6368788944*x^2 + 13154227632*x^3 + 16679216736*x^4 + 1450 
1174688*x^5 + 9142044912*x^6 + 4308320016*x^7 + 1541187648*x^8 + 420323904 
*x^9 + 86918832*x^10 + 13405392*x^11 + 1493856*x^12 + 113568*x^13 + 5264*x 
^14 + 112*x^15) + E^70*(688747536*x + 3252418920*x^2 + 7142567040*x^3 + 96 
72226200*x^4 + 9027411120*x^5 + 6147237096*x^6 + 3152429280*x^7 + 12384543 
60*x^8 + 375289200*x^9 + 87567480*x^10 + 15567552*x^11 + 2063880*x^12 + 19 
6560*x^13 + 12600*x^14 + 480*x^15 + 8*x^16) + E^75*(229582512*x + 11479125 
60*x^2 + 2678462640*x^3 + 3868890480*x^4 + 3868890480*x^5 + 2837186352*x^6 
 + 1576214640*x^7 + 675520560*x^8 + 225173520*x^9 + 58378320*x^10 + 116756 
64*x^11 + 1769040*x^12 + 196560*x^13 + 15120*x^14 + 720*x^15 + 16*x^16) + 
E^80*(43046721*x + 229582512*x^2 + 573956280*x^3 + 892820880*x^4 + 9672226 
20*x^5 + 773778096*x^6 + 472864392*x^7 + 225173520*x^8 + 84440070*x^9 + 25 
019280*x^10 + 5837832*x^11 + 1061424*x^12 + 147420*x^13 + 15120*x^14 + 108 
0*x^15 + 48*x^16 + x^17) + (502*x + 576*x^2 + 226*x^3 + 36*x^4 + 2*x^5 + E 
^5*(3072*x + 3520*x^2 + 1456*x^3 + 256*x^4 + 16*x^5) + E^10*(11520*x + 150 
24*x^2 + 7544*x^3 + 1800*x^4 + 200*x^5 + 8*x^6) + E^15*(27648*x + 40176*x^ 
2 + 23040*x^3 + 6496*x^4 + 896*x^5 + 48*x^6) + E^20*(49248*x + 81540*x^2 + 
 54972*x^3 + 19176*x^4 + 3608*x^5 + 340*x^6 + 12*x^7) + E^25*(62208*x + 11 
5344*x^2 + 88560*x^3 + 36000*x^4 + 8160*x^5 + 976*x^6 + 48*x^7) + E^30*(58 
320*x + 122472*x^2 + 108864*x^3 + 52920*x^4 + 15120*x^5 + 2520*x^6 + 224*x 
^7 + 8*x^8) + E^35*(34992*x + 81648*x^2 + 81648*x^3 + 45360*x^4 + 15120*x^ 
5 + 3024*x^6 + 336*x^7 + 16*x^8) + E^40*(13122*x + 34992*x^2 + 40824*x^3 + 
 27216*x^4 + 11340*x^5 + 3024*x^6 + 504*x^7 + 48*x^8 + 2*x^9))*Log[x] + x* 
Log[x]^2),x]
 

Output:

4/(251 + 288*x + 113*x^2 + 18*x^3 + x^4 + 8*E^35*(3 + x)^7 + E^40*(3 + x)^ 
8 + 4*E^30*(3 + x)^6*(10 + x) + 8*E^25*(3 + x)^5*(16 + 3*x) + 8*E^15*(3 + 
x)^3*(64 + 29*x + 3*x^2) + 2*E^20*(3 + x)^4*(152 + 49*x + 3*x^2) + 4*E^10* 
(3 + x)^2*(160 + 102*x + 19*x^2 + x^3) + 8*E^5*(192 + 220*x + 91*x^2 + 16* 
x^3 + x^4) + Log[x])
 

Rubi [F]

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 {-16 x^4-216 x^3-904 x^2-1152 x+e^5 \left (-128 x^4-1536 x^3-5824 x^2-7040 x\right )+e^{15} \left (-480 x^5-7168 x^4-38976 x^3-92160 x^2-80352 x\right )+e^{10} \left (-80 x^5-1600 x^4-10800 x^3-30176 x^2-30048 x\right )+e^{25} \left (-576 x^6-9760 x^5-65280 x^4-216000 x^3-354240 x^2-230688 x\right )+e^{20} \left (-144 x^6-3400 x^5-28864 x^4-115056 x^3-219888 x^2-163080 x\right )+e^{35} \left (-224 x^7-4032 x^6-30240 x^5-120960 x^4-272160 x^3-326592 x^2-163296 x\right )+e^{30} \left (-112 x^7-2688 x^6-25200 x^5-120960 x^4-317520 x^3-435456 x^2-244944 x\right )+e^{40} \left (-32 x^8-672 x^7-6048 x^6-30240 x^5-90720 x^4-163296 x^3-163296 x^2-69984 x\right )-4}{x^9+36 x^8+550 x^7+4644 x^6+23639 x^5+74124 x^4+139670 x^3+144576 x^2+\log ^2(x) x+63001 x+e^5 \left (16 x^9+544 x^8+7872 x^7+63264 x^6+308704 x^5+936640 x^4+1726352 x^3+1768256 x^2+771072 x\right )+e^{10} \left (8 x^{10}+408 x^9+8352 x^8+92880 x^7+628352 x^6+2708144 x^5+7485320 x^4+12856232 x^3+12495504 x^2+5250816 x\right )+e^{15} \left (112 x^{10}+4384 x^9+73872 x^8+705472 x^7+4219552 x^6+16432544 x^5+41757840 x^4+66894336 x^3+61398864 x^2+24634368 x\right )+e^{20} \left (28 x^{11}+1740 x^{10}+41596 x^9+537772 x^8+4285848 x^7+22350752 x^6+78004732 x^5+181099452 x^4+268957044 x^3+231559020 x^2+88006176 x\right )+e^{25} \left (336 x^{11}+14480 x^{10}+271056 x^9+2920080 x^8+20140928 x^7+93268000 x^6+294493200 x^5+627485328 x^4+865077840 x^3+697894704 x^2+250511616 x\right )+e^{30} \left (56 x^{12}+3888 x^{11}+102144 x^{10}+1458624 x^9+13024328 x^8+77750400 x^7+320091912 x^6+915313392 x^5+1790543232 x^4+2290471344 x^3+1729205496 x^2+584961264 x\right )+e^{35} \left (560 x^{12}+25680 x^{11}+516864 x^{10}+6071424 x^9+46486928 x^8+244526352 x^7+904257648 x^6+2356128432 x^5+4246618752 x^4+5049648864 x^3+3569522256 x^2+1137484944 x\right )+e^{40} \left (70 x^{13}+5100 x^{12}+141486 x^{11}+2158608 x^{10}[phone] x^9+137808408 x^8+641272212 x^7+2136903552 x^6+5085305874 x^5+8457998940 x^4+9357185934 x^3+6195088656 x^2+1859269302 x\right )+e^{45} \left (560 x^{13}+26560 x^{12}+560016 x^{11}+6988480 x^{10}[phone] x^9+334108800 x^8+1390828320 x^7+4205851776 x^6+9183475440 x^5+14137467840 x^4+14579591760 x^3+9051030720 x^2+2559734784 x\right )+e^{50} \left (56 x^{14}+4056 x^{13}+114904 x^{12}+1822216 x^{11}[phone] x^{10}[phone] x^9+672897456 x^8+2514459024 x^7+6918985656 x^6+13890511800 x^5+19822775544 x^4+19076921064 x^3+11112864336 x^2+2962842624 x\right )+e^{55} \left (336 x^{14}+16064 x^{13}+346656 x^{12}+4492224 x^{11}[phone] x^{10}[phone] x^9+1102901184 x^8+3729027456 x^7+9386848944 x^6+17390324160 x^5+23064696864 x^4+20751235776 x^3+11357248464 x^2+2857026816 x\right )+e^{60} \left (28 x^{15}+1908 x^{14}+53288 x^{13}+854136 x^{12}+8996724 x^{11}[phone] x^{10}[phone] x^9+1473828048 x^8+4516653636 x^7+10416007404 x^6+17828546472 x^5+21996618552 x^4+18514695852 x^3+9525548484 x^2+2261812896 x\right )+e^{65} \left (112 x^{15}+5264 x^{14}+113568 x^{13}+1493856 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+1541187648 x^8+4308320016 x^7+9142044912 x^6+14501174688 x^5+16679216736 x^4+13154227632 x^3+6368788944 x^2+1428513408 x\right )+e^{70} \left (8 x^{16}+480 x^{15}+12600 x^{14}+196560 x^{13}+2063880 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+1238454360 x^8+3152429280 x^7+6147237096 x^6+9027411120 x^5+9672226200 x^4+7142567040 x^3+3252418920 x^2+688747536 x\right )+e^{75} \left (16 x^{16}+720 x^{15}+15120 x^{14}+196560 x^{13}+1769040 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+675520560 x^8+1576214640 x^7+2837186352 x^6+3868890480 x^5+3868890480 x^4+2678462640 x^3+1147912560 x^2+229582512 x\right )+e^{80} \left (x^{17}+48 x^{16}+1080 x^{15}+15120 x^{14}+147420 x^{13}+1061424 x^{12}+5837832 x^{11}[phone] x^{10}[phone] x^9+225173520 x^8+472864392 x^7+773778096 x^6+967222620 x^5+892820880 x^4+573956280 x^3+229582512 x^2+43046721 x\right )+\left (2 x^5+36 x^4+226 x^3+576 x^2+502 x+e^5 \left (16 x^5+256 x^4+1456 x^3+3520 x^2+3072 x\right )+e^{10} \left (8 x^6+200 x^5+1800 x^4+7544 x^3+15024 x^2+11520 x\right )+e^{15} \left (48 x^6+896 x^5+6496 x^4+23040 x^3+40176 x^2+27648 x\right )+e^{20} \left (12 x^7+340 x^6+3608 x^5+19176 x^4+54972 x^3+81540 x^2+49248 x\right )+e^{25} \left (48 x^7+976 x^6+8160 x^5+36000 x^4+88560 x^3+115344 x^2+62208 x\right )+e^{30} \left (8 x^8+224 x^7+2520 x^6+15120 x^5+52920 x^4+108864 x^3+122472 x^2+58320 x\right )+e^{35} \left (16 x^8+336 x^7+3024 x^6+15120 x^5+45360 x^4+81648 x^3+81648 x^2+34992 x\right )+e^{40} \left (2 x^9+48 x^8+504 x^7+3024 x^6+11340 x^5+27216 x^4+40824 x^3+34992 x^2+13122 x\right )\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 \left (-8 e^{40} x^8-28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7-12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6-10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5-4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4-6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3-2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2-2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x-1\right )}{x \left (x^4+18 x^3+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+113 x^2+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+288 x+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 4 \int -\frac {8 e^{40} x^8+28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \frac {8 e^{40} x^8+28 \left (e^{30}+2 e^{35}+6 e^{40}\right ) x^7+12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^6+10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^5+4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^4+6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^3+2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x^2+2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right ) x+1}{x \left (e^{40} (x+3)^8+8 e^{35} (x+3)^7+4 e^{30} (x+10) (x+3)^6+8 e^{25} (3 x+16) (x+3)^5+2 e^{20} \left (3 x^2+49 x+152\right ) (x+3)^4+8 e^{15} \left (3 x^2+29 x+64\right ) (x+3)^3+4 e^{10} \left (x^3+19 x^2+102 x+160\right ) (x+3)^2+x^4+18 x^3+113 x^2+288 x+8 e^5 \left (x^4+16 x^3+91 x^2+220 x+192\right )+\log (x)+251\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (\frac {8 e^{40} x^7}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {28 e^{30} \left (1+2 e^5+6 e^{10}\right ) x^6}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {12 e^{20} \left (3+12 e^5+56 e^{10}+84 e^{15}+126 e^{20}\right ) x^5}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {10 e^{10} \left (2+12 e^5+85 e^{10}+244 e^{15}+630 e^{20}+756 e^{25}+756 e^{30}\right ) x^4}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {4 \left (1+8 e^5+100 e^{10}+448 e^{15}+1804 e^{20}+4080 e^{25}+7560 e^{30}+7560 e^{35}+5670 e^{40}\right ) x^3}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {6 \left (9+64 e^5+450 e^{10}+1624 e^{15}+4794 e^{20}+9000 e^{25}+13230 e^{30}+11340 e^{35}+6804 e^{40}\right ) x^2}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (113+728 e^5+3772 e^{10}+11520 e^{15}+27486 e^{20}+44280 e^{25}+54432 e^{30}+40824 e^{35}+20412 e^{40}\right ) x}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {2 \left (4+6 e^5+9 e^{10}\right )^2 \left (9+28 e^5+90 e^{10}+108 e^{15}+108 e^{20}\right )}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2}+\frac {1}{\left (e^{40} x^8+4 e^{30} \left (1+2 e^5 \left (1+3 e^5\right )\right ) x^7+6 e^{20} \left (1+4 e^5 \left (1+\frac {7}{6} e^5 \left (4+6 e^5+9 e^{10}\right )\right )\right ) x^6+4 e^{10} \left (1+6 e^5+\frac {85 e^{10}}{2}+122 e^{15}+315 e^{20}+378 e^{25}+378 e^{30}\right ) x^5+\left (1+2 e^5 \left (4+50 e^5+224 e^{10}+902 e^{15}+2040 e^{20}+3780 e^{25}+3780 e^{30}+2835 e^{35}\right )\right ) x^4+18 \left (1+\frac {2}{9} e^5 \left (32+225 e^5+812 e^{10}+2397 e^{15}+4500 e^{20}+6615 e^{25}+5670 e^{30}+3402 e^{35}\right )\right ) x^3+113 \left (1+\frac {2}{113} e^5 \left (364+1886 e^5+5760 e^{10}+13743 e^{15}+22140 e^{20}+27216 e^{25}+20412 e^{30}+10206 e^{35}\right )\right ) x^2+288 \left (1+\frac {55 e^5}{9}+\frac {1}{48} e^{10} \left (1252+3348 e^5+6795 e^{10}+9612 e^{15}+10206 e^{20}+6804 e^{25}+2916 e^{30}\right )\right ) x+\log (x)+251 \left (1+\frac {1536}{251} e^5 \left (1+\frac {15 e^5}{4}+9 e^{10} \left (1+\frac {3}{512} e^5 \left (304+384 e^5+360 e^{10}+216 e^{15}+81 e^{20}\right )\right )\right )\right )\right )^2 x}\right )dx\)

Input:

Int[(-4 - 1152*x - 904*x^2 - 216*x^3 - 16*x^4 + E^5*(-7040*x - 5824*x^2 - 
1536*x^3 - 128*x^4) + E^15*(-80352*x - 92160*x^2 - 38976*x^3 - 7168*x^4 - 
480*x^5) + E^10*(-30048*x - 30176*x^2 - 10800*x^3 - 1600*x^4 - 80*x^5) + E 
^25*(-230688*x - 354240*x^2 - 216000*x^3 - 65280*x^4 - 9760*x^5 - 576*x^6) 
 + E^20*(-163080*x - 219888*x^2 - 115056*x^3 - 28864*x^4 - 3400*x^5 - 144* 
x^6) + E^35*(-163296*x - 326592*x^2 - 272160*x^3 - 120960*x^4 - 30240*x^5 
- 4032*x^6 - 224*x^7) + E^30*(-244944*x - 435456*x^2 - 317520*x^3 - 120960 
*x^4 - 25200*x^5 - 2688*x^6 - 112*x^7) + E^40*(-69984*x - 163296*x^2 - 163 
296*x^3 - 90720*x^4 - 30240*x^5 - 6048*x^6 - 672*x^7 - 32*x^8))/(63001*x + 
 144576*x^2 + 139670*x^3 + 74124*x^4 + 23639*x^5 + 4644*x^6 + 550*x^7 + 36 
*x^8 + x^9 + E^5*(771072*x + 1768256*x^2 + 1726352*x^3 + 936640*x^4 + 3087 
04*x^5 + 63264*x^6 + 7872*x^7 + 544*x^8 + 16*x^9) + E^10*(5250816*x + 1249 
5504*x^2 + 12856232*x^3 + 7485320*x^4 + 2708144*x^5 + 628352*x^6 + 92880*x 
^7 + 8352*x^8 + 408*x^9 + 8*x^10) + E^15*(24634368*x + 61398864*x^2 + 6689 
4336*x^3 + 41757840*x^4 + 16432544*x^5 + 4219552*x^6 + 705472*x^7 + 73872* 
x^8 + 4384*x^9 + 112*x^10) + E^20*(88006176*x + 231559020*x^2 + 268957044* 
x^3 + 181099452*x^4 + 78004732*x^5 + 22350752*x^6 + 4285848*x^7 + 537772*x 
^8 + 41596*x^9 + 1740*x^10 + 28*x^11) + E^25*(250511616*x + 697894704*x^2 
+ 865077840*x^3 + 627485328*x^4 + 294493200*x^5 + 93268000*x^6 + 20140928* 
x^7 + 2920080*x^8 + 271056*x^9 + 14480*x^10 + 336*x^11) + E^30*(584961264* 
x + 1729205496*x^2 + 2290471344*x^3 + 1790543232*x^4 + 915313392*x^5 + 320 
091912*x^6 + 77750400*x^7 + 13024328*x^8 + 1458624*x^9 + 102144*x^10 + 388 
8*x^11 + 56*x^12) + E^35*(1137484944*x + 3569522256*x^2 + 5049648864*x^3 + 
 4246618752*x^4 + 2356128432*x^5 + 904257648*x^6 + 244526352*x^7 + 4648692 
8*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^12) + E^40*(1859269 
302*x + 6195088656*x^2 + 9357185934*x^3 + 8457998940*x^4 + 5085305874*x^5 
+ 2136903552*x^6 + 641272212*x^7 + 137808408*x^8 + 20901410*x^9 + 2158608* 
x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + E^45*(2559734784*x + 905103072 
0*x^2 + 14579591760*x^3 + 14137467840*x^4 + 9183475440*x^5 + 4205851776*x^ 
6 + 1390828320*x^7 + 334108800*x^8 + 57754080*x^9 + 6988480*x^10 + 560016* 
x^11 + 26560*x^12 + 560*x^13) + E^50*(2962842624*x + 11112864336*x^2 + 190 
76921064*x^3 + 19822775544*x^4 + 13890511800*x^5 + 6918985656*x^6 + 251445 
9024*x^7 + 672897456*x^8 + 132024816*x^9 + 18638400*x^10 + 1822216*x^11 + 
114904*x^12 + 4056*x^13 + 56*x^14) + E^55*(2857026816*x + 11357248464*x^2 
+ 20751235776*x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x^6 + 3 
729027456*x^7 + 1102901184*x^8 + 242580096*x^9 + 39132720*x^10 + 4492224*x 
^11 + 346656*x^12 + 16064*x^13 + 336*x^14) + E^60*(2261812896*x + 95255484 
84*x^2 + 18514695852*x^3 + 21996618552*x^4 + 17828546472*x^5 + 10416007404 
*x^6 + 4516653636*x^7 + 1473828048*x^8 + 362715408*x^9 + 66754908*x^10 + 8 
996724*x^11 + 854136*x^12 + 53288*x^13 + 1908*x^14 + 28*x^15) + E^65*(1428 
513408*x + 6368788944*x^2 + 13154227632*x^3 + 16679216736*x^4 + 1450117468 
8*x^5 + 9142044912*x^6 + 4308320016*x^7 + 1541187648*x^8 + 420323904*x^9 + 
 86918832*x^10 + 13405392*x^11 + 1493856*x^12 + 113568*x^13 + 5264*x^14 + 
112*x^15) + E^70*(688747536*x + 3252418920*x^2 + 7142567040*x^3 + 96722262 
00*x^4 + 9027411120*x^5 + 6147237096*x^6 + 3152429280*x^7 + 1238454360*x^8 
 + 375289200*x^9 + 87567480*x^10 + 15567552*x^11 + 2063880*x^12 + 196560*x 
^13 + 12600*x^14 + 480*x^15 + 8*x^16) + E^75*(229582512*x + 1147912560*x^2 
 + 2678462640*x^3 + 3868890480*x^4 + 3868890480*x^5 + 2837186352*x^6 + 157 
6214640*x^7 + 675520560*x^8 + 225173520*x^9 + 58378320*x^10 + 11675664*x^1 
1 + 1769040*x^12 + 196560*x^13 + 15120*x^14 + 720*x^15 + 16*x^16) + E^80*( 
43046721*x + 229582512*x^2 + 573956280*x^3 + 892820880*x^4 + 967222620*x^5 
 + 773778096*x^6 + 472864392*x^7 + 225173520*x^8 + 84440070*x^9 + 25019280 
*x^10 + 5837832*x^11 + 1061424*x^12 + 147420*x^13 + 15120*x^14 + 1080*x^15 
 + 48*x^16 + x^17) + (502*x + 576*x^2 + 226*x^3 + 36*x^4 + 2*x^5 + E^5*(30 
72*x + 3520*x^2 + 1456*x^3 + 256*x^4 + 16*x^5) + E^10*(11520*x + 15024*x^2 
 + 7544*x^3 + 1800*x^4 + 200*x^5 + 8*x^6) + E^15*(27648*x + 40176*x^2 + 23 
040*x^3 + 6496*x^4 + 896*x^5 + 48*x^6) + E^20*(49248*x + 81540*x^2 + 54972 
*x^3 + 19176*x^4 + 3608*x^5 + 340*x^6 + 12*x^7) + E^25*(62208*x + 115344*x 
^2 + 88560*x^3 + 36000*x^4 + 8160*x^5 + 976*x^6 + 48*x^7) + E^30*(58320*x 
+ 122472*x^2 + 108864*x^3 + 52920*x^4 + 15120*x^5 + 2520*x^6 + 224*x^7 + 8 
*x^8) + E^35*(34992*x + 81648*x^2 + 81648*x^3 + 45360*x^4 + 15120*x^5 + 30 
24*x^6 + 336*x^7 + 16*x^8) + E^40*(13122*x + 34992*x^2 + 40824*x^3 + 27216 
*x^4 + 11340*x^5 + 3024*x^6 + 504*x^7 + 48*x^8 + 2*x^9))*Log[x] + x*Log[x] 
^2),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(470\) vs. \(2(27)=54\).

Time = 15.28 (sec) , antiderivative size = 471, normalized size of antiderivative = 16.82

method	result	size
default	\(\frac {4}{251+8 \,{\mathrm e}^{5+4 \ln \left (x \right )}+20088 \,{\mathrm e}^{\ln \left (x \right )+15}+3772 \,{\mathrm e}^{10+2 \ln \left (x \right )}+7512 \,{\mathrm e}^{10+\ln \left (x \right )}+128 \,{\mathrm e}^{3 \ln \left (x \right )+5}+288 x +13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+5760 \,{\mathrm e}^{10}+31104 \,{\mathrm e}^{25}+1536 \,{\mathrm e}^{5}+6561 \,{\mathrm e}^{40}+\ln \left (x \right )+113 x^{2}+18 x^{3}+x^{4}+29160 \,{\mathrm e}^{30}+1512 \,{\mathrm e}^{35+5 \ln \left (x \right )}+24 \,{\mathrm e}^{40+7 \ln \left (x \right )}+5670 \,{\mathrm e}^{40+4 \ln \left (x \right )}+40770 \,{\mathrm e}^{20+\ln \left (x \right )}+6 \,{\mathrm e}^{20+6 \ln \left (x \right )}+22680 \,{\mathrm e}^{35+3 \ln \left (x \right )}+7560 \,{\mathrm e}^{30+4 \ln \left (x \right )}+24 \,{\mathrm e}^{25+6 \ln \left (x \right )}+1512 \,{\mathrm e}^{40+5 \ln \left (x \right )}+1260 \,{\mathrm e}^{30+5 \ln \left (x \right )}+252 \,{\mathrm e}^{40+6 \ln \left (x \right )}+40824 \,{\mathrm e}^{35+2 \ln \left (x \right )}+26460 \,{\mathrm e}^{30+3 \ln \left (x \right )}+61236 \,{\mathrm e}^{30+\ln \left (x \right )}+57672 \,{\mathrm e}^{\ln \left (x \right )+25}+168 \,{\mathrm e}^{35+6 \ln \left (x \right )}+4 \,{\mathrm e}^{30+7 \ln \left (x \right )}+728 \,{\mathrm e}^{5+2 \ln \left (x \right )}+11520 \,{\mathrm e}^{15+2 \ln \left (x \right )}+448 \,{\mathrm e}^{15+4 \ln \left (x \right )}+54432 \,{\mathrm e}^{30+2 \ln \left (x \right )}+18000 \,{\mathrm e}^{25+3 \ln \left (x \right )}+20412 \,{\mathrm e}^{40+2 \ln \left (x \right )}+112 \,{\mathrm e}^{30+6 \ln \left (x \right )}+4080 \,{\mathrm e}^{25+4 \ln \left (x \right )}+900 \,{\mathrm e}^{10+3 \ln \left (x \right )}+1760 \,{\mathrm e}^{5+\ln \left (x \right )}+100 \,{\mathrm e}^{10+4 \ln \left (x \right )}+44280 \,{\mathrm e}^{25+2 \ln \left (x \right )}+3248 \,{\mathrm e}^{15+3 \ln \left (x \right )}+40824 \,{\mathrm e}^{35+\ln \left (x \right )}+17496 \,{\mathrm e}^{40+\ln \left (x \right )}+{\mathrm e}^{40+8 \ln \left (x \right )}+4 \,{\mathrm e}^{10+5 \ln \left (x \right )}+27486 \,{\mathrm e}^{20+2 \ln \left (x \right )}+8 \,{\mathrm e}^{35+7 \ln \left (x \right )}+1804 \,{\mathrm e}^{4 \ln \left (x \right )+20}+488 \,{\mathrm e}^{25+5 \ln \left (x \right )}+24 \,{\mathrm e}^{15+5 \ln \left (x \right )}+170 \,{\mathrm e}^{20+5 \ln \left (x \right )}+9588 \,{\mathrm e}^{20+3 \ln \left (x \right )}+13608 \,{\mathrm e}^{40+3 \ln \left (x \right )}+7560 \,{\mathrm e}^{35+4 \ln \left (x \right )}+17496 \,{\mathrm e}^{35}}\)	\(471\)
risch	\(\frac {4}{251+61236 x \,{\mathrm e}^{30}+488 x^{5} {\mathrm e}^{25}+288 x +57672 x \,{\mathrm e}^{25}+44280 x^{2} {\mathrm e}^{25}+18000 x^{3} {\mathrm e}^{25}+4080 x^{4} {\mathrm e}^{25}+8 x^{4} {\mathrm e}^{5}+9588 \,{\mathrm e}^{20} x^{3}+20088 x \,{\mathrm e}^{15}+27486 x^{2} {\mathrm e}^{20}+7512 x \,{\mathrm e}^{10}+7560 \,{\mathrm e}^{30} x^{4}+4 \,{\mathrm e}^{30} x^{7}+112 \,{\mathrm e}^{30} x^{6}+1260 \,{\mathrm e}^{30} x^{5}+728 x^{2} {\mathrm e}^{5}+128 x^{3} {\mathrm e}^{5}+1760 x \,{\mathrm e}^{5}+40770 x \,{\mathrm e}^{20}+100 x^{4} {\mathrm e}^{10}+170 \,{\mathrm e}^{20} x^{5}+1804 \,{\mathrm e}^{20} x^{4}+6 \,{\mathrm e}^{20} x^{6}+13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+900 x^{3} {\mathrm e}^{10}+5760 \,{\mathrm e}^{10}+31104 \,{\mathrm e}^{25}+1536 \,{\mathrm e}^{5}+6561 \,{\mathrm e}^{40}+\ln \left (x \right )+113 x^{2}+18 x^{3}+x^{4}+448 x^{4} {\mathrm e}^{15}+4 \,{\mathrm e}^{10} x^{5}+11520 x^{2} {\mathrm e}^{15}+29160 \,{\mathrm e}^{30}+{\mathrm e}^{40} x^{8}+40824 x^{2} {\mathrm e}^{35}+3772 x^{2} {\mathrm e}^{10}+24 \,{\mathrm e}^{40} x^{7}+40824 x \,{\mathrm e}^{35}+24 \,{\mathrm e}^{25} x^{6}+20412 \,{\mathrm e}^{40} x^{2}+26460 x^{3} {\mathrm e}^{30}+7560 x^{4} {\mathrm e}^{35}+17496 \,{\mathrm e}^{40} x +54432 x^{2} {\mathrm e}^{30}+13608 \,{\mathrm e}^{40} x^{3}+1512 \,{\mathrm e}^{40} x^{5}+168 x^{6} {\mathrm e}^{35}+5670 \,{\mathrm e}^{40} x^{4}+1512 x^{5} {\mathrm e}^{35}+22680 x^{3} {\mathrm e}^{35}+252 x^{6} {\mathrm e}^{40}+8 x^{7} {\mathrm e}^{35}+3248 x^{3} {\mathrm e}^{15}+24 x^{5} {\mathrm e}^{15}+17496 \,{\mathrm e}^{35}}\)	\(478\)
parallelrisch	\(\frac {4}{251+61236 x \,{\mathrm e}^{30}+488 x^{5} {\mathrm e}^{25}+288 x +57672 x \,{\mathrm e}^{25}+44280 x^{2} {\mathrm e}^{25}+18000 x^{3} {\mathrm e}^{25}+4080 x^{4} {\mathrm e}^{25}+8 x^{4} {\mathrm e}^{5}+9588 \,{\mathrm e}^{20} x^{3}+20088 x \,{\mathrm e}^{15}+27486 x^{2} {\mathrm e}^{20}+7512 x \,{\mathrm e}^{10}+7560 \,{\mathrm e}^{30} x^{4}+4 \,{\mathrm e}^{30} x^{7}+112 \,{\mathrm e}^{30} x^{6}+1260 \,{\mathrm e}^{30} x^{5}+728 x^{2} {\mathrm e}^{5}+128 x^{3} {\mathrm e}^{5}+1760 x \,{\mathrm e}^{5}+40770 x \,{\mathrm e}^{20}+100 x^{4} {\mathrm e}^{10}+170 \,{\mathrm e}^{20} x^{5}+1804 \,{\mathrm e}^{20} x^{4}+6 \,{\mathrm e}^{20} x^{6}+13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+900 x^{3} {\mathrm e}^{10}+5760 \,{\mathrm e}^{10}+31104 \,{\mathrm e}^{25}+1536 \,{\mathrm e}^{5}+6561 \,{\mathrm e}^{40}+\ln \left (x \right )+113 x^{2}+18 x^{3}+x^{4}+448 x^{4} {\mathrm e}^{15}+4 \,{\mathrm e}^{10} x^{5}+11520 x^{2} {\mathrm e}^{15}+29160 \,{\mathrm e}^{30}+{\mathrm e}^{40} x^{8}+40824 x^{2} {\mathrm e}^{35}+3772 x^{2} {\mathrm e}^{10}+24 \,{\mathrm e}^{40} x^{7}+40824 x \,{\mathrm e}^{35}+24 \,{\mathrm e}^{25} x^{6}+20412 \,{\mathrm e}^{40} x^{2}+26460 x^{3} {\mathrm e}^{30}+7560 x^{4} {\mathrm e}^{35}+17496 \,{\mathrm e}^{40} x +54432 x^{2} {\mathrm e}^{30}+13608 \,{\mathrm e}^{40} x^{3}+1512 \,{\mathrm e}^{40} x^{5}+168 x^{6} {\mathrm e}^{35}+5670 \,{\mathrm e}^{40} x^{4}+1512 x^{5} {\mathrm e}^{35}+22680 x^{3} {\mathrm e}^{35}+252 x^{6} {\mathrm e}^{40}+8 x^{7} {\mathrm e}^{35}+3248 x^{3} {\mathrm e}^{15}+24 x^{5} {\mathrm e}^{15}+17496 \,{\mathrm e}^{35}}\)	\(478\)

Input:

int(((-32*x^8-672*x^7-6048*x^6-30240*x^5-90720*x^4-163296*x^3-163296*x^2-6 
9984*x)*exp(5)^8+(-224*x^7-4032*x^6-30240*x^5-120960*x^4-272160*x^3-326592 
*x^2-163296*x)*exp(5)^7+(-112*x^7-2688*x^6-25200*x^5-120960*x^4-317520*x^3 
-435456*x^2-244944*x)*exp(5)^6+(-576*x^6-9760*x^5-65280*x^4-216000*x^3-354 
240*x^2-230688*x)*exp(5)^5+(-144*x^6-3400*x^5-28864*x^4-115056*x^3-219888* 
x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80352*x)*exp 
(5)^3+(-80*x^5-1600*x^4-10800*x^3-30176*x^2-30048*x)*exp(5)^2+(-128*x^4-15 
36*x^3-5824*x^2-7040*x)*exp(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(63001*x+x 
*ln(x)^2+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^ 
11+58378320*x^10+225173520*x^9+675520560*x^8+1576214640*x^7+2837186352*x^6 
[phone]*x^5+3868890480*x^4+2678462640*x^3+1147912560*x^2+229582512*x)* 
exp(5)^15+(8*x^16+480*x^15+12600*x^14+196560*x^13+2063880*x^12+15567552*x^ 
11+87567480*x^10+375289200*x^9+1238454360*x^8+3152429280*x^7+6147237096*x^ 
6+9027411120*x^5+9672226200*x^4+7142567040*x^3+3252418920*x^2+688747536*x) 
*exp(5)^14+(112*x^15+5264*x^14+113568*x^13+1493856*x^12+13405392*x^11+8691 
8832*x^10+420323904*x^9+1541187648*x^8+4308320016*x^7+9142044912*x^6+14501 
174688*x^5+16679216736*x^4+13154227632*x^3+6368788944*x^2+1428513408*x)*ex 
p(5)^13+(28*x^15+1908*x^14+53288*x^13+854136*x^12+8996724*x^11+66754908*x^ 
10+362715408*x^9+1473828048*x^8+4516653636*x^7+10416007404*x^6+17828546472 
*x^5+21996618552*x^4+18514695852*x^3+9525548484*x^2+2261812896*x)*exp(5)^1 
2+(336*x^14+16064*x^13+346656*x^12+4492224*x^11+39132720*x^10+242580096*x^ 
9+1102901184*x^8+3729027456*x^7+9386848944*x^6+17390324160*x^5+23064696864 
*x^4+20751235776*x^3+11357248464*x^2+2857026816*x)*exp(5)^11+(56*x^14+4056 
*x^13+114904*x^12+1822216*x^11+18638400*x^10+132024816*x^9+672897456*x^8+2 
514459024*x^7+6918985656*x^6+13890511800*x^5+19822775544*x^4+19076921064*x 
^3+11112864336*x^2+2962842624*x)*exp(5)^10+(x^17+48*x^16+1080*x^15+15120*x 
^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440070*x^9+22517 
3520*x^8+472864392*x^7+773778096*x^6+967222620*x^5+892820880*x^4+573956280 
*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+5100*x^12+141486*x^11+21 
58608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+2136903552*x^6+5085305 
874*x^5+8457998940*x^4+9357185934*x^3+6195088656*x^2+1859269302*x)*exp(5)^ 
8+(560*x^12+25680*x^11+516864*x^10+6071424*x^9+46486928*x^8+244526352*x^7+ 
904257648*x^6+2356128432*x^5+4246618752*x^4+5049648864*x^3+3569522256*x^2+ 
1137484944*x)*exp(5)^7+(56*x^12+3888*x^11+102144*x^10+1458624*x^9+13024328 
*x^8+77750400*x^7+320091912*x^6+915313392*x^5+1790543232*x^4+2290471344*x^ 
3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+14480*x^10+271056*x^9+292 
0080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627485328*x^4+865077840*x 
^3+697894704*x^2+250511616*x)*exp(5)^5+(28*x^11+1740*x^10+41596*x^9+537772 
*x^8+4285848*x^7+22350752*x^6+78004732*x^5+181099452*x^4+268957044*x^3+231 
559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73872*x^8+705472*x^7+42 
19552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2+24634368*x)* 
exp(5)^3+(8*x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320 
*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^9+544*x^8+7872*x^ 
7+63264*x^6+308704*x^5+936640*x^4+1726352*x^3+1768256*x^2+771072*x)*exp(5) 
+(560*x^13+26560*x^12+560016*x^11+6988480*x^10+57754080*x^9+334108800*x^8+ 
1390828320*x^7+4205851776*x^6+9183475440*x^5+14137467840*x^4+14579591760*x 
^3+9051030720*x^2+2559734784*x)*exp(5)^9+((2*x^9+48*x^8+504*x^7+3024*x^6+1 
1340*x^5+27216*x^4+40824*x^3+34992*x^2+13122*x)*exp(5)^8+(16*x^8+336*x^7+3 
024*x^6+15120*x^5+45360*x^4+81648*x^3+81648*x^2+34992*x)*exp(5)^7+(8*x^8+2 
24*x^7+2520*x^6+15120*x^5+52920*x^4+108864*x^3+122472*x^2+58320*x)*exp(5)^ 
6+(48*x^7+976*x^6+8160*x^5+36000*x^4+88560*x^3+115344*x^2+62208*x)*exp(5)^ 
5+(12*x^7+340*x^6+3608*x^5+19176*x^4+54972*x^3+81540*x^2+49248*x)*exp(5)^4 
+(48*x^6+896*x^5+6496*x^4+23040*x^3+40176*x^2+27648*x)*exp(5)^3+(8*x^6+200 
*x^5+1800*x^4+7544*x^3+15024*x^2+11520*x)*exp(5)^2+(16*x^5+256*x^4+1456*x^ 
3+3520*x^2+3072*x)*exp(5)+2*x^5+36*x^4+226*x^3+576*x^2+502*x)*ln(x)+36*x^8 
+x^9+550*x^7+4644*x^6+144576*x^2+139670*x^3+74124*x^4+23639*x^5),x,method= 
_RETURNVERBOSE)
 

Output:

4/(251+8*exp(5+4*ln(x))+20088*exp(ln(x)+15)+3772*exp(10+2*ln(x))+7512*exp( 
10+ln(x))+128*exp(3*ln(x)+5)+288*x+13824*exp(15)+24624*exp(20)+5760*exp(10 
)+31104*exp(25)+1536*exp(5)+6561*exp(40)+ln(x)+113*x^2+18*x^3+x^4+29160*ex 
p(30)+1512*exp(35+5*ln(x))+24*exp(40+7*ln(x))+5670*exp(40+4*ln(x))+40770*e 
xp(20+ln(x))+6*exp(20+6*ln(x))+22680*exp(35+3*ln(x))+7560*exp(30+4*ln(x))+ 
24*exp(25+6*ln(x))+1512*exp(40+5*ln(x))+1260*exp(30+5*ln(x))+252*exp(40+6* 
ln(x))+40824*exp(35+2*ln(x))+26460*exp(30+3*ln(x))+61236*exp(30+ln(x))+576 
72*exp(ln(x)+25)+168*exp(35+6*ln(x))+4*exp(30+7*ln(x))+728*exp(5+2*ln(x))+ 
11520*exp(15+2*ln(x))+448*exp(15+4*ln(x))+54432*exp(30+2*ln(x))+18000*exp( 
25+3*ln(x))+20412*exp(40+2*ln(x))+112*exp(30+6*ln(x))+4080*exp(25+4*ln(x)) 
+900*exp(10+3*ln(x))+1760*exp(5+ln(x))+100*exp(10+4*ln(x))+44280*exp(25+2* 
ln(x))+3248*exp(15+3*ln(x))+40824*exp(35+ln(x))+17496*exp(40+ln(x))+exp(40 
+8*ln(x))+4*exp(10+5*ln(x))+27486*exp(20+2*ln(x))+8*exp(35+7*ln(x))+1804*e 
xp(4*ln(x)+20)+488*exp(25+5*ln(x))+24*exp(15+5*ln(x))+170*exp(20+5*ln(x))+ 
9588*exp(20+3*ln(x))+13608*exp(40+3*ln(x))+7560*exp(35+4*ln(x))+17496*exp( 
35))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 285 vs. \(2 (27) = 54\).

Time = 0.13 (sec) , antiderivative size = 285, normalized size of antiderivative = 10.18 \[ \text {the integral} =\frac {4}{x^{4} + 18 \, x^{3} + 113 \, x^{2} + {\left (x^{8} + 24 \, x^{7} + 252 \, x^{6} + 1512 \, x^{5} + 5670 \, x^{4} + 13608 \, x^{3} + 20412 \, x^{2} + 17496 \, x + 6561\right )} e^{40} + 8 \, {\left (x^{7} + 21 \, x^{6} + 189 \, x^{5} + 945 \, x^{4} + 2835 \, x^{3} + 5103 \, x^{2} + 5103 \, x + 2187\right )} e^{35} + 4 \, {\left (x^{7} + 28 \, x^{6} + 315 \, x^{5} + 1890 \, x^{4} + 6615 \, x^{3} + 13608 \, x^{2} + 15309 \, x + 7290\right )} e^{30} + 8 \, {\left (3 \, x^{6} + 61 \, x^{5} + 510 \, x^{4} + 2250 \, x^{3} + 5535 \, x^{2} + 7209 \, x + 3888\right )} e^{25} + 2 \, {\left (3 \, x^{6} + 85 \, x^{5} + 902 \, x^{4} + 4794 \, x^{3} + 13743 \, x^{2} + 20385 \, x + 12312\right )} e^{20} + 8 \, {\left (3 \, x^{5} + 56 \, x^{4} + 406 \, x^{3} + 1440 \, x^{2} + 2511 \, x + 1728\right )} e^{15} + 4 \, {\left (x^{5} + 25 \, x^{4} + 225 \, x^{3} + 943 \, x^{2} + 1878 \, x + 1440\right )} e^{10} + 8 \, {\left (x^{4} + 16 \, x^{3} + 91 \, x^{2} + 220 \, x + 192\right )} e^{5} + 288 \, x + \log \left (x\right ) + 251} \] Input:

integrate(((-32*x^8-672*x^7-6048*x^6-30240*x^5-90720*x^4-163296*x^3-163296 
*x^2-69984*x)*exp(5)^8+(-224*x^7-4032*x^6-30240*x^5-120960*x^4-272160*x^3- 
326592*x^2-163296*x)*exp(5)^7+(-112*x^7-2688*x^6-25200*x^5-120960*x^4-3175 
20*x^3-435456*x^2-244944*x)*exp(5)^6+(-576*x^6-9760*x^5-65280*x^4-216000*x 
^3-354240*x^2-230688*x)*exp(5)^5+(-144*x^6-3400*x^5-28864*x^4-115056*x^3-2 
19888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80352* 
x)*exp(5)^3+(-80*x^5-1600*x^4-10800*x^3-30176*x^2-30048*x)*exp(5)^2+(-128* 
x^4-1536*x^3-5824*x^2-7040*x)*exp(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(630 
01*x+(8*x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4 
[phone]*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^16+720*x^15+15120*x^1 
4+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+225173520*x^9+67552 
0560*x^8+1576214640*x^7+2837186352*x^6+3868890480*x^5+3868890480*x^4+26784 
62640*x^3+1147912560*x^2+229582512*x)*exp(5)^15+(8*x^16+480*x^15+12600*x^1 
4+196560*x^13+2063880*x^12+15567552*x^11+87567480*x^10+375289200*x^9+12384 
54360*x^8+3152429280*x^7+6147237096*x^6+9027411120*x^5+9672226200*x^4+7142 
567040*x^3+3252418920*x^2+688747536*x)*exp(5)^14+(112*x^15+5264*x^14+11356 
8*x^13+1493856*x^12+13405392*x^11+86918832*x^10+420323904*x^9+1541187648*x 
^8+4308320016*x^7+9142044912*x^6+14501174688*x^5+16679216736*x^4+131542276 
32*x^3+6368788944*x^2+1428513408*x)*exp(5)^13+(28*x^15+1908*x^14+53288*x^1 
3+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516 
653636*x^7+10416007404*x^6+17828546472*x^5+21996618552*x^4+18514695852*x^3 
[phone]*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346656*x^12+4 
492224*x^11+39132720*x^10+242580096*x^9+1102901184*x^8+3729027456*x^7+9386 
848944*x^6+17390324160*x^5+23064696864*x^4+20751235776*x^3+11357248464*x^2 
[phone]*x)*exp(5)^11+x*log(x)^2+(56*x^14+4056*x^13+114904*x^12+1822216 
*x^11+18638400*x^10+132024816*x^9+672897456*x^8+2514459024*x^7+6918985656* 
x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+11112864336*x^2+296284 
2624*x)*exp(5)^10+23639*x^5+144576*x^2+4644*x^6+550*x^7+(x^17+48*x^16+1080 
*x^15+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440 
070*x^9+225173520*x^8+472864392*x^7+773778096*x^6+967222620*x^5+892820880* 
x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+5100*x^12+1 
41486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+213690355 
2*x^6+5085305874*x^5+8457998940*x^4+9357185934*x^3+6195088656*x^2+18592693 
02*x)*exp(5)^8+(560*x^12+25680*x^11+516864*x^10+6071424*x^9+46486928*x^8+2 
44526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+5049648864*x^3+35 
69522256*x^2+1137484944*x)*exp(5)^7+(56*x^12+3888*x^11+102144*x^10+1458624 
*x^9+13024328*x^8+77750400*x^7+320091912*x^6+915313392*x^5+1790543232*x^4+ 
2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+14480*x^10+2 
71056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627485328*x^ 
4+865077840*x^3+697894704*x^2+250511616*x)*exp(5)^5+(28*x^11+1740*x^10+415 
96*x^9+537772*x^8+4285848*x^7+22350752*x^6+78004732*x^5+181099452*x^4+2689 
57044*x^3+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73872*x^8+ 
705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2 
[phone]*x)*exp(5)^3+(560*x^13+26560*x^12+560016*x^11+6988480*x^10+577540 
80*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^5+14137467 
840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9+((2*x^9+48*x 
^8+504*x^7+3024*x^6+11340*x^5+27216*x^4+40824*x^3+34992*x^2+13122*x)*exp(5 
)^8+(16*x^8+336*x^7+3024*x^6+15120*x^5+45360*x^4+81648*x^3+81648*x^2+34992 
*x)*exp(5)^7+(8*x^8+224*x^7+2520*x^6+15120*x^5+52920*x^4+108864*x^3+122472 
*x^2+58320*x)*exp(5)^6+(48*x^7+976*x^6+8160*x^5+36000*x^4+88560*x^3+115344 
*x^2+62208*x)*exp(5)^5+(12*x^7+340*x^6+3608*x^5+19176*x^4+54972*x^3+81540* 
x^2+49248*x)*exp(5)^4+(48*x^6+896*x^5+6496*x^4+23040*x^3+40176*x^2+27648*x 
)*exp(5)^3+(8*x^6+200*x^5+1800*x^4+7544*x^3+15024*x^2+11520*x)*exp(5)^2+(1 
6*x^5+256*x^4+1456*x^3+3520*x^2+3072*x)*exp(5)+2*x^5+36*x^4+226*x^3+576*x^ 
2+502*x)*log(x)+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1 
726352*x^3+1768256*x^2+771072*x)*exp(5)+74124*x^4+139670*x^3+x^9+36*x^8),x 
, algorithm="fricas")
 

Output:

4/(x^4 + 18*x^3 + 113*x^2 + (x^8 + 24*x^7 + 252*x^6 + 1512*x^5 + 5670*x^4 
+ 13608*x^3 + 20412*x^2 + 17496*x + 6561)*e^40 + 8*(x^7 + 21*x^6 + 189*x^5 
 + 945*x^4 + 2835*x^3 + 5103*x^2 + 5103*x + 2187)*e^35 + 4*(x^7 + 28*x^6 + 
 315*x^5 + 1890*x^4 + 6615*x^3 + 13608*x^2 + 15309*x + 7290)*e^30 + 8*(3*x 
^6 + 61*x^5 + 510*x^4 + 2250*x^3 + 5535*x^2 + 7209*x + 3888)*e^25 + 2*(3*x 
^6 + 85*x^5 + 902*x^4 + 4794*x^3 + 13743*x^2 + 20385*x + 12312)*e^20 + 8*( 
3*x^5 + 56*x^4 + 406*x^3 + 1440*x^2 + 2511*x + 1728)*e^15 + 4*(x^5 + 25*x^ 
4 + 225*x^3 + 943*x^2 + 1878*x + 1440)*e^10 + 8*(x^4 + 16*x^3 + 91*x^2 + 2 
20*x + 192)*e^5 + 288*x + log(x) + 251)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 456 vs. \(2 (24) = 48\).

Time = 1.71 (sec) , antiderivative size = 456, normalized size of antiderivative = 16.29 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 4 x^{7} e^{30} + 8 x^{7} e^{35} + 24 x^{7} e^{40} + 6 x^{6} e^{20} + 24 x^{6} e^{25} + 112 x^{6} e^{30} + 168 x^{6} e^{35} + 252 x^{6} e^{40} + 4 x^{5} e^{10} + 24 x^{5} e^{15} + 170 x^{5} e^{20} + 488 x^{5} e^{25} + 1260 x^{5} e^{30} + 1512 x^{5} e^{35} + 1512 x^{5} e^{40} + x^{4} + 8 x^{4} e^{5} + 100 x^{4} e^{10} + 448 x^{4} e^{15} + 1804 x^{4} e^{20} + 4080 x^{4} e^{25} + 7560 x^{4} e^{30} + 7560 x^{4} e^{35} + 5670 x^{4} e^{40} + 18 x^{3} + 128 x^{3} e^{5} + 900 x^{3} e^{10} + 3248 x^{3} e^{15} + 9588 x^{3} e^{20} + 18000 x^{3} e^{25} + 26460 x^{3} e^{30} + 22680 x^{3} e^{35} + 13608 x^{3} e^{40} + 113 x^{2} + 728 x^{2} e^{5} + 3772 x^{2} e^{10} + 11520 x^{2} e^{15} + 27486 x^{2} e^{20} + 44280 x^{2} e^{25} + 54432 x^{2} e^{30} + 40824 x^{2} e^{35} + 20412 x^{2} e^{40} + 288 x + 1760 x e^{5} + 7512 x e^{10} + 20088 x e^{15} + 40770 x e^{20} + 57672 x e^{25} + 61236 x e^{30} + 40824 x e^{35} + 17496 x e^{40} + \log {\left (x \right )} + 251 + 1536 e^{5} + 5760 e^{10} + 13824 e^{15} + 24624 e^{20} + 31104 e^{25} + 29160 e^{30} + 17496 e^{35} + 6561 e^{40}} \] Input:

integrate(((-32*x**8-672*x**7-6048*x**6-30240*x**5-90720*x**4-163296*x**3- 
163296*x**2-69984*x)*exp(5)**8+(-224*x**7-4032*x**6-30240*x**5-120960*x**4 
-272160*x**3-326592*x**2-163296*x)*exp(5)**7+(-112*x**7-2688*x**6-25200*x* 
*5-120960*x**4-317520*x**3-435456*x**2-244944*x)*exp(5)**6+(-576*x**6-9760 
*x**5-65280*x**4-216000*x**3-354240*x**2-230688*x)*exp(5)**5+(-144*x**6-34 
00*x**5-28864*x**4-115056*x**3-219888*x**2-163080*x)*exp(5)**4+(-480*x**5- 
7168*x**4-38976*x**3-92160*x**2-80352*x)*exp(5)**3+(-80*x**5-1600*x**4-108 
00*x**3-30176*x**2-30048*x)*exp(5)**2+(-128*x**4-1536*x**3-5824*x**2-7040* 
x)*exp(5)-16*x**4-216*x**3-904*x**2-1152*x-4)/(63001*x+(8*x**16+480*x**15+ 
12600*x**14+196560*x**13+2063880*x**12+15567552*x**11+87567480*x**10+37528 
9200*x**9+1238454360*x**8+3152429280*x**7+6147237096*x**6+9027411120*x**5+ 
9672226200*x**4+7142567040*x**3+3252418920*x**2+688747536*x)*exp(5)**14+(1 
12*x**15+5264*x**14+113568*x**13+1493856*x**12+13405392*x**11+86918832*x** 
10+420323904*x**9+1541187648*x**8+4308320016*x**7+9142044912*x**6+14501174 
688*x**5+16679216736*x**4+13154227632*x**3+6368788944*x**2+1428513408*x)*e 
xp(5)**13+(28*x**15+1908*x**14+53288*x**13+854136*x**12+8996724*x**11+6675 
4908*x**10+362715408*x**9+1473828048*x**8+4516653636*x**7+10416007404*x**6 
[phone]*x**5+21996618552*x**4+18514695852*x**3+9525548484*x**2+226181 
2896*x)*exp(5)**12+(336*x**14+16064*x**13+346656*x**12+4492224*x**11+39132 
720*x**10+242580096*x**9+1102901184*x**8+3729027456*x**7+9386848944*x**6+1 
7390324160*x**5+23064696864*x**4+20751235776*x**3+11357248464*x**2+2857026 
816*x)*exp(5)**11+(56*x**14+4056*x**13+114904*x**12+1822216*x**11+18638400 
*x**10+132024816*x**9+672897456*x**8+2514459024*x**7+6918985656*x**6+13890 
511800*x**5+19822775544*x**4+19076921064*x**3+11112864336*x**2+2962842624* 
x)*exp(5)**10+144576*x**2+x*ln(x)**2+x**9+550*x**7+23639*x**5+139670*x**3+ 
36*x**8+74124*x**4+(560*x**12+25680*x**11+516864*x**10+6071424*x**9+464869 
28*x**8+244526352*x**7+904257648*x**6+2356128432*x**5+4246618752*x**4+5049 
648864*x**3+3569522256*x**2+1137484944*x)*exp(5)**7+(56*x**12+3888*x**11+1 
02144*x**10+1458624*x**9+13024328*x**8+77750400*x**7+320091912*x**6+915313 
392*x**5+1790543232*x**4+2290471344*x**3+1729205496*x**2+584961264*x)*exp( 
5)**6+(336*x**11+14480*x**10+271056*x**9+2920080*x**8+20140928*x**7+932680 
00*x**6+294493200*x**5+627485328*x**4+865077840*x**3+697894704*x**2+250511 
616*x)*exp(5)**5+(28*x**11+1740*x**10+41596*x**9+537772*x**8+4285848*x**7+ 
22350752*x**6+78004732*x**5+181099452*x**4+268957044*x**3+231559020*x**2+8 
8006176*x)*exp(5)**4+(112*x**10+4384*x**9+73872*x**8+705472*x**7+4219552*x 
**6+16432544*x**5+41757840*x**4+66894336*x**3+61398864*x**2+24634368*x)*ex 
p(5)**3+(8*x**10+408*x**9+8352*x**8+92880*x**7+628352*x**6+2708144*x**5+74 
85320*x**4+12856232*x**3+12495504*x**2+5250816*x)*exp(5)**2+(16*x**16+720* 
x**15+15120*x**14+196560*x**13+1769040*x**12+11675664*x**11+58378320*x**10 
[phone]*x**9+675520560*x**8+1576214640*x**7+2837186352*x**6+3868890480* 
x**5+3868890480*x**4+2678462640*x**3+1147912560*x**2+229582512*x)*exp(5)** 
15+((2*x**9+48*x**8+504*x**7+3024*x**6+11340*x**5+27216*x**4+40824*x**3+34 
992*x**2+13122*x)*exp(5)**8+(16*x**8+336*x**7+3024*x**6+15120*x**5+45360*x 
**4+81648*x**3+81648*x**2+34992*x)*exp(5)**7+(8*x**8+224*x**7+2520*x**6+15 
120*x**5+52920*x**4+108864*x**3+122472*x**2+58320*x)*exp(5)**6+(48*x**7+97 
6*x**6+8160*x**5+36000*x**4+88560*x**3+115344*x**2+62208*x)*exp(5)**5+(12* 
x**7+340*x**6+3608*x**5+19176*x**4+54972*x**3+81540*x**2+49248*x)*exp(5)** 
4+(48*x**6+896*x**5+6496*x**4+23040*x**3+40176*x**2+27648*x)*exp(5)**3+(8* 
x**6+200*x**5+1800*x**4+7544*x**3+15024*x**2+11520*x)*exp(5)**2+(16*x**5+2 
56*x**4+1456*x**3+3520*x**2+3072*x)*exp(5)+2*x**5+36*x**4+226*x**3+576*x** 
2+502*x)*ln(x)+(x**17+48*x**16+1080*x**15+15120*x**14+147420*x**13+1061424 
*x**12+5837832*x**11+25019280*x**10+84440070*x**9+225173520*x**8+472864392 
*x**7+773778096*x**6+967222620*x**5+892820880*x**4+573956280*x**3+22958251 
2*x**2+43046721*x)*exp(5)**16+(70*x**13+5100*x**12+141486*x**11+2158608*x* 
*10+20901410*x**9+137808408*x**8+641272212*x**7+2136903552*x**6+5085305874 
*x**5+8457998940*x**4+9357185934*x**3+6195088656*x**2+1859269302*x)*exp(5) 
**8+(16*x**9+544*x**8+7872*x**7+63264*x**6+308704*x**5+936640*x**4+1726352 
*x**3+1768256*x**2+771072*x)*exp(5)+(560*x**13+26560*x**12+560016*x**11+69 
88480*x**10+57754080*x**9+334108800*x**8+1390828320*x**7+4205851776*x**6+9 
183475440*x**5+14137467840*x**4+14579591760*x**3+9051030720*x**2+255973478 
4*x)*exp(5)**9+4644*x**6),x)
 

Output:

4/(x**8*exp(40) + 4*x**7*exp(30) + 8*x**7*exp(35) + 24*x**7*exp(40) + 6*x* 
*6*exp(20) + 24*x**6*exp(25) + 112*x**6*exp(30) + 168*x**6*exp(35) + 252*x 
**6*exp(40) + 4*x**5*exp(10) + 24*x**5*exp(15) + 170*x**5*exp(20) + 488*x* 
*5*exp(25) + 1260*x**5*exp(30) + 1512*x**5*exp(35) + 1512*x**5*exp(40) + x 
**4 + 8*x**4*exp(5) + 100*x**4*exp(10) + 448*x**4*exp(15) + 1804*x**4*exp( 
20) + 4080*x**4*exp(25) + 7560*x**4*exp(30) + 7560*x**4*exp(35) + 5670*x** 
4*exp(40) + 18*x**3 + 128*x**3*exp(5) + 900*x**3*exp(10) + 3248*x**3*exp(1 
5) + 9588*x**3*exp(20) + 18000*x**3*exp(25) + 26460*x**3*exp(30) + 22680*x 
**3*exp(35) + 13608*x**3*exp(40) + 113*x**2 + 728*x**2*exp(5) + 3772*x**2* 
exp(10) + 11520*x**2*exp(15) + 27486*x**2*exp(20) + 44280*x**2*exp(25) + 5 
4432*x**2*exp(30) + 40824*x**2*exp(35) + 20412*x**2*exp(40) + 288*x + 1760 
*x*exp(5) + 7512*x*exp(10) + 20088*x*exp(15) + 40770*x*exp(20) + 57672*x*e 
xp(25) + 61236*x*exp(30) + 40824*x*exp(35) + 17496*x*exp(40) + log(x) + 25 
1 + 1536*exp(5) + 5760*exp(10) + 13824*exp(15) + 24624*exp(20) + 31104*exp 
(25) + 29160*exp(30) + 17496*exp(35) + 6561*exp(40))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 274 vs. \(2 (27) = 54\).

Time = 0.62 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.79 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 4 \, x^{7} {\left (6 \, e^{40} + 2 \, e^{35} + e^{30}\right )} + 2 \, x^{6} {\left (126 \, e^{40} + 84 \, e^{35} + 56 \, e^{30} + 12 \, e^{25} + 3 \, e^{20}\right )} + 2 \, x^{5} {\left (756 \, e^{40} + 756 \, e^{35} + 630 \, e^{30} + 244 \, e^{25} + 85 \, e^{20} + 12 \, e^{15} + 2 \, e^{10}\right )} + x^{4} {\left (5670 \, e^{40} + 7560 \, e^{35} + 7560 \, e^{30} + 4080 \, e^{25} + 1804 \, e^{20} + 448 \, e^{15} + 100 \, e^{10} + 8 \, e^{5} + 1\right )} + 2 \, x^{3} {\left (6804 \, e^{40} + 11340 \, e^{35} + 13230 \, e^{30} + 9000 \, e^{25} + 4794 \, e^{20} + 1624 \, e^{15} + 450 \, e^{10} + 64 \, e^{5} + 9\right )} + x^{2} {\left (20412 \, e^{40} + 40824 \, e^{35} + 54432 \, e^{30} + 44280 \, e^{25} + 27486 \, e^{20} + 11520 \, e^{15} + 3772 \, e^{10} + 728 \, e^{5} + 113\right )} + 2 \, x {\left (8748 \, e^{40} + 20412 \, e^{35} + 30618 \, e^{30} + 28836 \, e^{25} + 20385 \, e^{20} + 10044 \, e^{15} + 3756 \, e^{10} + 880 \, e^{5} + 144\right )} + 6561 \, e^{40} + 17496 \, e^{35} + 29160 \, e^{30} + 31104 \, e^{25} + 24624 \, e^{20} + 13824 \, e^{15} + 5760 \, e^{10} + 1536 \, e^{5} + \log \left (x\right ) + 251} \] Input:

integrate(((-32*x^8-672*x^7-6048*x^6-30240*x^5-90720*x^4-163296*x^3-163296 
*x^2-69984*x)*exp(5)^8+(-224*x^7-4032*x^6-30240*x^5-120960*x^4-272160*x^3- 
326592*x^2-163296*x)*exp(5)^7+(-112*x^7-2688*x^6-25200*x^5-120960*x^4-3175 
20*x^3-435456*x^2-244944*x)*exp(5)^6+(-576*x^6-9760*x^5-65280*x^4-216000*x 
^3-354240*x^2-230688*x)*exp(5)^5+(-144*x^6-3400*x^5-28864*x^4-115056*x^3-2 
19888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80352* 
x)*exp(5)^3+(-80*x^5-1600*x^4-10800*x^3-30176*x^2-30048*x)*exp(5)^2+(-128* 
x^4-1536*x^3-5824*x^2-7040*x)*exp(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(630 
01*x+(8*x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4 
[phone]*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^16+720*x^15+15120*x^1 
4+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+225173520*x^9+67552 
0560*x^8+1576214640*x^7+2837186352*x^6+3868890480*x^5+3868890480*x^4+26784 
62640*x^3+1147912560*x^2+229582512*x)*exp(5)^15+(8*x^16+480*x^15+12600*x^1 
4+196560*x^13+2063880*x^12+15567552*x^11+87567480*x^10+375289200*x^9+12384 
54360*x^8+3152429280*x^7+6147237096*x^6+9027411120*x^5+9672226200*x^4+7142 
567040*x^3+3252418920*x^2+688747536*x)*exp(5)^14+(112*x^15+5264*x^14+11356 
8*x^13+1493856*x^12+13405392*x^11+86918832*x^10+420323904*x^9+1541187648*x 
^8+4308320016*x^7+9142044912*x^6+14501174688*x^5+16679216736*x^4+131542276 
32*x^3+6368788944*x^2+1428513408*x)*exp(5)^13+(28*x^15+1908*x^14+53288*x^1 
3+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516 
653636*x^7+10416007404*x^6+17828546472*x^5+21996618552*x^4+18514695852*x^3 
[phone]*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346656*x^12+4 
492224*x^11+39132720*x^10+242580096*x^9+1102901184*x^8+3729027456*x^7+9386 
848944*x^6+17390324160*x^5+23064696864*x^4+20751235776*x^3+11357248464*x^2 
[phone]*x)*exp(5)^11+x*log(x)^2+(56*x^14+4056*x^13+114904*x^12+1822216 
*x^11+18638400*x^10+132024816*x^9+672897456*x^8+2514459024*x^7+6918985656* 
x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+11112864336*x^2+296284 
2624*x)*exp(5)^10+23639*x^5+144576*x^2+4644*x^6+550*x^7+(x^17+48*x^16+1080 
*x^15+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440 
070*x^9+225173520*x^8+472864392*x^7+773778096*x^6+967222620*x^5+892820880* 
x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+5100*x^12+1 
41486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+213690355 
2*x^6+5085305874*x^5+8457998940*x^4+9357185934*x^3+6195088656*x^2+18592693 
02*x)*exp(5)^8+(560*x^12+25680*x^11+516864*x^10+6071424*x^9+46486928*x^8+2 
44526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+5049648864*x^3+35 
69522256*x^2+1137484944*x)*exp(5)^7+(56*x^12+3888*x^11+102144*x^10+1458624 
*x^9+13024328*x^8+77750400*x^7+320091912*x^6+915313392*x^5+1790543232*x^4+ 
2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+14480*x^10+2 
71056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627485328*x^ 
4+865077840*x^3+697894704*x^2+250511616*x)*exp(5)^5+(28*x^11+1740*x^10+415 
96*x^9+537772*x^8+4285848*x^7+22350752*x^6+78004732*x^5+181099452*x^4+2689 
57044*x^3+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73872*x^8+ 
705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2 
[phone]*x)*exp(5)^3+(560*x^13+26560*x^12+560016*x^11+6988480*x^10+577540 
80*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^5+14137467 
840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9+((2*x^9+48*x 
^8+504*x^7+3024*x^6+11340*x^5+27216*x^4+40824*x^3+34992*x^2+13122*x)*exp(5 
)^8+(16*x^8+336*x^7+3024*x^6+15120*x^5+45360*x^4+81648*x^3+81648*x^2+34992 
*x)*exp(5)^7+(8*x^8+224*x^7+2520*x^6+15120*x^5+52920*x^4+108864*x^3+122472 
*x^2+58320*x)*exp(5)^6+(48*x^7+976*x^6+8160*x^5+36000*x^4+88560*x^3+115344 
*x^2+62208*x)*exp(5)^5+(12*x^7+340*x^6+3608*x^5+19176*x^4+54972*x^3+81540* 
x^2+49248*x)*exp(5)^4+(48*x^6+896*x^5+6496*x^4+23040*x^3+40176*x^2+27648*x 
)*exp(5)^3+(8*x^6+200*x^5+1800*x^4+7544*x^3+15024*x^2+11520*x)*exp(5)^2+(1 
6*x^5+256*x^4+1456*x^3+3520*x^2+3072*x)*exp(5)+2*x^5+36*x^4+226*x^3+576*x^ 
2+502*x)*log(x)+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1 
726352*x^3+1768256*x^2+771072*x)*exp(5)+74124*x^4+139670*x^3+x^9+36*x^8),x 
, algorithm="maxima")
 

Output:

4/(x^8*e^40 + 4*x^7*(6*e^40 + 2*e^35 + e^30) + 2*x^6*(126*e^40 + 84*e^35 + 
 56*e^30 + 12*e^25 + 3*e^20) + 2*x^5*(756*e^40 + 756*e^35 + 630*e^30 + 244 
*e^25 + 85*e^20 + 12*e^15 + 2*e^10) + x^4*(5670*e^40 + 7560*e^35 + 7560*e^ 
30 + 4080*e^25 + 1804*e^20 + 448*e^15 + 100*e^10 + 8*e^5 + 1) + 2*x^3*(680 
4*e^40 + 11340*e^35 + 13230*e^30 + 9000*e^25 + 4794*e^20 + 1624*e^15 + 450 
*e^10 + 64*e^5 + 9) + x^2*(20412*e^40 + 40824*e^35 + 54432*e^30 + 44280*e^ 
25 + 27486*e^20 + 11520*e^15 + 3772*e^10 + 728*e^5 + 113) + 2*x*(8748*e^40 
 + 20412*e^35 + 30618*e^30 + 28836*e^25 + 20385*e^20 + 10044*e^15 + 3756*e 
^10 + 880*e^5 + 144) + 6561*e^40 + 17496*e^35 + 29160*e^30 + 31104*e^25 + 
24624*e^20 + 13824*e^15 + 5760*e^10 + 1536*e^5 + log(x) + 251)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 375 vs. \(2 (27) = 54\).

Time = 1.75 (sec) , antiderivative size = 375, normalized size of antiderivative = 13.39 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 24 \, x^{7} e^{40} + 8 \, x^{7} e^{35} + 4 \, x^{7} e^{30} + 252 \, x^{6} e^{40} + 168 \, x^{6} e^{35} + 112 \, x^{6} e^{30} + 24 \, x^{6} e^{25} + 6 \, x^{6} e^{20} + 1512 \, x^{5} e^{40} + 1512 \, x^{5} e^{35} + 1260 \, x^{5} e^{30} + 488 \, x^{5} e^{25} + 170 \, x^{5} e^{20} + 24 \, x^{5} e^{15} + 4 \, x^{5} e^{10} + 5670 \, x^{4} e^{40} + 7560 \, x^{4} e^{35} + 7560 \, x^{4} e^{30} + 4080 \, x^{4} e^{25} + 1804 \, x^{4} e^{20} + 448 \, x^{4} e^{15} + 100 \, x^{4} e^{10} + 8 \, x^{4} e^{5} + x^{4} + 13608 \, x^{3} e^{40} + 22680 \, x^{3} e^{35} + 26460 \, x^{3} e^{30} + 18000 \, x^{3} e^{25} + 9588 \, x^{3} e^{20} + 3248 \, x^{3} e^{15} + 900 \, x^{3} e^{10} + 128 \, x^{3} e^{5} + 18 \, x^{3} + 20412 \, x^{2} e^{40} + 40824 \, x^{2} e^{35} + 54432 \, x^{2} e^{30} + 44280 \, x^{2} e^{25} + 27486 \, x^{2} e^{20} + 11520 \, x^{2} e^{15} + 3772 \, x^{2} e^{10} + 728 \, x^{2} e^{5} + 113 \, x^{2} + 17496 \, x e^{40} + 40824 \, x e^{35} + 61236 \, x e^{30} + 57672 \, x e^{25} + 40770 \, x e^{20} + 20088 \, x e^{15} + 7512 \, x e^{10} + 1760 \, x e^{5} + 288 \, x + 6561 \, e^{40} + 17496 \, e^{35} + 29160 \, e^{30} + 31104 \, e^{25} + 24624 \, e^{20} + 13824 \, e^{15} + 5760 \, e^{10} + 1536 \, e^{5} + \log \left (x\right ) + 251} \] Input:

integrate(((-32*x^8-672*x^7-6048*x^6-30240*x^5-90720*x^4-163296*x^3-163296 
*x^2-69984*x)*exp(5)^8+(-224*x^7-4032*x^6-30240*x^5-120960*x^4-272160*x^3- 
326592*x^2-163296*x)*exp(5)^7+(-112*x^7-2688*x^6-25200*x^5-120960*x^4-3175 
20*x^3-435456*x^2-244944*x)*exp(5)^6+(-576*x^6-9760*x^5-65280*x^4-216000*x 
^3-354240*x^2-230688*x)*exp(5)^5+(-144*x^6-3400*x^5-28864*x^4-115056*x^3-2 
19888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80352* 
x)*exp(5)^3+(-80*x^5-1600*x^4-10800*x^3-30176*x^2-30048*x)*exp(5)^2+(-128* 
x^4-1536*x^3-5824*x^2-7040*x)*exp(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(630 
01*x+(8*x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4 
[phone]*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^16+720*x^15+15120*x^1 
4+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+225173520*x^9+67552 
0560*x^8+1576214640*x^7+2837186352*x^6+3868890480*x^5+3868890480*x^4+26784 
62640*x^3+1147912560*x^2+229582512*x)*exp(5)^15+(8*x^16+480*x^15+12600*x^1 
4+196560*x^13+2063880*x^12+15567552*x^11+87567480*x^10+375289200*x^9+12384 
54360*x^8+3152429280*x^7+6147237096*x^6+9027411120*x^5+9672226200*x^4+7142 
567040*x^3+3252418920*x^2+688747536*x)*exp(5)^14+(112*x^15+5264*x^14+11356 
8*x^13+1493856*x^12+13405392*x^11+86918832*x^10+420323904*x^9+1541187648*x 
^8+4308320016*x^7+9142044912*x^6+14501174688*x^5+16679216736*x^4+131542276 
32*x^3+6368788944*x^2+1428513408*x)*exp(5)^13+(28*x^15+1908*x^14+53288*x^1 
3+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516 
653636*x^7+10416007404*x^6+17828546472*x^5+21996618552*x^4+18514695852*x^3 
[phone]*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346656*x^12+4 
492224*x^11+39132720*x^10+242580096*x^9+1102901184*x^8+3729027456*x^7+9386 
848944*x^6+17390324160*x^5+23064696864*x^4+20751235776*x^3+11357248464*x^2 
[phone]*x)*exp(5)^11+x*log(x)^2+(56*x^14+4056*x^13+114904*x^12+1822216 
*x^11+18638400*x^10+132024816*x^9+672897456*x^8+2514459024*x^7+6918985656* 
x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+11112864336*x^2+296284 
2624*x)*exp(5)^10+23639*x^5+144576*x^2+4644*x^6+550*x^7+(x^17+48*x^16+1080 
*x^15+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440 
070*x^9+225173520*x^8+472864392*x^7+773778096*x^6+967222620*x^5+892820880* 
x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+5100*x^12+1 
41486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+213690355 
2*x^6+5085305874*x^5+8457998940*x^4+9357185934*x^3+6195088656*x^2+18592693 
02*x)*exp(5)^8+(560*x^12+25680*x^11+516864*x^10+6071424*x^9+46486928*x^8+2 
44526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+5049648864*x^3+35 
69522256*x^2+1137484944*x)*exp(5)^7+(56*x^12+3888*x^11+102144*x^10+1458624 
*x^9+13024328*x^8+77750400*x^7+320091912*x^6+915313392*x^5+1790543232*x^4+ 
2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+14480*x^10+2 
71056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627485328*x^ 
4+865077840*x^3+697894704*x^2+250511616*x)*exp(5)^5+(28*x^11+1740*x^10+415 
96*x^9+537772*x^8+4285848*x^7+22350752*x^6+78004732*x^5+181099452*x^4+2689 
57044*x^3+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73872*x^8+ 
705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2 
[phone]*x)*exp(5)^3+(560*x^13+26560*x^12+560016*x^11+6988480*x^10+577540 
80*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^5+14137467 
840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9+((2*x^9+48*x 
^8+504*x^7+3024*x^6+11340*x^5+27216*x^4+40824*x^3+34992*x^2+13122*x)*exp(5 
)^8+(16*x^8+336*x^7+3024*x^6+15120*x^5+45360*x^4+81648*x^3+81648*x^2+34992 
*x)*exp(5)^7+(8*x^8+224*x^7+2520*x^6+15120*x^5+52920*x^4+108864*x^3+122472 
*x^2+58320*x)*exp(5)^6+(48*x^7+976*x^6+8160*x^5+36000*x^4+88560*x^3+115344 
*x^2+62208*x)*exp(5)^5+(12*x^7+340*x^6+3608*x^5+19176*x^4+54972*x^3+81540* 
x^2+49248*x)*exp(5)^4+(48*x^6+896*x^5+6496*x^4+23040*x^3+40176*x^2+27648*x 
)*exp(5)^3+(8*x^6+200*x^5+1800*x^4+7544*x^3+15024*x^2+11520*x)*exp(5)^2+(1 
6*x^5+256*x^4+1456*x^3+3520*x^2+3072*x)*exp(5)+2*x^5+36*x^4+226*x^3+576*x^ 
2+502*x)*log(x)+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1 
726352*x^3+1768256*x^2+771072*x)*exp(5)+74124*x^4+139670*x^3+x^9+36*x^8),x 
, algorithm="giac")
 

Output:

4/(x^8*e^40 + 24*x^7*e^40 + 8*x^7*e^35 + 4*x^7*e^30 + 252*x^6*e^40 + 168*x 
^6*e^35 + 112*x^6*e^30 + 24*x^6*e^25 + 6*x^6*e^20 + 1512*x^5*e^40 + 1512*x 
^5*e^35 + 1260*x^5*e^30 + 488*x^5*e^25 + 170*x^5*e^20 + 24*x^5*e^15 + 4*x^ 
5*e^10 + 5670*x^4*e^40 + 7560*x^4*e^35 + 7560*x^4*e^30 + 4080*x^4*e^25 + 1 
804*x^4*e^20 + 448*x^4*e^15 + 100*x^4*e^10 + 8*x^4*e^5 + x^4 + 13608*x^3*e 
^40 + 22680*x^3*e^35 + 26460*x^3*e^30 + 18000*x^3*e^25 + 9588*x^3*e^20 + 3 
248*x^3*e^15 + 900*x^3*e^10 + 128*x^3*e^5 + 18*x^3 + 20412*x^2*e^40 + 4082 
4*x^2*e^35 + 54432*x^2*e^30 + 44280*x^2*e^25 + 27486*x^2*e^20 + 11520*x^2* 
e^15 + 3772*x^2*e^10 + 728*x^2*e^5 + 113*x^2 + 17496*x*e^40 + 40824*x*e^35 
 + 61236*x*e^30 + 57672*x*e^25 + 40770*x*e^20 + 20088*x*e^15 + 7512*x*e^10 
 + 1760*x*e^5 + 288*x + 6561*e^40 + 17496*e^35 + 29160*e^30 + 31104*e^25 + 
 24624*e^20 + 13824*e^15 + 5760*e^10 + 1536*e^5 + log(x) + 251)
 

Mupad [B] (verification not implemented)

Time = 3.65 (sec) , antiderivative size = 271, normalized size of antiderivative = 9.68 \[ \text {the integral} =\frac {4}{1536\,{\mathrm {e}}^5+5760\,{\mathrm {e}}^{10}+13824\,{\mathrm {e}}^{15}+24624\,{\mathrm {e}}^{20}+31104\,{\mathrm {e}}^{25}+29160\,{\mathrm {e}}^{30}+17496\,{\mathrm {e}}^{35}+6561\,{\mathrm {e}}^{40}+\ln \left (x\right )+x\,\left (1760\,{\mathrm {e}}^5+7512\,{\mathrm {e}}^{10}+20088\,{\mathrm {e}}^{15}+40770\,{\mathrm {e}}^{20}+57672\,{\mathrm {e}}^{25}+61236\,{\mathrm {e}}^{30}+40824\,{\mathrm {e}}^{35}+17496\,{\mathrm {e}}^{40}+288\right )+x^6\,\left (6\,{\mathrm {e}}^{20}+24\,{\mathrm {e}}^{25}+112\,{\mathrm {e}}^{30}+168\,{\mathrm {e}}^{35}+252\,{\mathrm {e}}^{40}\right )+x^8\,{\mathrm {e}}^{40}+x^4\,\left (8\,{\mathrm {e}}^5+100\,{\mathrm {e}}^{10}+448\,{\mathrm {e}}^{15}+1804\,{\mathrm {e}}^{20}+4080\,{\mathrm {e}}^{25}+7560\,{\mathrm {e}}^{30}+7560\,{\mathrm {e}}^{35}+5670\,{\mathrm {e}}^{40}+1\right )+x^3\,\left (128\,{\mathrm {e}}^5+900\,{\mathrm {e}}^{10}+3248\,{\mathrm {e}}^{15}+9588\,{\mathrm {e}}^{20}+18000\,{\mathrm {e}}^{25}+26460\,{\mathrm {e}}^{30}+22680\,{\mathrm {e}}^{35}+13608\,{\mathrm {e}}^{40}+18\right )+x^2\,\left (728\,{\mathrm {e}}^5+3772\,{\mathrm {e}}^{10}+11520\,{\mathrm {e}}^{15}+27486\,{\mathrm {e}}^{20}+44280\,{\mathrm {e}}^{25}+54432\,{\mathrm {e}}^{30}+40824\,{\mathrm {e}}^{35}+20412\,{\mathrm {e}}^{40}+113\right )+x^7\,\left (4\,{\mathrm {e}}^{30}+8\,{\mathrm {e}}^{35}+24\,{\mathrm {e}}^{40}\right )+x^5\,\left (4\,{\mathrm {e}}^{10}+24\,{\mathrm {e}}^{15}+170\,{\mathrm {e}}^{20}+488\,{\mathrm {e}}^{25}+1260\,{\mathrm {e}}^{30}+1512\,{\mathrm {e}}^{35}+1512\,{\mathrm {e}}^{40}\right )+251} \] Input:

int(-(1152*x + exp(20)*(163080*x + 219888*x^2 + 115056*x^3 + 28864*x^4 + 3 
400*x^5 + 144*x^6) + exp(25)*(230688*x + 354240*x^2 + 216000*x^3 + 65280*x 
^4 + 9760*x^5 + 576*x^6) + exp(35)*(163296*x + 326592*x^2 + 272160*x^3 + 1 
20960*x^4 + 30240*x^5 + 4032*x^6 + 224*x^7) + exp(30)*(244944*x + 435456*x 
^2 + 317520*x^3 + 120960*x^4 + 25200*x^5 + 2688*x^6 + 112*x^7) + exp(40)*( 
69984*x + 163296*x^2 + 163296*x^3 + 90720*x^4 + 30240*x^5 + 6048*x^6 + 672 
*x^7 + 32*x^8) + exp(5)*(7040*x + 5824*x^2 + 1536*x^3 + 128*x^4) + exp(10) 
*(30048*x + 30176*x^2 + 10800*x^3 + 1600*x^4 + 80*x^5) + exp(15)*(80352*x 
+ 92160*x^2 + 38976*x^3 + 7168*x^4 + 480*x^5) + 904*x^2 + 216*x^3 + 16*x^4 
 + 4)/(63001*x + exp(80)*(43046721*x + 229582512*x^2 + 573956280*x^3 + 892 
820880*x^4 + 967222620*x^5 + 773778096*x^6 + 472864392*x^7 + 225173520*x^8 
 + 84440070*x^9 + 25019280*x^10 + 5837832*x^11 + 1061424*x^12 + 147420*x^1 
3 + 15120*x^14 + 1080*x^15 + 48*x^16 + x^17) + x*log(x)^2 + exp(30)*(58496 
1264*x + 1729205496*x^2 + 2290471344*x^3 + 1790543232*x^4 + 915313392*x^5 
+ 320091912*x^6 + 77750400*x^7 + 13024328*x^8 + 1458624*x^9 + 102144*x^10 
+ 3888*x^11 + 56*x^12) + exp(75)*(229582512*x + 1147912560*x^2 + 267846264 
0*x^3 + 3868890480*x^4 + 3868890480*x^5 + 2837186352*x^6 + 1576214640*x^7 
+ 675520560*x^8 + 225173520*x^9 + 58378320*x^10 + 11675664*x^11 + 1769040* 
x^12 + 196560*x^13 + 15120*x^14 + 720*x^15 + 16*x^16) + exp(60)*(226181289 
6*x + 9525548484*x^2 + 18514695852*x^3 + 21996618552*x^4 + 17828546472*x^5 
 + 10416007404*x^6 + 4516653636*x^7 + 1473828048*x^8 + 362715408*x^9 + 667 
54908*x^10 + 8996724*x^11 + 854136*x^12 + 53288*x^13 + 1908*x^14 + 28*x^15 
) + exp(20)*(88006176*x + 231559020*x^2 + 268957044*x^3 + 181099452*x^4 + 
78004732*x^5 + 22350752*x^6 + 4285848*x^7 + 537772*x^8 + 41596*x^9 + 1740* 
x^10 + 28*x^11) + exp(35)*(1137484944*x + 3569522256*x^2 + 5049648864*x^3 
+ 4246618752*x^4 + 2356128432*x^5 + 904257648*x^6 + 244526352*x^7 + 464869 
28*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^12) + exp(40)*(185 
9269302*x + 6195088656*x^2 + 9357185934*x^3 + 8457998940*x^4 + 5085305874* 
x^5 + 2136903552*x^6 + 641272212*x^7 + 137808408*x^8 + 20901410*x^9 + 2158 
608*x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + exp(45)*(2559734784*x + 90 
51030720*x^2 + 14579591760*x^3 + 14137467840*x^4 + 9183475440*x^5 + 420585 
1776*x^6 + 1390828320*x^7 + 334108800*x^8 + 57754080*x^9 + 6988480*x^10 + 
560016*x^11 + 26560*x^12 + 560*x^13) + log(x)*(502*x + exp(10)*(11520*x + 
15024*x^2 + 7544*x^3 + 1800*x^4 + 200*x^5 + 8*x^6) + exp(15)*(27648*x + 40 
176*x^2 + 23040*x^3 + 6496*x^4 + 896*x^5 + 48*x^6) + exp(20)*(49248*x + 81 
540*x^2 + 54972*x^3 + 19176*x^4 + 3608*x^5 + 340*x^6 + 12*x^7) + exp(25)*( 
62208*x + 115344*x^2 + 88560*x^3 + 36000*x^4 + 8160*x^5 + 976*x^6 + 48*x^7 
) + exp(35)*(34992*x + 81648*x^2 + 81648*x^3 + 45360*x^4 + 15120*x^5 + 302 
4*x^6 + 336*x^7 + 16*x^8) + exp(30)*(58320*x + 122472*x^2 + 108864*x^3 + 5 
2920*x^4 + 15120*x^5 + 2520*x^6 + 224*x^7 + 8*x^8) + exp(40)*(13122*x + 34 
992*x^2 + 40824*x^3 + 27216*x^4 + 11340*x^5 + 3024*x^6 + 504*x^7 + 48*x^8 
+ 2*x^9) + exp(5)*(3072*x + 3520*x^2 + 1456*x^3 + 256*x^4 + 16*x^5) + 576* 
x^2 + 226*x^3 + 36*x^4 + 2*x^5) + exp(70)*(688747536*x + 3252418920*x^2 + 
7142567040*x^3 + 9672226200*x^4 + 9027411120*x^5 + 6147237096*x^6 + 315242 
9280*x^7 + 1238454360*x^8 + 375289200*x^9 + 87567480*x^10 + 15567552*x^11 
+ 2063880*x^12 + 196560*x^13 + 12600*x^14 + 480*x^15 + 8*x^16) + exp(5)*(7 
71072*x + 1768256*x^2 + 1726352*x^3 + 936640*x^4 + 308704*x^5 + 63264*x^6 
+ 7872*x^7 + 544*x^8 + 16*x^9) + exp(55)*(2857026816*x + 11357248464*x^2 + 
 20751235776*x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x^6 + 37 
29027456*x^7 + 1102901184*x^8 + 242580096*x^9 + 39132720*x^10 + 4492224*x^ 
11 + 346656*x^12 + 16064*x^13 + 336*x^14) + exp(50)*(2962842624*x + 111128 
64336*x^2 + 19076921064*x^3 + 19822775544*x^4 + 13890511800*x^5 + 69189856 
56*x^6 + 2514459024*x^7 + 672897456*x^8 + 132024816*x^9 + 18638400*x^10 + 
1822216*x^11 + 114904*x^12 + 4056*x^13 + 56*x^14) + exp(65)*(1428513408*x 
+ 6368788944*x^2 + 13154227632*x^3 + 16679216736*x^4 + 14501174688*x^5 + 9 
142044912*x^6 + 4308320016*x^7 + 1541187648*x^8 + 420323904*x^9 + 86918832 
*x^10 + 13405392*x^11 + 1493856*x^12 + 113568*x^13 + 5264*x^14 + 112*x^15) 
 + exp(25)*(250511616*x + 697894704*x^2 + 865077840*x^3 + 627485328*x^4 + 
294493200*x^5 + 93268000*x^6 + 20140928*x^7 + 2920080*x^8 + 271056*x^9 + 1 
4480*x^10 + 336*x^11) + 144576*x^2 + 139670*x^3 + 74124*x^4 + 23639*x^5 + 
4644*x^6 + 550*x^7 + 36*x^8 + x^9 + exp(10)*(5250816*x + 12495504*x^2 + 12 
856232*x^3 + 7485320*x^4 + 2708144*x^5 + 628352*x^6 + 92880*x^7 + 8352*x^8 
 + 408*x^9 + 8*x^10) + exp(15)*(24634368*x + 61398864*x^2 + 66894336*x^3 + 
 41757840*x^4 + 16432544*x^5 + 4219552*x^6 + 705472*x^7 + 73872*x^8 + 4384 
*x^9 + 112*x^10)),x)
 

Output:

4/(1536*exp(5) + 5760*exp(10) + 13824*exp(15) + 24624*exp(20) + 31104*exp( 
25) + 29160*exp(30) + 17496*exp(35) + 6561*exp(40) + log(x) + x*(1760*exp( 
5) + 7512*exp(10) + 20088*exp(15) + 40770*exp(20) + 57672*exp(25) + 61236* 
exp(30) + 40824*exp(35) + 17496*exp(40) + 288) + x^6*(6*exp(20) + 24*exp(2 
5) + 112*exp(30) + 168*exp(35) + 252*exp(40)) + x^8*exp(40) + x^4*(8*exp(5 
) + 100*exp(10) + 448*exp(15) + 1804*exp(20) + 4080*exp(25) + 7560*exp(30) 
 + 7560*exp(35) + 5670*exp(40) + 1) + x^3*(128*exp(5) + 900*exp(10) + 3248 
*exp(15) + 9588*exp(20) + 18000*exp(25) + 26460*exp(30) + 22680*exp(35) + 
13608*exp(40) + 18) + x^2*(728*exp(5) + 3772*exp(10) + 11520*exp(15) + 274 
86*exp(20) + 44280*exp(25) + 54432*exp(30) + 40824*exp(35) + 20412*exp(40) 
 + 113) + x^7*(4*exp(30) + 8*exp(35) + 24*exp(40)) + x^5*(4*exp(10) + 24*e 
xp(15) + 170*exp(20) + 488*exp(25) + 1260*exp(30) + 1512*exp(35) + 1512*ex 
p(40)) + 251)
 

Reduce [B] (verification not implemented)

Time = 0.24 (sec) , antiderivative size = 431, normalized size of antiderivative = 15.39 \[ \text {the integral} =\frac {4}{251+288 x +900 e^{10} x^{3}+6561 e^{40}+1536 e^{5}+113 x^{2}+e^{40} x^{8}+24 e^{40} x^{7}+252 e^{40} x^{6}+1512 e^{40} x^{5}+5670 e^{40} x^{4}+13608 e^{40} x^{3}+20412 e^{40} x^{2}+17496 e^{40} x +8 e^{35} x^{7}+168 e^{35} x^{6}+1512 e^{35} x^{5}+7560 e^{35} x^{4}+22680 e^{35} x^{3}+40824 e^{35} x^{2}+40824 e^{35} x +4 e^{30} x^{7}+112 e^{30} x^{6}+1260 e^{30} x^{5}+7560 e^{30} x^{4}+26460 e^{30} x^{3}+54432 e^{30} x^{2}+61236 e^{30} x +24 e^{25} x^{6}+488 e^{25} x^{5}+4080 e^{25} x^{4}+18000 e^{25} x^{3}+44280 e^{25} x^{2}+57672 e^{25} x +6 e^{20} x^{6}+170 e^{20} x^{5}+24 e^{15} x^{5}+448 e^{15} x^{4}+3248 e^{15} x^{3}+11520 e^{15} x^{2}+20088 e^{15} x +17496 e^{35}+29160 e^{30}+31104 e^{25}+13824 e^{15}+1804 e^{20} x^{4}+100 e^{10} x^{4}+3772 e^{10} x^{2}+7512 e^{10} x +18 x^{3}+40770 e^{20} x +27486 e^{20} x^{2}+5760 e^{10}+\mathrm {log}\left (x \right )+24624 e^{20}+x^{4}+8 e^{5} x^{4}+128 e^{5} x^{3}+4 e^{10} x^{5}+728 e^{5} x^{2}+1760 e^{5} x +9588 e^{20} x^{3}} \] Input:

int(((-32*x^8-672*x^7-6048*x^6-30240*x^5-90720*x^4-163296*x^3-163296*x^2-6 
9984*x)*exp(5)^8+(-224*x^7-4032*x^6-30240*x^5-120960*x^4-272160*x^3-326592 
*x^2-163296*x)*exp(5)^7+(-112*x^7-2688*x^6-25200*x^5-120960*x^4-317520*x^3 
-435456*x^2-244944*x)*exp(5)^6+(-576*x^6-9760*x^5-65280*x^4-216000*x^3-354 
240*x^2-230688*x)*exp(5)^5+(-144*x^6-3400*x^5-28864*x^4-115056*x^3-219888* 
x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80352*x)*exp 
(5)^3+(-80*x^5-1600*x^4-10800*x^3-30176*x^2-30048*x)*exp(5)^2+(-128*x^4-15 
36*x^3-5824*x^2-7040*x)*exp(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(x*log(x)^ 
2+63001*x+23639*x^5+((2*x^9+48*x^8+504*x^7+3024*x^6+11340*x^5+27216*x^4+40 
824*x^3+34992*x^2+13122*x)*exp(5)^8+(16*x^8+336*x^7+3024*x^6+15120*x^5+453 
60*x^4+81648*x^3+81648*x^2+34992*x)*exp(5)^7+(8*x^8+224*x^7+2520*x^6+15120 
*x^5+52920*x^4+108864*x^3+122472*x^2+58320*x)*exp(5)^6+(48*x^7+976*x^6+816 
0*x^5+36000*x^4+88560*x^3+115344*x^2+62208*x)*exp(5)^5+(12*x^7+340*x^6+360 
8*x^5+19176*x^4+54972*x^3+81540*x^2+49248*x)*exp(5)^4+(48*x^6+896*x^5+6496 
*x^4+23040*x^3+40176*x^2+27648*x)*exp(5)^3+(8*x^6+200*x^5+1800*x^4+7544*x^ 
3+15024*x^2+11520*x)*exp(5)^2+(16*x^5+256*x^4+1456*x^3+3520*x^2+3072*x)*ex 
p(5)+2*x^5+36*x^4+226*x^3+576*x^2+502*x)*log(x)+(x^17+48*x^16+1080*x^15+15 
120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440070*x^9+ 
225173520*x^8+472864392*x^7+773778096*x^6+967222620*x^5+892820880*x^4+5739 
56280*x^3+229582512*x^2+43046721*x)*exp(5)^16+144576*x^2+(70*x^13+5100*x^1 
2+141486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+213690 
3552*x^6+5085305874*x^5+8457998940*x^4+9357185934*x^3+6195088656*x^2+18592 
69302*x)*exp(5)^8+(560*x^12+25680*x^11+516864*x^10+6071424*x^9+46486928*x^ 
8+244526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+5049648864*x^3 
[phone]*x^2+1137484944*x)*exp(5)^7+(56*x^12+3888*x^11+102144*x^10+1458 
624*x^9+13024328*x^8+77750400*x^7+320091912*x^6+915313392*x^5+1790543232*x 
^4+2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+14480*x^1 
0+271056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627485328 
*x^4+865077840*x^3+697894704*x^2+250511616*x)*exp(5)^5+(28*x^11+1740*x^10+ 
41596*x^9+537772*x^8+4285848*x^7+22350752*x^6+78004732*x^5+181099452*x^4+2 
68957044*x^3+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73872*x 
^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864* 
x^2+24634368*x)*exp(5)^3+(8*x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+270 
8144*x^5+7485320*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^1 
6+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10 
[phone]*x^9+675520560*x^8+1576214640*x^7+2837186352*x^6+3868890480*x^5+ 
3868890480*x^4+2678462640*x^3+1147912560*x^2+229582512*x)*exp(5)^15+4644*x 
^6+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1726352*x^3+17 
68256*x^2+771072*x)*exp(5)+(560*x^13+26560*x^12+560016*x^11+6988480*x^10+5 
7754080*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^5+141 
37467840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9+36*x^8+ 
550*x^7+74124*x^4+139670*x^3+(8*x^16+480*x^15+12600*x^14+196560*x^13+20638 
80*x^12+15567552*x^11+87567480*x^10+375289200*x^9+1238454360*x^8+315242928 
0*x^7+6147237096*x^6+9027411120*x^5+9672226200*x^4+7142567040*x^3+32524189 
20*x^2+688747536*x)*exp(5)^14+(112*x^15+5264*x^14+113568*x^13+1493856*x^12 
[phone]*x^11+86918832*x^10+420323904*x^9+1541187648*x^8+4308320016*x^7+9 
142044912*x^6+14501174688*x^5+16679216736*x^4+13154227632*x^3+6368788944*x 
^2+1428513408*x)*exp(5)^13+(28*x^15+1908*x^14+53288*x^13+854136*x^12+89967 
24*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516653636*x^7+10416007 
404*x^6+17828546472*x^5+21996618552*x^4+18514695852*x^3+9525548484*x^2+226 
1812896*x)*exp(5)^12+(336*x^14+16064*x^13+346656*x^12+4492224*x^11+3913272 
0*x^10+242580096*x^9+1102901184*x^8+3729027456*x^7+9386848944*x^6+17390324 
160*x^5+23064696864*x^4+20751235776*x^3+11357248464*x^2+2857026816*x)*exp( 
5)^11+(56*x^14+4056*x^13+114904*x^12+1822216*x^11+18638400*x^10+132024816* 
x^9+672897456*x^8+2514459024*x^7+6918985656*x^6+13890511800*x^5+1982277554 
4*x^4+19076921064*x^3+11112864336*x^2+2962842624*x)*exp(5)^10+x^9),x)
 

Output:

4/(log(x) + e**40*x**8 + 24*e**40*x**7 + 252*e**40*x**6 + 1512*e**40*x**5 
+ 5670*e**40*x**4 + 13608*e**40*x**3 + 20412*e**40*x**2 + 17496*e**40*x + 
6561*e**40 + 8*e**35*x**7 + 168*e**35*x**6 + 1512*e**35*x**5 + 7560*e**35* 
x**4 + 22680*e**35*x**3 + 40824*e**35*x**2 + 40824*e**35*x + 17496*e**35 + 
 4*e**30*x**7 + 112*e**30*x**6 + 1260*e**30*x**5 + 7560*e**30*x**4 + 26460 
*e**30*x**3 + 54432*e**30*x**2 + 61236*e**30*x + 29160*e**30 + 24*e**25*x* 
*6 + 488*e**25*x**5 + 4080*e**25*x**4 + 18000*e**25*x**3 + 44280*e**25*x** 
2 + 57672*e**25*x + 31104*e**25 + 6*e**20*x**6 + 170*e**20*x**5 + 1804*e** 
20*x**4 + 9588*e**20*x**3 + 27486*e**20*x**2 + 40770*e**20*x + 24624*e**20 
 + 24*e**15*x**5 + 448*e**15*x**4 + 3248*e**15*x**3 + 11520*e**15*x**2 + 2 
0088*e**15*x + 13824*e**15 + 4*e**10*x**5 + 100*e**10*x**4 + 900*e**10*x** 
3 + 3772*e**10*x**2 + 7512*e**10*x + 5760*e**10 + 8*e**5*x**4 + 128*e**5*x 
**3 + 728*e**5*x**2 + 1760*e**5*x + 1536*e**5 + x**4 + 18*x**3 + 113*x**2 
+ 288*x + 251)