Integrand size = 1752, antiderivative size = 28 \[ \text {the integral} =\frac {4}{-5+\left (x+\left (3+x+\left (1+e^5 (3+x)\right )^2\right )^2\right )^2+\log (x)} \]
Leaf count is larger than twice the leaf count of optimal. \(157\) vs. \(2(28)=56\).
Time = 0.69 (sec) , antiderivative size = 157, normalized size of antiderivative = 5.61 \[ \text {the integral} =\frac {4}{251+288 x+113 x^2+18 x^3+x^4+8 e^{35} (3+x)^7+e^{40} (3+x)^8+4 e^{30} (3+x)^6 (10+x)+8 e^{25} (3+x)^5 (16+3 x)+8 e^{15} (3+x)^3 \left (64+29 x+3 x^2\right )+2 e^{20} (3+x)^4 \left (152+49 x+3 x^2\right )+4 e^{10} (3+x)^2 \left (160+102 x+19 x^2+x^3\right )+8 e^5 \left (192+220 x+91 x^2+16 x^3+x^4\right )+\log (x)} \]
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]
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])
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}+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\right )+e^{45} \left (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\right )+e^{50} \left (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+2962842624 x\right )+e^{55} \left (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\right )+e^{60} \left (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\right )+e^{65} \left (112 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+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}+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\right )+e^{75} \left (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+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}+25019280 x^{10}+84440070 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\) |
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]
3.30.36.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(470\) vs. \(2(27)=54\).
Time = 19.83 (sec) , antiderivative size = 471, normalized size of antiderivative = 16.82
method | result | size |
default | \(\frac {4}{251+6561 \,{\mathrm e}^{40}+6 \,{\mathrm e}^{20+6 \ln \left (x \right )}+17496 \,{\mathrm e}^{40+\ln \left (x \right )}+54432 \,{\mathrm e}^{30+2 \ln \left (x \right )}+11520 \,{\mathrm e}^{2 \ln \left (x \right )+15}+22680 \,{\mathrm e}^{35+3 \ln \left (x \right )}+40824 \,{\mathrm e}^{35+\ln \left (x \right )}+168 \,{\mathrm e}^{35+6 \ln \left (x \right )}+5670 \,{\mathrm e}^{40+4 \ln \left (x \right )}+288 x +17496 \,{\mathrm e}^{35}+1760 \,{\mathrm e}^{5+\ln \left (x \right )}+13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+31104 \,{\mathrm e}^{25}+5760 \,{\mathrm e}^{10}+\ln \left (x \right )+1536 \,{\mathrm e}^{5}+x^{4}+18 x^{3}+113 x^{2}+29160 \,{\mathrm e}^{30}+24 \,{\mathrm e}^{25+6 \ln \left (x \right )}+1512 \,{\mathrm e}^{35+5 \ln \left (x \right )}+112 \,{\mathrm e}^{30+6 \ln \left (x \right )}+900 \,{\mathrm e}^{3 \ln \left (x \right )+10}+3248 \,{\mathrm e}^{3 \ln \left (x \right )+15}+9588 \,{\mathrm e}^{3 \ln \left (x \right )+20}+61236 \,{\mathrm e}^{30+\ln \left (x \right )}+7512 \,{\mathrm e}^{10+\ln \left (x \right )}+20412 \,{\mathrm e}^{2 \ln \left (x \right )+40}+448 \,{\mathrm e}^{4 \ln \left (x \right )+15}+1260 \,{\mathrm e}^{30+5 \ln \left (x \right )}+18000 \,{\mathrm e}^{3 \ln \left (x \right )+25}+7560 \,{\mathrm e}^{30+4 \ln \left (x \right )}+488 \,{\mathrm e}^{25+5 \ln \left (x \right )}+44280 \,{\mathrm e}^{25+2 \ln \left (x \right )}+1512 \,{\mathrm e}^{40+5 \ln \left (x \right )}+7560 \,{\mathrm e}^{35+4 \ln \left (x \right )}+27486 \,{\mathrm e}^{2 \ln \left (x \right )+20}+40770 \,{\mathrm e}^{\ln \left (x \right )+20}+20088 \,{\mathrm e}^{\ln \left (x \right )+15}+1804 \,{\mathrm e}^{4 \ln \left (x \right )+20}+4080 \,{\mathrm e}^{25+4 \ln \left (x \right )}+24 \,{\mathrm e}^{5 \ln \left (x \right )+15}+3772 \,{\mathrm e}^{2 \ln \left (x \right )+10}+{\mathrm e}^{40+8 \ln \left (x \right )}+24 \,{\mathrm e}^{40+7 \ln \left (x \right )}+252 \,{\mathrm e}^{40+6 \ln \left (x \right )}+4 \,{\mathrm e}^{7 \ln \left (x \right )+30}+100 \,{\mathrm e}^{4 \ln \left (x \right )+10}+8 \,{\mathrm e}^{4 \ln \left (x \right )+5}+728 \,{\mathrm e}^{2 \ln \left (x \right )+5}+170 \,{\mathrm e}^{5 \ln \left (x \right )+20}+8 \,{\mathrm e}^{35+7 \ln \left (x \right )}+4 \,{\mathrm e}^{5 \ln \left (x \right )+10}+40824 \,{\mathrm e}^{35+2 \ln \left (x \right )}+26460 \,{\mathrm e}^{30+3 \ln \left (x \right )}+13608 \,{\mathrm e}^{40+3 \ln \left (x \right )}+128 \,{\mathrm e}^{3 \ln \left (x \right )+5}+57672 \,{\mathrm e}^{\ln \left (x \right )+25}}\) | \(471\) |
risch | \(\frac {4}{251+6561 \,{\mathrm e}^{40}+6 \,{\mathrm e}^{20} x^{6}+100 x^{4} {\mathrm e}^{10}+3772 x^{2} {\mathrm e}^{10}+24 x^{5} {\mathrm e}^{15}+4 x^{5} {\mathrm e}^{10}+448 x^{4} {\mathrm e}^{15}+288 x +20088 x \,{\mathrm e}^{15}+27486 x^{2} {\mathrm e}^{20}+7512 x \,{\mathrm e}^{10}+57672 x \,{\mathrm e}^{25}+44280 x^{2} {\mathrm e}^{25}+18000 x^{3} {\mathrm e}^{25}+4080 x^{4} {\mathrm e}^{25}+1512 x^{5} {\mathrm e}^{35}+22680 x^{3} {\mathrm e}^{35}+728 x^{2} {\mathrm e}^{5}+8 x^{4} {\mathrm e}^{5}+128 x^{3} {\mathrm e}^{5}+24 x^{6} {\mathrm e}^{25}+17496 \,{\mathrm e}^{35}+11520 x^{2} {\mathrm e}^{15}+40770 x \,{\mathrm e}^{20}+900 x^{3} {\mathrm e}^{10}+13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+31104 \,{\mathrm e}^{25}+5760 \,{\mathrm e}^{10}+1760 x \,{\mathrm e}^{5}+\ln \left (x \right )+1536 \,{\mathrm e}^{5}+x^{4}+18 x^{3}+113 x^{2}+7560 x^{4} {\mathrm e}^{35}+5670 x^{4} {\mathrm e}^{40}+7560 x^{4} {\mathrm e}^{30}+488 x^{5} {\mathrm e}^{25}+17496 x \,{\mathrm e}^{40}+61236 x \,{\mathrm e}^{30}+40824 x \,{\mathrm e}^{35}+9588 \,{\mathrm e}^{20} x^{3}+26460 \,{\mathrm e}^{30} x^{3}+54432 \,{\mathrm e}^{30} x^{2}+170 \,{\mathrm e}^{20} x^{5}+1804 \,{\mathrm e}^{20} x^{4}+20412 x^{2} {\mathrm e}^{40}+40824 x^{2} {\mathrm e}^{35}+1512 x^{5} {\mathrm e}^{40}+29160 \,{\mathrm e}^{30}+1260 x^{5} {\mathrm e}^{30}+13608 x^{3} {\mathrm e}^{40}+3248 x^{3} {\mathrm e}^{15}+4 x^{7} {\mathrm e}^{30}+168 \,{\mathrm e}^{35} x^{6}+112 \,{\mathrm e}^{30} x^{6}+{\mathrm e}^{40} x^{8}+24 \,{\mathrm e}^{40} x^{7}+252 \,{\mathrm e}^{40} x^{6}+8 \,{\mathrm e}^{35} x^{7}}\) | \(478\) |
parallelrisch | \(\frac {4}{251+6561 \,{\mathrm e}^{40}+6 \,{\mathrm e}^{20} x^{6}+100 x^{4} {\mathrm e}^{10}+3772 x^{2} {\mathrm e}^{10}+24 x^{5} {\mathrm e}^{15}+4 x^{5} {\mathrm e}^{10}+448 x^{4} {\mathrm e}^{15}+288 x +20088 x \,{\mathrm e}^{15}+27486 x^{2} {\mathrm e}^{20}+7512 x \,{\mathrm e}^{10}+57672 x \,{\mathrm e}^{25}+44280 x^{2} {\mathrm e}^{25}+18000 x^{3} {\mathrm e}^{25}+4080 x^{4} {\mathrm e}^{25}+1512 x^{5} {\mathrm e}^{35}+22680 x^{3} {\mathrm e}^{35}+728 x^{2} {\mathrm e}^{5}+8 x^{4} {\mathrm e}^{5}+128 x^{3} {\mathrm e}^{5}+24 x^{6} {\mathrm e}^{25}+17496 \,{\mathrm e}^{35}+11520 x^{2} {\mathrm e}^{15}+40770 x \,{\mathrm e}^{20}+900 x^{3} {\mathrm e}^{10}+13824 \,{\mathrm e}^{15}+24624 \,{\mathrm e}^{20}+31104 \,{\mathrm e}^{25}+5760 \,{\mathrm e}^{10}+1760 x \,{\mathrm e}^{5}+\ln \left (x \right )+1536 \,{\mathrm e}^{5}+x^{4}+18 x^{3}+113 x^{2}+7560 x^{4} {\mathrm e}^{35}+5670 x^{4} {\mathrm e}^{40}+7560 x^{4} {\mathrm e}^{30}+488 x^{5} {\mathrm e}^{25}+17496 x \,{\mathrm e}^{40}+61236 x \,{\mathrm e}^{30}+40824 x \,{\mathrm e}^{35}+9588 \,{\mathrm e}^{20} x^{3}+26460 \,{\mathrm e}^{30} x^{3}+54432 \,{\mathrm e}^{30} x^{2}+170 \,{\mathrm e}^{20} x^{5}+1804 \,{\mathrm e}^{20} x^{4}+20412 x^{2} {\mathrm e}^{40}+40824 x^{2} {\mathrm e}^{35}+1512 x^{5} {\mathrm e}^{40}+29160 \,{\mathrm e}^{30}+1260 x^{5} {\mathrm e}^{30}+13608 x^{3} {\mathrm e}^{40}+3248 x^{3} {\mathrm e}^{15}+4 x^{7} {\mathrm e}^{30}+168 \,{\mathrm e}^{35} x^{6}+112 \,{\mathrm e}^{30} x^{6}+{\mathrm e}^{40} x^{8}+24 \,{\mathrm e}^{40} x^{7}+252 \,{\mathrm e}^{40} x^{6}+8 \,{\mathrm e}^{35} x^{7}}\) | \(478\) |
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 +3868890480*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+(560*x^13+26560*x^12+56 0016*x^11+6988480*x^10+57754080*x^9+334108800*x^8+1390828320*x^7+420585177 6*x^6+9183475440*x^5+14137467840*x^4+14579591760*x^3+9051030720*x^2+255973 4784*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+1 5024*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)+(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)+550*x^ 7+36*x^8+x^9+4644*x^6+23639*x^5+74124*x^4+139670*x^3+144576*x^2),x,method= _RETURNVERBOSE)
4/(251+6561*exp(40)+6*exp(20+6*ln(x))+17496*exp(40+ln(x))+54432*exp(30+2*l n(x))+11520*exp(2*ln(x)+15)+22680*exp(35+3*ln(x))+40824*exp(35+ln(x))+168* exp(35+6*ln(x))+5670*exp(40+4*ln(x))+288*x+17496*exp(35)+1760*exp(5+ln(x)) +13824*exp(15)+24624*exp(20)+31104*exp(25)+5760*exp(10)+ln(x)+1536*exp(5)+ x^4+18*x^3+113*x^2+29160*exp(30)+24*exp(25+6*ln(x))+1512*exp(35+5*ln(x))+1 12*exp(30+6*ln(x))+900*exp(3*ln(x)+10)+3248*exp(3*ln(x)+15)+9588*exp(3*ln( x)+20)+61236*exp(30+ln(x))+7512*exp(10+ln(x))+20412*exp(2*ln(x)+40)+448*ex p(4*ln(x)+15)+1260*exp(30+5*ln(x))+18000*exp(3*ln(x)+25)+7560*exp(30+4*ln( x))+488*exp(25+5*ln(x))+44280*exp(25+2*ln(x))+1512*exp(40+5*ln(x))+7560*ex p(35+4*ln(x))+27486*exp(2*ln(x)+20)+40770*exp(ln(x)+20)+20088*exp(ln(x)+15 )+1804*exp(4*ln(x)+20)+4080*exp(25+4*ln(x))+24*exp(5*ln(x)+15)+3772*exp(2* ln(x)+10)+exp(40+8*ln(x))+24*exp(40+7*ln(x))+252*exp(40+6*ln(x))+4*exp(7*l n(x)+30)+100*exp(4*ln(x)+10)+8*exp(4*ln(x)+5)+728*exp(2*ln(x)+5)+170*exp(5 *ln(x)+20)+8*exp(35+7*ln(x))+4*exp(5*ln(x)+10)+40824*exp(35+2*ln(x))+26460 *exp(30+3*ln(x))+13608*exp(40+3*ln(x))+128*exp(3*ln(x)+5)+57672*exp(ln(x)+ 25))
Leaf count of result is larger than twice the leaf count of optimal. 285 vs. \(2 (27) = 54\).
Time = 0.29 (sec) , antiderivative size = 285, normalized size of antiderivative = 10.18 \[ \text {the integral} =\frac {4}{x^{4} + 18 \, x^{3} + 113 \, x^{2} + {\left (x^{8} + 24 \, x^{7} + 252 \, x^{6} + 1512 \, x^{5} + 5670 \, x^{4} + 13608 \, x^{3} + 20412 \, x^{2} + 17496 \, x + 6561\right )} e^{40} + 8 \, {\left (x^{7} + 21 \, x^{6} + 189 \, x^{5} + 945 \, x^{4} + 2835 \, x^{3} + 5103 \, x^{2} + 5103 \, x + 2187\right )} e^{35} + 4 \, {\left (x^{7} + 28 \, x^{6} + 315 \, x^{5} + 1890 \, x^{4} + 6615 \, x^{3} + 13608 \, x^{2} + 15309 \, x + 7290\right )} e^{30} + 8 \, {\left (3 \, x^{6} + 61 \, x^{5} + 510 \, x^{4} + 2250 \, x^{3} + 5535 \, x^{2} + 7209 \, x + 3888\right )} e^{25} + 2 \, {\left (3 \, x^{6} + 85 \, x^{5} + 902 \, x^{4} + 4794 \, x^{3} + 13743 \, x^{2} + 20385 \, x + 12312\right )} e^{20} + 8 \, {\left (3 \, x^{5} + 56 \, x^{4} + 406 \, x^{3} + 1440 \, x^{2} + 2511 \, x + 1728\right )} e^{15} + 4 \, {\left (x^{5} + 25 \, x^{4} + 225 \, x^{3} + 943 \, x^{2} + 1878 \, x + 1440\right )} e^{10} + 8 \, {\left (x^{4} + 16 \, x^{3} + 91 \, x^{2} + 220 \, x + 192\right )} e^{5} + 288 \, x + \log \left (x\right ) + 251} \]
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+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+5 8378320*x^10+225173520*x^9+675520560*x^8+1576214640*x^7+2837186352*x^6+386 8890480*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+8 7567480*x^10+375289200*x^9+1238454360*x^8+3152429280*x^7+6147237096*x^6+90 27411120*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+86918832 *x^10+420323904*x^9+1541187648*x^8+4308320016*x^7+9142044912*x^6+145011746 88*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+8996724*x^11+66754908*x^10+3 62715408*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)^12+(3 36*x^14+16064*x^13+346656*x^12+4492224*x^11+39132720*x^10+242580096*x^9+11 02901184*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^1 3+114904*x^12+1822216*x^11+18638400*x^10+132024816*x^9+672897456*x^8+25144 59024*x^7+6918985656*x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+1 1112864336*x^2+2962842624*x)*exp(5)^10+23639*x^5+74124*x^4+144576*x^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+1413746784 0*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+(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)*log(x)+4644*x^6+139670*x^3+x^9+550*x^7+36*x^8+x*log(x)^2+(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+89 2820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+510 0*x^12+141486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+2 136903552*x^6+5085305874*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+464869 28*x^8+244526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+504964886 4*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+1790543 232*x^4+2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+1448 0*x^10+271056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+6274 85328*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+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73 872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+6139 8864*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),x , algorithm=\
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)
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 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 4 x^{7} e^{30} + 8 x^{7} e^{35} + 24 x^{7} e^{40} + 6 x^{6} e^{20} + 24 x^{6} e^{25} + 112 x^{6} e^{30} + 168 x^{6} e^{35} + 252 x^{6} e^{40} + 4 x^{5} e^{10} + 24 x^{5} e^{15} + 170 x^{5} e^{20} + 488 x^{5} e^{25} + 1260 x^{5} e^{30} + 1512 x^{5} e^{35} + 1512 x^{5} e^{40} + x^{4} + 8 x^{4} e^{5} + 100 x^{4} e^{10} + 448 x^{4} e^{15} + 1804 x^{4} e^{20} + 4080 x^{4} e^{25} + 7560 x^{4} e^{30} + 7560 x^{4} e^{35} + 5670 x^{4} e^{40} + 18 x^{3} + 128 x^{3} e^{5} + 900 x^{3} e^{10} + 3248 x^{3} e^{15} + 9588 x^{3} e^{20} + 18000 x^{3} e^{25} + 26460 x^{3} e^{30} + 22680 x^{3} e^{35} + 13608 x^{3} e^{40} + 113 x^{2} + 728 x^{2} e^{5} + 3772 x^{2} e^{10} + 11520 x^{2} e^{15} + 27486 x^{2} e^{20} + 44280 x^{2} e^{25} + 54432 x^{2} e^{30} + 40824 x^{2} e^{35} + 20412 x^{2} e^{40} + 288 x + 1760 x e^{5} + 7512 x e^{10} + 20088 x e^{15} + 40770 x e^{20} + 57672 x e^{25} + 61236 x e^{30} + 40824 x e^{35} + 17496 x e^{40} + \log {\left (x \right )} + 251 + 1536 e^{5} + 5760 e^{10} + 13824 e^{15} + 24624 e^{20} + 31104 e^{25} + 29160 e^{30} + 17496 e^{35} + 6561 e^{40}} \]
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+144576*x**2+74124*x **4+x**9+23639*x**5+4644*x**6+(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+(560*x**12+25680*x**11+516864*x**10+6071424*x**9+46486928*x**8+2445263 52*x**7+904257648*x**6+2356128432*x**5+4246618752*x**4+5049648864*x**3+356 9522256*x**2+1137484944*x)*exp(5)**7+(56*x**12+3888*x**11+102144*x**10+145 8624*x**9+13024328*x**8+77750400*x**7+320091912*x**6+915313392*x**5+179054 3232*x**4+2290471344*x**3+1729205496*x**2+584961264*x)*exp(5)**6+(336*x**1 1+14480*x**10+271056*x**9+2920080*x**8+20140928*x**7+93268000*x**6+2944932 00*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+7 8004732*x**5+181099452*x**4+268957044*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**1 0+408*x**9+8352*x**8+92880*x**7+628352*x**6+2708144*x**5+7485320*x**4+1285 6232*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+225173520*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+139670*x**3+ 550*x**7+36*x**8+(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+325241 8920*x**2+688747536*x)*exp(5)**14+(112*x**15+5264*x**14+113568*x**13+14938 56*x**12+13405392*x**11+86918832*x**10+420323904*x**9+1541187648*x**8+4308 320016*x**7+9142044912*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+8996724*x**11+66754908*x**10+362715408*x**9+1473828048*x **8+4516653636*x**7+10416007404*x**6+17828546472*x**5+21996618552*x**4+185 14695852*x**3+9525548484*x**2+2261812896*x)*exp(5)**12+(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+20751 235776*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+190769210 64*x**3+11112864336*x**2+2962842624*x)*exp(5)**10+(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+33 4108800*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+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+8 1648*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+36 08*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+18 00*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)+( 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+229582512*x**2+43046721* x)*exp(5)**16+x*ln(x)**2),x)
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))
Leaf count of result is larger than twice the leaf count of optimal. 274 vs. \(2 (27) = 54\).
Time = 0.76 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.79 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 4 \, x^{7} {\left (6 \, e^{40} + 2 \, e^{35} + e^{30}\right )} + 2 \, x^{6} {\left (126 \, e^{40} + 84 \, e^{35} + 56 \, e^{30} + 12 \, e^{25} + 3 \, e^{20}\right )} + 2 \, x^{5} {\left (756 \, e^{40} + 756 \, e^{35} + 630 \, e^{30} + 244 \, e^{25} + 85 \, e^{20} + 12 \, e^{15} + 2 \, e^{10}\right )} + x^{4} {\left (5670 \, e^{40} + 7560 \, e^{35} + 7560 \, e^{30} + 4080 \, e^{25} + 1804 \, e^{20} + 448 \, e^{15} + 100 \, e^{10} + 8 \, e^{5} + 1\right )} + 2 \, x^{3} {\left (6804 \, e^{40} + 11340 \, e^{35} + 13230 \, e^{30} + 9000 \, e^{25} + 4794 \, e^{20} + 1624 \, e^{15} + 450 \, e^{10} + 64 \, e^{5} + 9\right )} + x^{2} {\left (20412 \, e^{40} + 40824 \, e^{35} + 54432 \, e^{30} + 44280 \, e^{25} + 27486 \, e^{20} + 11520 \, e^{15} + 3772 \, e^{10} + 728 \, e^{5} + 113\right )} + 2 \, x {\left (8748 \, e^{40} + 20412 \, e^{35} + 30618 \, e^{30} + 28836 \, e^{25} + 20385 \, e^{20} + 10044 \, e^{15} + 3756 \, e^{10} + 880 \, e^{5} + 144\right )} + 6561 \, e^{40} + 17496 \, e^{35} + 29160 \, e^{30} + 31104 \, e^{25} + 24624 \, e^{20} + 13824 \, e^{15} + 5760 \, e^{10} + 1536 \, e^{5} + \log \left (x\right ) + 251} \]
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+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+5 8378320*x^10+225173520*x^9+675520560*x^8+1576214640*x^7+2837186352*x^6+386 8890480*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+8 7567480*x^10+375289200*x^9+1238454360*x^8+3152429280*x^7+6147237096*x^6+90 27411120*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+86918832 *x^10+420323904*x^9+1541187648*x^8+4308320016*x^7+9142044912*x^6+145011746 88*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+8996724*x^11+66754908*x^10+3 62715408*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)^12+(3 36*x^14+16064*x^13+346656*x^12+4492224*x^11+39132720*x^10+242580096*x^9+11 02901184*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^1 3+114904*x^12+1822216*x^11+18638400*x^10+132024816*x^9+672897456*x^8+25144 59024*x^7+6918985656*x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+1 1112864336*x^2+2962842624*x)*exp(5)^10+23639*x^5+74124*x^4+144576*x^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+1413746784 0*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+(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)*log(x)+4644*x^6+139670*x^3+x^9+550*x^7+36*x^8+x*log(x)^2+(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+89 2820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+510 0*x^12+141486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+2 136903552*x^6+5085305874*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+464869 28*x^8+244526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+504964886 4*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+1790543 232*x^4+2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+1448 0*x^10+271056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+6274 85328*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+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73 872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+6139 8864*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),x , algorithm=\
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)
Leaf count of result is larger than twice the leaf count of optimal. 375 vs. \(2 (27) = 54\).
Time = 1.99 (sec) , antiderivative size = 375, normalized size of antiderivative = 13.39 \[ \text {the integral} =\frac {4}{x^{8} e^{40} + 24 \, x^{7} e^{40} + 8 \, x^{7} e^{35} + 4 \, x^{7} e^{30} + 252 \, x^{6} e^{40} + 168 \, x^{6} e^{35} + 112 \, x^{6} e^{30} + 24 \, x^{6} e^{25} + 6 \, x^{6} e^{20} + 1512 \, x^{5} e^{40} + 1512 \, x^{5} e^{35} + 1260 \, x^{5} e^{30} + 488 \, x^{5} e^{25} + 170 \, x^{5} e^{20} + 24 \, x^{5} e^{15} + 4 \, x^{5} e^{10} + 5670 \, x^{4} e^{40} + 7560 \, x^{4} e^{35} + 7560 \, x^{4} e^{30} + 4080 \, x^{4} e^{25} + 1804 \, x^{4} e^{20} + 448 \, x^{4} e^{15} + 100 \, x^{4} e^{10} + 8 \, x^{4} e^{5} + x^{4} + 13608 \, x^{3} e^{40} + 22680 \, x^{3} e^{35} + 26460 \, x^{3} e^{30} + 18000 \, x^{3} e^{25} + 9588 \, x^{3} e^{20} + 3248 \, x^{3} e^{15} + 900 \, x^{3} e^{10} + 128 \, x^{3} e^{5} + 18 \, x^{3} + 20412 \, x^{2} e^{40} + 40824 \, x^{2} e^{35} + 54432 \, x^{2} e^{30} + 44280 \, x^{2} e^{25} + 27486 \, x^{2} e^{20} + 11520 \, x^{2} e^{15} + 3772 \, x^{2} e^{10} + 728 \, x^{2} e^{5} + 113 \, x^{2} + 17496 \, x e^{40} + 40824 \, x e^{35} + 61236 \, x e^{30} + 57672 \, x e^{25} + 40770 \, x e^{20} + 20088 \, x e^{15} + 7512 \, x e^{10} + 1760 \, x e^{5} + 288 \, x + 6561 \, e^{40} + 17496 \, e^{35} + 29160 \, e^{30} + 31104 \, e^{25} + 24624 \, e^{20} + 13824 \, e^{15} + 5760 \, e^{10} + 1536 \, e^{5} + \log \left (x\right ) + 251} \]
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+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+5 8378320*x^10+225173520*x^9+675520560*x^8+1576214640*x^7+2837186352*x^6+386 8890480*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+8 7567480*x^10+375289200*x^9+1238454360*x^8+3152429280*x^7+6147237096*x^6+90 27411120*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+86918832 *x^10+420323904*x^9+1541187648*x^8+4308320016*x^7+9142044912*x^6+145011746 88*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+8996724*x^11+66754908*x^10+3 62715408*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)^12+(3 36*x^14+16064*x^13+346656*x^12+4492224*x^11+39132720*x^10+242580096*x^9+11 02901184*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^1 3+114904*x^12+1822216*x^11+18638400*x^10+132024816*x^9+672897456*x^8+25144 59024*x^7+6918985656*x^6+13890511800*x^5+19822775544*x^4+19076921064*x^3+1 1112864336*x^2+2962842624*x)*exp(5)^10+23639*x^5+74124*x^4+144576*x^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+1413746784 0*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+(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)*log(x)+4644*x^6+139670*x^3+x^9+550*x^7+36*x^8+x*log(x)^2+(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+89 2820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(70*x^13+510 0*x^12+141486*x^11+2158608*x^10+20901410*x^9+137808408*x^8+641272212*x^7+2 136903552*x^6+5085305874*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+464869 28*x^8+244526352*x^7+904257648*x^6+2356128432*x^5+4246618752*x^4+504964886 4*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+1790543 232*x^4+2290471344*x^3+1729205496*x^2+584961264*x)*exp(5)^6+(336*x^11+1448 0*x^10+271056*x^9+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+6274 85328*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+231559020*x^2+88006176*x)*exp(5)^4+(112*x^10+4384*x^9+73 872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+6139 8864*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),x , algorithm=\
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)
Time = 13.20 (sec) , antiderivative size = 271, normalized size of antiderivative = 9.68 \[ \text {the integral} =\frac {4}{1536\,{\mathrm {e}}^5+5760\,{\mathrm {e}}^{10}+13824\,{\mathrm {e}}^{15}+24624\,{\mathrm {e}}^{20}+31104\,{\mathrm {e}}^{25}+29160\,{\mathrm {e}}^{30}+17496\,{\mathrm {e}}^{35}+6561\,{\mathrm {e}}^{40}+\ln \left (x\right )+x\,\left (1760\,{\mathrm {e}}^5+7512\,{\mathrm {e}}^{10}+20088\,{\mathrm {e}}^{15}+40770\,{\mathrm {e}}^{20}+57672\,{\mathrm {e}}^{25}+61236\,{\mathrm {e}}^{30}+40824\,{\mathrm {e}}^{35}+17496\,{\mathrm {e}}^{40}+288\right )+x^6\,\left (6\,{\mathrm {e}}^{20}+24\,{\mathrm {e}}^{25}+112\,{\mathrm {e}}^{30}+168\,{\mathrm {e}}^{35}+252\,{\mathrm {e}}^{40}\right )+x^8\,{\mathrm {e}}^{40}+x^4\,\left (8\,{\mathrm {e}}^5+100\,{\mathrm {e}}^{10}+448\,{\mathrm {e}}^{15}+1804\,{\mathrm {e}}^{20}+4080\,{\mathrm {e}}^{25}+7560\,{\mathrm {e}}^{30}+7560\,{\mathrm {e}}^{35}+5670\,{\mathrm {e}}^{40}+1\right )+x^3\,\left (128\,{\mathrm {e}}^5+900\,{\mathrm {e}}^{10}+3248\,{\mathrm {e}}^{15}+9588\,{\mathrm {e}}^{20}+18000\,{\mathrm {e}}^{25}+26460\,{\mathrm {e}}^{30}+22680\,{\mathrm {e}}^{35}+13608\,{\mathrm {e}}^{40}+18\right )+x^2\,\left (728\,{\mathrm {e}}^5+3772\,{\mathrm {e}}^{10}+11520\,{\mathrm {e}}^{15}+27486\,{\mathrm {e}}^{20}+44280\,{\mathrm {e}}^{25}+54432\,{\mathrm {e}}^{30}+40824\,{\mathrm {e}}^{35}+20412\,{\mathrm {e}}^{40}+113\right )+x^7\,\left (4\,{\mathrm {e}}^{30}+8\,{\mathrm {e}}^{35}+24\,{\mathrm {e}}^{40}\right )+x^5\,\left (4\,{\mathrm {e}}^{10}+24\,{\mathrm {e}}^{15}+170\,{\mathrm {e}}^{20}+488\,{\mathrm {e}}^{25}+1260\,{\mathrm {e}}^{30}+1512\,{\mathrm {e}}^{35}+1512\,{\mathrm {e}}^{40}\right )+251} \]
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)
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)