3.60.36 \(\int \frac {-4-1152 x-904 x^2-216 x^3-16 x^4+e^5 (-7040 x-5824 x^2-1536 x^3-128 x^4)+e^{15} (-80352 x-92160 x^2-38976 x^3-7168 x^4-480 x^5)+e^{10} (-30048 x-30176 x^2-10800 x^3-1600 x^4-80 x^5)+e^{25} (-230688 x-354240 x^2-216000 x^3-65280 x^4-9760 x^5-576 x^6)+e^{20} (-163080 x-219888 x^2-115056 x^3-28864 x^4-3400 x^5-144 x^6)+e^{35} (-163296 x-326592 x^2-272160 x^3-120960 x^4-30240 x^5-4032 x^6-224 x^7)+e^{30} (-244944 x-435456 x^2-317520 x^3-120960 x^4-25200 x^5-2688 x^6-112 x^7)+e^{40} (-69984 x-163296 x^2-163296 x^3-90720 x^4-30240 x^5-6048 x^6-672 x^7-32 x^8)}{63001 x+144576 x^2+139670 x^3+74124 x^4+23639 x^5+4644 x^6+550 x^7+36 x^8+x^9+e^5 (771072 x+1768256 x^2+1726352 x^3+936640 x^4+308704 x^5+63264 x^6+7872 x^7+544 x^8+16 x^9)+e^{10} (5250816 x+12495504 x^2+12856232 x^3+7485320 x^4+2708144 x^5+628352 x^6+92880 x^7+8352 x^8+408 x^9+8 x^{10})+e^{15} (24634368 x+61398864 x^2+66894336 x^3+41757840 x^4+16432544 x^5+4219552 x^6+705472 x^7+73872 x^8+4384 x^9+112 x^{10})+e^{20} (88006176 x+231559020 x^2+268957044 x^3+181099452 x^4+78004732 x^5+22350752 x^6+4285848 x^7+537772 x^8+41596 x^9+1740 x^{10}+28 x^{11})+e^{25} (250511616 x+697894704 x^2+865077840 x^3+627485328 x^4+294493200 x^5+93268000 x^6+20140928 x^7+2920080 x^8+271056 x^9+14480 x^{10}+336 x^{11})+e^{30} (584961264 x+1729205496 x^2+2290471344 x^3+1790543232 x^4+915313392 x^5+320091912 x^6+77750400 x^7+13024328 x^8+1458624 x^9+102144 x^{10}+3888 x^{11}+56 x^{12})+e^{35} (1137484944 x+3569522256 x^2+5049648864 x^3+4246618752 x^4+2356128432 x^5+904257648 x^6+244526352 x^7+46486928 x^8+6071424 x^9+516864 x^{10}+25680 x^{11}+560 x^{12})+e^{40} (1859269302 x+6195088656 x^2+9357185934 x^3+8457998940 x^4+5085305874 x^5+2136903552 x^6+641272212 x^7+137808408 x^8+20901410 x^9+2158608 x^{10}+141486 x^{11}+5100 x^{12}+70 x^{13})+e^{45} (2559734784 x+9051030720 x^2+14579591760 x^3+14137467840 x^4+9183475440 x^5+4205851776 x^6+1390828320 x^7+334108800 x^8+57754080 x^9+6988480 x^{10}+560016 x^{11}+26560 x^{12}+560 x^{13})+e^{50} (2962842624 x+11112864336 x^2+19076921064 x^3+19822775544 x^4+13890511800 x^5+6918985656 x^6+2514459024 x^7+672897456 x^8+132024816 x^9+18638400 x^{10}+1822216 x^{11}+114904 x^{12}+4056 x^{13}+56 x^{14})+e^{55} (2857026816 x+11357248464 x^2+20751235776 x^3+23064696864 x^4+17390324160 x^5+9386848944 x^6+3729027456 x^7+1102901184 x^8+242580096 x^9+39132720 x^{10}+4492224 x^{11}+346656 x^{12}+16064 x^{13}+336 x^{14})+e^{60} (2261812896 x+9525548484 x^2+18514695852 x^3+21996618552 x^4+17828546472 x^5+10416007404 x^6+4516653636 x^7+1473828048 x^8+362715408 x^9+66754908 x^{10}+8996724 x^{11}+854136 x^{12}+53288 x^{13}+1908 x^{14}+28 x^{15})+e^{65} (1428513408 x+6368788944 x^2+13154227632 x^3+16679216736 x^4+14501174688 x^5+9142044912 x^6+4308320016 x^7+1541187648 x^8+420323904 x^9+86918832 x^{10}+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+9672226200 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+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})+e^{80} (43046721 x+229582512 x^2+573956280 x^3+892820880 x^4+967222620 x^5+773778096 x^6+472864392 x^7+225173520 x^8+84440070 x^9+25019280 x^{10}+5837832 x^{11}+1061424 x^{12}+147420 x^{13}+15120 x^{14}+1080 x^{15}+48 x^{16}+x^{17})+(502 x+576 x^2+226 x^3+36 x^4+2 x^5+e^5 (3072 x+3520 x^2+1456 x^3+256 x^4+16 x^5)+e^{10} (11520 x+15024 x^2+7544 x^3+1800 x^4+200 x^5+8 x^6)+e^{15} (27648 x+40176 x^2+23040 x^3+6496 x^4+896 x^5+48 x^6)+e^{20} (49248 x+81540 x^2+54972 x^3+19176 x^4+3608 x^5+340 x^6+12 x^7)+e^{25} (62208 x+115344 x^2+88560 x^3+36000 x^4+8160 x^5+976 x^6+48 x^7)+e^{30} (58320 x+122472 x^2+108864 x^3+52920 x^4+15120 x^5+2520 x^6+224 x^7+8 x^8)+e^{35} (34992 x+81648 x^2+81648 x^3+45360 x^4+15120 x^5+3024 x^6+336 x^7+16 x^8)+e^{40} (13122 x+34992 x^2+40824 x^3+27216 x^4+11340 x^5+3024 x^6+504 x^7+48 x^8+2 x^9)) \log (x)+x \log ^2(x)} \, dx\)
Optimal. Leaf size=28 \[ \frac {4}{-5+\left (x+\left (3+x+\left (1+e^5 (3+x)\right )^2\right )^2\right )^2+\log (x)} \]
________________________________________________________________________________________
Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
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 - 11
2*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 + 1
768256*x^2 + 1726352*x^3 + 936640*x^4 + 308704*x^5 + 63264*x^6 + 7872*x^7 + 544*x^8 + 16*x^9) + E^10*(5250816*
x + 12495504*x^2 + 12856232*x^3 + 7485320*x^4 + 2708144*x^5 + 628352*x^6 + 92880*x^7 + 8352*x^8 + 408*x^9 + 8*
x^10) + E^15*(24634368*x + 61398864*x^2 + 66894336*x^3 + 41757840*x^4 + 16432544*x^5 + 4219552*x^6 + 705472*x^
7 + 73872*x^8 + 4384*x^9 + 112*x^10) + E^20*(88006176*x + 231559020*x^2 + 268957044*x^3 + 181099452*x^4 + 7800
4732*x^5 + 22350752*x^6 + 4285848*x^7 + 537772*x^8 + 41596*x^9 + 1740*x^10 + 28*x^11) + E^25*(250511616*x + 69
7894704*x^2 + 865077840*x^3 + 627485328*x^4 + 294493200*x^5 + 93268000*x^6 + 20140928*x^7 + 2920080*x^8 + 2710
56*x^9 + 14480*x^10 + 336*x^11) + E^30*(584961264*x + 1729205496*x^2 + 2290471344*x^3 + 1790543232*x^4 + 91531
3392*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 + 2445263
52*x^7 + 46486928*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^12) + E^40*(1859269302*x + 6195088656*x
^2 + 9357185934*x^3 + 8457998940*x^4 + 5085305874*x^5 + 2136903552*x^6 + 641272212*x^7 + 137808408*x^8 + 20901
410*x^9 + 2158608*x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + E^45*(2559734784*x + 9051030720*x^2 + 1457959176
0*x^3 + 14137467840*x^4 + 9183475440*x^5 + 4205851776*x^6 + 1390828320*x^7 + 334108800*x^8 + 57754080*x^9 + 69
88480*x^10 + 560016*x^11 + 26560*x^12 + 560*x^13) + E^50*(2962842624*x + 11112864336*x^2 + 19076921064*x^3 + 1
9822775544*x^4 + 13890511800*x^5 + 6918985656*x^6 + 2514459024*x^7 + 672897456*x^8 + 132024816*x^9 + 18638400*
x^10 + 1822216*x^11 + 114904*x^12 + 4056*x^13 + 56*x^14) + E^55*(2857026816*x + 11357248464*x^2 + 20751235776*
x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x^6 + 3729027456*x^7 + 1102901184*x^8 + 242580096*x^9 + 3
9132720*x^10 + 4492224*x^11 + 346656*x^12 + 16064*x^13 + 336*x^14) + E^60*(2261812896*x + 9525548484*x^2 + 185
14695852*x^3 + 21996618552*x^4 + 17828546472*x^5 + 10416007404*x^6 + 4516653636*x^7 + 1473828048*x^8 + 3627154
08*x^9 + 66754908*x^10 + 8996724*x^11 + 854136*x^12 + 53288*x^13 + 1908*x^14 + 28*x^15) + E^65*(1428513408*x +
6368788944*x^2 + 13154227632*x^3 + 16679216736*x^4 + 14501174688*x^5 + 9142044912*x^6 + 4308320016*x^7 + 1541
187648*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 + 9672226200*x^4 + 9027411120*x^5 + 6147237096*x^6 + 3
152429280*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 + 38688
90480*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) + E^80*(43046721*x + 229582512*x^2 + 573956280*x
^3 + 892820880*x^4 + 967222620*x^5 + 773778096*x^6 + 472864392*x^7 + 225173520*x^8 + 84440070*x^9 + 25019280*x
^10 + 5837832*x^11 + 1061424*x^12 + 147420*x^13 + 15120*x^14 + 1080*x^15 + 48*x^16 + x^17) + (502*x + 576*x^2
+ 226*x^3 + 36*x^4 + 2*x^5 + E^5*(3072*x + 3520*x^2 + 1456*x^3 + 256*x^4 + 16*x^5) + E^10*(11520*x + 15024*x^2
+ 7544*x^3 + 1800*x^4 + 200*x^5 + 8*x^6) + E^15*(27648*x + 40176*x^2 + 23040*x^3 + 6496*x^4 + 896*x^5 + 48*x^
6) + E^20*(49248*x + 81540*x^2 + 54972*x^3 + 19176*x^4 + 3608*x^5 + 340*x^6 + 12*x^7) + E^25*(62208*x + 115344
*x^2 + 88560*x^3 + 36000*x^4 + 8160*x^5 + 976*x^6 + 48*x^7) + E^30*(58320*x + 122472*x^2 + 108864*x^3 + 52920*
x^4 + 15120*x^5 + 2520*x^6 + 224*x^7 + 8*x^8) + E^35*(34992*x + 81648*x^2 + 81648*x^3 + 45360*x^4 + 15120*x^5
+ 3024*x^6 + 336*x^7 + 16*x^8) + E^40*(13122*x + 34992*x^2 + 40824*x^3 + 27216*x^4 + 11340*x^5 + 3024*x^6 + 50
4*x^7 + 48*x^8 + 2*x^9))*Log[x] + x*Log[x]^2),x]
[Out]
$Aborted
Rubi steps
Aborted
________________________________________________________________________________________
Mathematica [B] time = 0.69, size = 157, normalized size = 5.61 \begin {gather*} \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)} \end {gather*}
Antiderivative was successfully verified.
[In]
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*(-8
0352*x - 92160*x^2 - 38976*x^3 - 7168*x^4 - 480*x^5) + E^10*(-30048*x - 30176*x^2 - 10800*x^3 - 1600*x^4 - 80*
x^5) + E^25*(-230688*x - 354240*x^2 - 216000*x^3 - 65280*x^4 - 9760*x^5 - 576*x^6) + E^20*(-163080*x - 219888*
x^2 - 115056*x^3 - 28864*x^4 - 3400*x^5 - 144*x^6) + E^35*(-163296*x - 326592*x^2 - 272160*x^3 - 120960*x^4 -
30240*x^5 - 4032*x^6 - 224*x^7) + E^30*(-244944*x - 435456*x^2 - 317520*x^3 - 120960*x^4 - 25200*x^5 - 2688*x^
6 - 112*x^7) + E^40*(-69984*x - 163296*x^2 - 163296*x^3 - 90720*x^4 - 30240*x^5 - 6048*x^6 - 672*x^7 - 32*x^8)
)/(63001*x + 144576*x^2 + 139670*x^3 + 74124*x^4 + 23639*x^5 + 4644*x^6 + 550*x^7 + 36*x^8 + x^9 + E^5*(771072
*x + 1768256*x^2 + 1726352*x^3 + 936640*x^4 + 308704*x^5 + 63264*x^6 + 7872*x^7 + 544*x^8 + 16*x^9) + E^10*(52
50816*x + 12495504*x^2 + 12856232*x^3 + 7485320*x^4 + 2708144*x^5 + 628352*x^6 + 92880*x^7 + 8352*x^8 + 408*x^
9 + 8*x^10) + E^15*(24634368*x + 61398864*x^2 + 66894336*x^3 + 41757840*x^4 + 16432544*x^5 + 4219552*x^6 + 705
472*x^7 + 73872*x^8 + 4384*x^9 + 112*x^10) + E^20*(88006176*x + 231559020*x^2 + 268957044*x^3 + 181099452*x^4
+ 78004732*x^5 + 22350752*x^6 + 4285848*x^7 + 537772*x^8 + 41596*x^9 + 1740*x^10 + 28*x^11) + E^25*(250511616*
x + 697894704*x^2 + 865077840*x^3 + 627485328*x^4 + 294493200*x^5 + 93268000*x^6 + 20140928*x^7 + 2920080*x^8
+ 271056*x^9 + 14480*x^10 + 336*x^11) + E^30*(584961264*x + 1729205496*x^2 + 2290471344*x^3 + 1790543232*x^4 +
915313392*x^5 + 320091912*x^6 + 77750400*x^7 + 13024328*x^8 + 1458624*x^9 + 102144*x^10 + 3888*x^11 + 56*x^12
) + E^35*(1137484944*x + 3569522256*x^2 + 5049648864*x^3 + 4246618752*x^4 + 2356128432*x^5 + 904257648*x^6 + 2
44526352*x^7 + 46486928*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^12) + E^40*(1859269302*x + 619508
8656*x^2 + 9357185934*x^3 + 8457998940*x^4 + 5085305874*x^5 + 2136903552*x^6 + 641272212*x^7 + 137808408*x^8 +
20901410*x^9 + 2158608*x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + E^45*(2559734784*x + 9051030720*x^2 + 1457
9591760*x^3 + 14137467840*x^4 + 9183475440*x^5 + 4205851776*x^6 + 1390828320*x^7 + 334108800*x^8 + 57754080*x^
9 + 6988480*x^10 + 560016*x^11 + 26560*x^12 + 560*x^13) + E^50*(2962842624*x + 11112864336*x^2 + 19076921064*x
^3 + 19822775544*x^4 + 13890511800*x^5 + 6918985656*x^6 + 2514459024*x^7 + 672897456*x^8 + 132024816*x^9 + 186
38400*x^10 + 1822216*x^11 + 114904*x^12 + 4056*x^13 + 56*x^14) + E^55*(2857026816*x + 11357248464*x^2 + 207512
35776*x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x^6 + 3729027456*x^7 + 1102901184*x^8 + 242580096*x
^9 + 39132720*x^10 + 4492224*x^11 + 346656*x^12 + 16064*x^13 + 336*x^14) + E^60*(2261812896*x + 9525548484*x^2
+ 18514695852*x^3 + 21996618552*x^4 + 17828546472*x^5 + 10416007404*x^6 + 4516653636*x^7 + 1473828048*x^8 + 3
62715408*x^9 + 66754908*x^10 + 8996724*x^11 + 854136*x^12 + 53288*x^13 + 1908*x^14 + 28*x^15) + E^65*(14285134
08*x + 6368788944*x^2 + 13154227632*x^3 + 16679216736*x^4 + 14501174688*x^5 + 9142044912*x^6 + 4308320016*x^7
+ 1541187648*x^8 + 420323904*x^9 + 86918832*x^10 + 13405392*x^11 + 1493856*x^12 + 113568*x^13 + 5264*x^14 + 11
2*x^15) + E^70*(688747536*x + 3252418920*x^2 + 7142567040*x^3 + 9672226200*x^4 + 9027411120*x^5 + 6147237096*x
^6 + 3152429280*x^7 + 1238454360*x^8 + 375289200*x^9 + 87567480*x^10 + 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 + 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) + E^80*(43046721*x + 229582512*x^2 + 57395
6280*x^3 + 892820880*x^4 + 967222620*x^5 + 773778096*x^6 + 472864392*x^7 + 225173520*x^8 + 84440070*x^9 + 2501
9280*x^10 + 5837832*x^11 + 1061424*x^12 + 147420*x^13 + 15120*x^14 + 1080*x^15 + 48*x^16 + x^17) + (502*x + 57
6*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 +
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 + 1512
0*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]
[Out]
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^1
0*(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])
________________________________________________________________________________________
fricas [B] time = 0.79, size = 285, normalized size = 10.18 \begin {gather*} \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 \relax (x) + 251} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^7-403
2*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^4-31
7520*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^3-219888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80
352*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)*ex
p(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(63001*x+74124*x^4+139670*x^3+144576*x^2+4644*x^6+23639*x^5+550*x^7+36*x
^8+x^9+x*log(x)^2+((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+(1
6*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+64
96*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)+(x^17+48*x^16+1080*x^1
5+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440070*x^9+225173520*x^8+472864392*x^7+7737
78096*x^6+967222620*x^5+892820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(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+6147237
096*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+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)*exp(5)^13+(28*x^15+1908*x^14+5
3288*x^13+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516653636*x^7+10416007404*x^6+1
7828546472*x^5+21996618552*x^4+18514695852*x^3+9525548484*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346
656*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+182221
6*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)*exp(5)^10+(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+185
9269302*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+2356
128432*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+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627
485328*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
+73872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2+24634368*x)*exp(5)^3+(8*
x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)
^2+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+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+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1726352*x^3+1768256*x^2+771072*x)*exp(5)+(560*x
^13+26560*x^12+560016*x^11+6988480*x^10+57754080*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^
5+14137467840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9),x, algorithm="fricas")
[Out]
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 + 220*x + 192)*e^5 + 288*x + log(x) + 251)
________________________________________________________________________________________
giac [B] time = 6.69, size = 375, normalized size = 13.39 \begin {gather*} \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 \relax (x) + 251} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^7-403
2*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^4-31
7520*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^3-219888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80
352*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)*ex
p(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(63001*x+74124*x^4+139670*x^3+144576*x^2+4644*x^6+23639*x^5+550*x^7+36*x
^8+x^9+x*log(x)^2+((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+(1
6*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+64
96*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)+(x^17+48*x^16+1080*x^1
5+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440070*x^9+225173520*x^8+472864392*x^7+7737
78096*x^6+967222620*x^5+892820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(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+6147237
096*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+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)*exp(5)^13+(28*x^15+1908*x^14+5
3288*x^13+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516653636*x^7+10416007404*x^6+1
7828546472*x^5+21996618552*x^4+18514695852*x^3+9525548484*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346
656*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+182221
6*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)*exp(5)^10+(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+185
9269302*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+2356
128432*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+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627
485328*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
+73872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2+24634368*x)*exp(5)^3+(8*
x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)
^2+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+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+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1726352*x^3+1768256*x^2+771072*x)*exp(5)+(560*x
^13+26560*x^12+560016*x^11+6988480*x^10+57754080*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^
5+14137467840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9),x, algorithm="giac")
[Out]
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 + 44
280*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)
________________________________________________________________________________________
maple [B] time = 0.21, size = 376, normalized size = 13.43
|
|
|
| method |
result |
size |
|
|
|
| risch |
\(\frac {4}{251+288 x +7512 x \,{\mathrm e}^{10}+27486 x^{2} {\mathrm e}^{20}+24624 \,{\mathrm e}^{20}+20088 x \,{\mathrm e}^{15}+31104 \,{\mathrm e}^{25}+5760 \,{\mathrm e}^{10}+1760 x \,{\mathrm e}^{5}+\ln \relax (x )+1536 \,{\mathrm e}^{5}+x^{4}+18 x^{3}+113 x^{2}+4 x^{7} {\mathrm e}^{30}+20412 x^{2} {\mathrm e}^{40}+448 x^{4} {\mathrm e}^{15}+44280 x^{2} {\mathrm e}^{25}+18000 x^{3} {\mathrm e}^{25}+4080 x^{4} {\mathrm e}^{25}+57672 x \,{\mathrm e}^{25}+728 x^{2} {\mathrm e}^{5}+8 x^{4} {\mathrm e}^{5}+128 x^{3} {\mathrm e}^{5}+3772 \,{\mathrm e}^{10} x^{2}+17496 \,{\mathrm e}^{35}+11520 x^{2} {\mathrm e}^{15}+40770 x \,{\mathrm e}^{20}+900 x^{3} {\mathrm e}^{10}+13824 \,{\mathrm e}^{15}+6 \,{\mathrm e}^{20} x^{6}+170 x^{5} {\mathrm e}^{20}+1804 x^{4} {\mathrm e}^{20}+100 x^{4} {\mathrm e}^{10}+6561 \,{\mathrm e}^{40}+13608 \,{\mathrm e}^{40} x^{3}+7560 \,{\mathrm e}^{35} x^{4}+1260 \,{\mathrm e}^{30} x^{5}+24 \,{\mathrm e}^{25} x^{6}+22680 \,{\mathrm e}^{35} x^{3}+7560 \,{\mathrm e}^{30} x^{4}+488 \,{\mathrm e}^{25} x^{5}+17496 \,{\mathrm e}^{40} x +40824 \,{\mathrm e}^{35} x^{2}+26460 \,{\mathrm e}^{30} x^{3}+40824 \,{\mathrm e}^{35} x +54432 \,{\mathrm e}^{30} x^{2}+61236 \,{\mathrm e}^{30} x +29160 \,{\mathrm e}^{30}+{\mathrm e}^{40} x^{8}+24 \,{\mathrm e}^{40} x^{7}+252 \,{\mathrm e}^{40} x^{6}+8 \,{\mathrm e}^{35} x^{7}+1512 \,{\mathrm e}^{40} x^{5}+168 \,{\mathrm e}^{35} x^{6}+5670 \,{\mathrm e}^{40} x^{4}+1512 \,{\mathrm e}^{35} x^{5}+112 \,{\mathrm e}^{30} x^{6}+9588 x^{3} {\mathrm e}^{20}+24 x^{5} {\mathrm e}^{15}+4 x^{5} {\mathrm e}^{10}+3248 x^{3} {\mathrm e}^{15}}\) |
\(376\) |
|
|
|
| |
| |
| |
| |
|
|
|
|
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((-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
^6-3400*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^4-1536*x^3-5824*x^2-7040*x)*exp(5)-1
6*x^4-216*x^3-904*x^2-1152*x-4)/(63001*x+x^9+550*x^7+36*x^8+74124*x^4+139670*x^3+144576*x^2+4644*x^6+23639*x^5
+x*ln(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+892820880*x^4+573956280*x^3+229582512*x^2+43046721*x)
*exp(5)^16+(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+(5
6*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)*exp(5)^10+((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+453
60*x^4+81648*x^3+81648*x^2+34992*x)*exp(5)^7+(8*x^8+224*x^7+2520*x^6+15120*x^5+52920*x^4+108864*x^3+122472*x^2
+58320*x)*exp(5)^6+(48*x^7+976*x^6+8160*x^5+36000*x^4+88560*x^3+115344*x^2+62208*x)*exp(5)^5+(12*x^7+340*x^6+3
608*x^5+19176*x^4+54972*x^3+81540*x^2+49248*x)*exp(5)^4+(48*x^6+896*x^5+6496*x^4+23040*x^3+40176*x^2+27648*x)*
exp(5)^3+(8*x^6+200*x^5+1800*x^4+7544*x^3+15024*x^2+11520*x)*exp(5)^2+(16*x^5+256*x^4+1456*x^3+3520*x^2+3072*x
)*exp(5)+2*x^5+36*x^4+226*x^3+576*x^2+502*x)*ln(x)+(28*x^11+1740*x^10+41596*x^9+537772*x^8+4285848*x^7+2235075
2*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+73872*x^8
+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2+24634368*x)*exp(5)^3+(8*x^10+408*x
^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)^2+(16*x^1
6+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+225173520*x^9+675520560*x^8+1576214
640*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+3152
429280*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+86918832*x^10+420323904*x^9+1541187648*x^8+430832001
6*x^7+9142044912*x^6+14501174688*x^5+16679216736*x^4+13154227632*x^3+6368788944*x^2+1428513408*x)*exp(5)^13+(2
8*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)^12+(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+(70*x^13+5100*x^12+141486*x^11+2158608*x^10+209014
10*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+244526352*x^7+904257648*x^6+2
356128432*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+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+
627485328*x^4+865077840*x^3+697894704*x^2+250511616*x)*exp(5)^5),x,method=_RETURNVERBOSE)
[Out]
4/(251+288*x+7512*x*exp(10)+27486*x^2*exp(20)+24624*exp(20)+20088*x*exp(15)+31104*exp(25)+5760*exp(10)+1760*x*
exp(5)+ln(x)+1536*exp(5)+x^4+18*x^3+113*x^2+4*x^7*exp(30)+20412*x^2*exp(40)+448*x^4*exp(15)+44280*x^2*exp(25)+
18000*x^3*exp(25)+4080*x^4*exp(25)+57672*x*exp(25)+728*x^2*exp(5)+8*x^4*exp(5)+128*x^3*exp(5)+3772*exp(10)*x^2
+17496*exp(35)+11520*x^2*exp(15)+40770*x*exp(20)+900*x^3*exp(10)+13824*exp(15)+6*exp(20)*x^6+170*x^5*exp(20)+1
804*x^4*exp(20)+100*x^4*exp(10)+6561*exp(40)+13608*exp(40)*x^3+7560*exp(35)*x^4+1260*exp(30)*x^5+24*exp(25)*x^
6+22680*exp(35)*x^3+7560*exp(30)*x^4+488*exp(25)*x^5+17496*exp(40)*x+40824*exp(35)*x^2+26460*exp(30)*x^3+40824
*exp(35)*x+54432*exp(30)*x^2+61236*exp(30)*x+29160*exp(30)+exp(40)*x^8+24*exp(40)*x^7+252*exp(40)*x^6+8*exp(35
)*x^7+1512*exp(40)*x^5+168*exp(35)*x^6+5670*exp(40)*x^4+1512*exp(35)*x^5+112*exp(30)*x^6+9588*x^3*exp(20)+24*x
^5*exp(15)+4*x^5*exp(10)+3248*x^3*exp(15))
________________________________________________________________________________________
maxima [B] time = 0.94, size = 274, normalized size = 9.79 \begin {gather*} \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 \relax (x) + 251} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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^7-403
2*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^4-31
7520*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^3-219888*x^2-163080*x)*exp(5)^4+(-480*x^5-7168*x^4-38976*x^3-92160*x^2-80
352*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)*ex
p(5)-16*x^4-216*x^3-904*x^2-1152*x-4)/(63001*x+74124*x^4+139670*x^3+144576*x^2+4644*x^6+23639*x^5+550*x^7+36*x
^8+x^9+x*log(x)^2+((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+(1
6*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+64
96*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)+(x^17+48*x^16+1080*x^1
5+15120*x^14+147420*x^13+1061424*x^12+5837832*x^11+25019280*x^10+84440070*x^9+225173520*x^8+472864392*x^7+7737
78096*x^6+967222620*x^5+892820880*x^4+573956280*x^3+229582512*x^2+43046721*x)*exp(5)^16+(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+6147237
096*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+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)*exp(5)^13+(28*x^15+1908*x^14+5
3288*x^13+854136*x^12+8996724*x^11+66754908*x^10+362715408*x^9+1473828048*x^8+4516653636*x^7+10416007404*x^6+1
7828546472*x^5+21996618552*x^4+18514695852*x^3+9525548484*x^2+2261812896*x)*exp(5)^12+(336*x^14+16064*x^13+346
656*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+182221
6*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)*exp(5)^10+(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+185
9269302*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+2356
128432*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+2920080*x^8+20140928*x^7+93268000*x^6+294493200*x^5+627
485328*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
+73872*x^8+705472*x^7+4219552*x^6+16432544*x^5+41757840*x^4+66894336*x^3+61398864*x^2+24634368*x)*exp(5)^3+(8*
x^10+408*x^9+8352*x^8+92880*x^7+628352*x^6+2708144*x^5+7485320*x^4+12856232*x^3+12495504*x^2+5250816*x)*exp(5)
^2+(16*x^16+720*x^15+15120*x^14+196560*x^13+1769040*x^12+11675664*x^11+58378320*x^10+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+(16*x^9+544*x^8+7872*x^7+63264*x^6+308704*x^5+936640*x^4+1726352*x^3+1768256*x^2+771072*x)*exp(5)+(560*x
^13+26560*x^12+560016*x^11+6988480*x^10+57754080*x^9+334108800*x^8+1390828320*x^7+4205851776*x^6+9183475440*x^
5+14137467840*x^4+14579591760*x^3+9051030720*x^2+2559734784*x)*exp(5)^9),x, algorithm="maxima")
[Out]
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*(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) + x^2*(20412*e^40 + 40824*e^35 + 54432*e^30 + 4428
0*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 + 288
36*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)
________________________________________________________________________________________
mupad [B] time = 6.30, size = 271, normalized size = 9.68 \begin {gather*} \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 \relax (x)+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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(1152*x + exp(20)*(163080*x + 219888*x^2 + 115056*x^3 + 28864*x^4 + 3400*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 +
120960*x^4 + 30240*x^5 + 4032*x^6 + 224*x^7) + exp(30)*(244944*x + 435456*x^2 + 317520*x^3 + 120960*x^4 + 252
00*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 + 892820880*x^4 + 967222620*x^5 + 7
73778096*x^6 + 472864392*x^7 + 225173520*x^8 + 84440070*x^9 + 25019280*x^10 + 5837832*x^11 + 1061424*x^12 + 14
7420*x^13 + 15120*x^14 + 1080*x^15 + 48*x^16 + x^17) + x*log(x)^2 + exp(30)*(584961264*x + 1729205496*x^2 + 22
90471344*x^3 + 1790543232*x^4 + 915313392*x^5 + 320091912*x^6 + 77750400*x^7 + 13024328*x^8 + 1458624*x^9 + 10
2144*x^10 + 3888*x^11 + 56*x^12) + exp(75)*(229582512*x + 1147912560*x^2 + 2678462640*x^3 + 3868890480*x^4 + 3
868890480*x^5 + 2837186352*x^6 + 1576214640*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) + exp(60)*(2261812896*x + 9525548484*x^2 + 1
8514695852*x^3 + 21996618552*x^4 + 17828546472*x^5 + 10416007404*x^6 + 4516653636*x^7 + 1473828048*x^8 + 36271
5408*x^9 + 66754908*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 + 4
1596*x^9 + 1740*x^10 + 28*x^11) + exp(35)*(1137484944*x + 3569522256*x^2 + 5049648864*x^3 + 4246618752*x^4 + 2
356128432*x^5 + 904257648*x^6 + 244526352*x^7 + 46486928*x^8 + 6071424*x^9 + 516864*x^10 + 25680*x^11 + 560*x^
12) + exp(40)*(1859269302*x + 6195088656*x^2 + 9357185934*x^3 + 8457998940*x^4 + 5085305874*x^5 + 2136903552*x
^6 + 641272212*x^7 + 137808408*x^8 + 20901410*x^9 + 2158608*x^10 + 141486*x^11 + 5100*x^12 + 70*x^13) + exp(45
)*(2559734784*x + 9051030720*x^2 + 14579591760*x^3 + 14137467840*x^4 + 9183475440*x^5 + 4205851776*x^6 + 13908
28320*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 + 40176*x^2 + 2304
0*x^3 + 6496*x^4 + 896*x^5 + 48*x^6) + exp(20)*(49248*x + 81540*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 + 3024*x^6 + 336*x^7 + 16*x^8) + exp(30)*(58320*x + 1
22472*x^2 + 108864*x^3 + 52920*x^4 + 15120*x^5 + 2520*x^6 + 224*x^7 + 8*x^8) + exp(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) + 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 + 71425670
40*x^3 + 9672226200*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) + exp(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) + exp(55)*(
2857026816*x + 11357248464*x^2 + 20751235776*x^3 + 23064696864*x^4 + 17390324160*x^5 + 9386848944*x^6 + 372902
7456*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 + 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) + 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 + 14480*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
+ 12856232*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)
[Out]
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) + 6123
6*exp(30) + 40824*exp(35) + 17496*exp(40) + 288) + x^6*(6*exp(20) + 24*exp(25) + 112*exp(30) + 168*exp(35) + 2
52*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)
+ 27486*exp(20) + 44280*exp(25) + 54432*exp(30) + 40824*exp(35) + 20412*exp(40) + 113) + x^7*(4*exp(30) + 8*e
xp(35) + 24*exp(40)) + x^5*(4*exp(10) + 24*exp(15) + 170*exp(20) + 488*exp(25) + 1260*exp(30) + 1512*exp(35) +
1512*exp(40)) + 251)
________________________________________________________________________________________
sympy [B] time = 3.68, size = 456, normalized size = 16.29 \begin {gather*} \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 {\relax (x )} + 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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
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**3-35424
0*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**4-1536*x**3-5824*x**2-7040*x)*exp(5)-16*x**4-216*x**3-904*x**2-1152*x-4)/(63001*x+74124*x**4+13
9670*x**3+144576*x**2+4644*x**6+23639*x**5+550*x**7+36*x**8+x**9+x*ln(x)**2+((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+122
472*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+230
40*x**3+40176*x**2+27648*x)*exp(5)**3+(8*x**6+200*x**5+1800*x**4+7544*x**3+15024*x**2+11520*x)*exp(5)**2+(16*x
**5+256*x**4+1456*x**3+3520*x**2+3072*x)*exp(5)+2*x**5+36*x**4+226*x**3+576*x**2+502*x)*ln(x)+(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+47
2864392*x**7+773778096*x**6+967222620*x**5+892820880*x**4+573956280*x**3+229582512*x**2+43046721*x)*exp(5)**16
+(8*x**16+480*x**15+12600*x**14+196560*x**13+2063880*x**12+15567552*x**11+87567480*x**10+375289200*x**9+123845
4360*x**8+3152429280*x**7+6147237096*x**6+9027411120*x**5+9672226200*x**4+7142567040*x**3+3252418920*x**2+6887
47536*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+14501174688*x**5+16679216736*x**4+13154227632*x**3+6368788
944*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+(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+1
32024816*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)*exp(5)**10+(70*x**13+5100*x**12+141486*x**11+2158608*x**10+20901410*x**9+1378
08408*x**8+641272212*x**7+2136903552*x**6+5085305874*x**5+8457998940*x**4+9357185934*x**3+6195088656*x**2+1859
269302*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**1
1+102144*x**10+1458624*x**9+13024328*x**8+77750400*x**7+320091912*x**6+915313392*x**5+1790543232*x**4+22904713
44*x**3+1729205496*x**2+584961264*x)*exp(5)**6+(336*x**11+14480*x**10+271056*x**9+2920080*x**8+20140928*x**7+9
3268000*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+231559020
*x**2+88006176*x)*exp(5)**4+(112*x**10+4384*x**9+73872*x**8+705472*x**7+4219552*x**6+16432544*x**5+41757840*x*
*4+66894336*x**3+61398864*x**2+24634368*x)*exp(5)**3+(8*x**10+408*x**9+8352*x**8+92880*x**7+628352*x**6+270814
4*x**5+7485320*x**4+12856232*x**3+12495504*x**2+5250816*x)*exp(5)**2+(16*x**16+720*x**15+15120*x**14+196560*x*
*13+1769040*x**12+11675664*x**11+58378320*x**10+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+(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+560
016*x**11+6988480*x**10+57754080*x**9+334108800*x**8+1390828320*x**7+4205851776*x**6+9183475440*x**5+141374678
40*x**4+14579591760*x**3+9051030720*x**2+2559734784*x)*exp(5)**9),x)
[Out]
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(15) + 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) + 54432*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) + 5
7672*x*exp(25) + 61236*x*exp(30) + 40824*x*exp(35) + 17496*x*exp(40) + log(x) + 251 + 1536*exp(5) + 5760*exp(1
0) + 13824*exp(15) + 24624*exp(20) + 31104*exp(25) + 29160*exp(30) + 17496*exp(35) + 6561*exp(40))
________________________________________________________________________________________