\(\int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9)+e^{12} (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9)+e^8 (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10})+e^4 (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10})}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8)+e^{28} (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8)+e^{24} (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9)+e^{20} (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9)+e^{16} (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10})+e^{12} (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10})+e^8 (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11})+e^4 (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11})} \, dx\) [1030]

Optimal result

Integrand size = 726, antiderivative size = 34 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\frac {1}{4+\frac {\left (x+5 \left (e^4+\frac {x+\frac {4 x}{4+x}}{x}\right )^2\right )^2}{x^2}} \]

[Out]

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

Rubi [F]

\[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx \]

[In]

Int[(10485760*x + 18874368*x^2 + 14155776*x^3 + 5914624*x^4 + 1545728*x^5 + 267520*x^6 + 31232*x^7 + 2384*x^8
+ 106*x^9 + 2*x^10 + E^16*(655360*x + 1310720*x^2 + 1146880*x^3 + 573440*x^4 + 179200*x^5 + 35840*x^6 + 4480*x
^7 + 320*x^8 + 10*x^9) + E^12*(5242880*x + 10158080*x^2 + 8519680*x^3 + 4034560*x^4 + 1177600*x^5 + 216320*x^6
+ 24320*x^7 + 1520*x^8 + 40*x^9) + E^8*(15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 2956288*x^5
+ 512000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + E^4*(20971520*x + 38535168*x^2 + 29884416*x^3 + 128
81920*x^4 + 3414016*x^5 + 581120*x^6 + 64512*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2097152000 + 2516582400*x +
1515192320*x^2 + 626524160*x^3 + 201646080*x^4 + 52879360*x^5 + 11408640*x^6 + 2030720*x^7 + 297885*x^8 + 3514
0*x^9 + 3110*x^10 + 180*x^11 + 5*x^12 + E^32*(8192000 + 16384000*x + 14336000*x^2 + 7168000*x^3 + 2240000*x^4
+ 448000*x^5 + 56000*x^6 + 4000*x^7 + 125*x^8) + E^28*(131072000 + 245760000*x + 200704000*x^2 + 93184000*x^3
+ 26880000*x^4 + 4928000*x^5 + 560000*x^6 + 36000*x^7 + 1000*x^8) + E^24*(917504000 + 1612185600*x + 123166720
0*x^2 + 534732800*x^3 + 144614400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^7 + 6700*x^8 + 100*x^9) + E^20*(
3670016000 + 6042419200*x + 4333568000*x^2 + 1776230400*x^3 + 459110400*x^4 + 77952000*x^5 + 8780800*x^6 + 644
000*x^7 + 28600*x^8 + 600*x^9) + E^16*(9175040000 + 14155776000*x + 9581035520*x^2 + 3757015040*x^3 + 95132416
0*x^4 + 164334080*x^5 + 19918400*x^6 + 1702880*x^7 + 100110*x^8 + 3740*x^9 + 70*x^10) + E^12*(14680064000 + 21
233664000*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 244779520*x^5 + 33366400*x^6 + 3407840*x^7 +
251800*x^8 + 12080*x^9 + 280*x^10) + E^8*(14680064000 + 19922944000*x + 12332564480*x^2 + 4699586560*x^3 + 12
57328640*x^4 + 253757440*x^5 + 39852480*x^6 + 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060*x^10 + 20*x^11) + E^
4*(8388608000 + 10695475200*x + 6464471040*x^2 + 2527723520*x^3 + 731463680*x^4 + 166676480*x^5 + 30293760*x^6
+ 4308960*x^7 + 462280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11)),x]

[Out]

(48373 + 181420*E^4 + 170170*E^8 - 127988*E^12 - 415141*E^16 - 421352*E^20 - 237620*E^24 - 65416*E^28 + 10011*
E^32 + 17212*E^36 + 7066*E^40 + 1404*E^44 + 117*E^48)/(15*(1280*(2 + E^4)^4 + 256*(2 + E^4)^2*(12 + 15*E^4 + 5
*E^8)*x + 32*(116 + 236*E^4 + 211*E^8 + 90*E^12 + 15*E^16)*x^2 + 16*(52 + 71*E^4 + 57*E^8 + 25*E^12 + 5*E^16)*
x^3 + (149 + 100*E^4 + 62*E^8 + 20*E^12 + 5*E^16)*x^4 + 2*(9 + 2*E^4 + E^8)*x^5 + x^6)) - (2*(961 - 19038*E^4
- 53715*E^8 - 50688*E^12 - 12582*E^16 + 12276*E^20 + 12650*E^24 + 6096*E^28 + 1957*E^32 + 410*E^36 + 41*E^40)*
Defer[Int][(-20480 - 12288*x - 3712*x^2 - 832*x^3 - 149*x^4 - 18*x^5 - x^6 - 5*E^16*(4 + x)^4 - 20*E^12*(4 + x
)^3*(8 + x) - 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) - 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x
^4 + x^5))^(-1), x])/5 + (256*(2 + E^4)^2*(465156 + 5071875*E^4 + 13706735*E^8 + 15023294*E^12 + 3153188*E^16
- 10365919*E^20 - 13861085*E^24 - 9073852*E^28 - 3395068*E^32 - 437291*E^36 + 280197*E^40 + 191678*E^44 + 5656
4*E^48 + 8775*E^52 + 585*E^56)*Defer[Int][(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E
^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912
*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))^(-2), x])/15 + (64*(896516 + 39172012*E^4 + 167537831*E^8 + 310023782
*E^12 + 280249981*E^16 + 52163080*E^20 - 174186249*E^24 - 235333478*E^28 - 162228091*E^32 - 68339060*E^36 - 14
603699*E^40 + 1981530*E^44 + 2864479*E^48 + 1134336*E^52 + 252117*E^56 + 31590*E^60 + 1755*E^64)*Defer[Int][x/
(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x)
+ 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))^2
, x])/15 - (16*(1087500 - 7522067*E^4 - 47648589*E^8 - 102244143*E^12 - 108736455*E^16 - 44623535*E^20 + 33347
931*E^24 + 64766901*E^28 + 49681809*E^32 + 22667655*E^36 + 5759489*E^40 - 7149*E^44 - 688141*E^48 - 311685*E^5
2 - 74639*E^56 - 9945*E^60 - 585*E^64)*Defer[Int][x^2/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5
+ x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(
10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))^2, x])/5 - (4*(3950215 - 2314152*E^4 - 56784080*E^8 - 142
604224*E^12 - 169871900*E^16 - 95270872*E^20 + 13065616*E^24 + 67891184*E^28 + 58660442*E^32 + 28324904*E^36 +
8010384*E^40 + 750944*E^44 - 448252*E^48 - 252328*E^52 - 65744*E^56 - 9360*E^60 - 585*E^64)*Defer[Int][x^3/(2
0480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) +
2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))^2,
x])/15 - (4*(330327 + 349174*E^4 - 2220687*E^8 - 6767424*E^12 - 8697237*E^16 - 5687498*E^20 - 720019*E^24 + 21
27408*E^28 + 2110309*E^32 + 1033474*E^36 + 298003*E^40 + 49680*E^44 + 4313*E^48 + 210*E^52 + 15*E^56)*Defer[In
t][x^4/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(
8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 +
x^5))^2, x])/15 + (2*(2135 + 2872*E^4 - 1100*E^8 - 4728*E^12 - 3622*E^16 - 1016*E^20 + 20*E^24 + 56*E^28 + 7*E
^32)*Defer[Int][x/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*
(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3
+ 25*x^4 + x^5)), x])/5 + (2*(413 + 694*E^4 + 435*E^8 + 44*E^12 - 117*E^16 - 66*E^20 - 11*E^24)*Defer[Int][x^2
/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x)
+ 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)),
x])/5 + (2*(35 + 60*E^4 + 34*E^8 + 12*E^12 + 3*E^16)*Defer[Int][x^3/(20480 + 12288*x + 3712*x^2 + 832*x^3 + 1
49*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 +
x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)), x])/5 + (2*(1 + E^4)^2*Defer[Int][x^4/(20
480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2
*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5)), x])
/5

Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {2 \left (-19681280 \left (1+\frac {e^4 \left (-273856-1445592 e^4-2979112 e^8-3263831 e^{12}-1871478 e^{16}-165955 e^{20}+645616 e^{24}+615610 e^{28}+328964 e^{32}+122162 e^{36}+32904 e^{40}+6221 e^{44}+738 e^{48}+41 e^{52}\right )}{15376}\right )-50290688 \left (1+\frac {e^4 \left (-279636-3949012 e^4-10086545 e^8-12735510 e^{12}-8665919 e^{16}-2057411 e^{20}+1811630 e^{24}+2236024 e^{28}+1299558 e^{32}+506082 e^{36}+141683 e^{40}+27942 e^{44}+3485 e^{48}+205 e^{52}\right )}{196448}\right ) x-28823168 \left (1+\frac {e^4 \left (1336564-5790417 e^4-21316796 e^8-31233470 e^{12}-24535704 e^{16}-8734047 e^{20}+2364680 e^{24}+4851000 e^{28}+3124372 e^{32}+1274025 e^{36}+367956 e^{40}+75186 e^{44}+9840 e^{48}+615 e^{52}\right )}{900724}\right ) x^2-7438528 \left (1+\frac {e^4 \left (1231447-428651 e^4-5518414 e^8-9587746 e^{12}-8466299 e^{16}-3830109 e^{20}-28516 e^{24}+1182304 e^{28}+873985 e^{32}+371195 e^{36}+108626 e^{40}+22582 e^{44}+3075 e^{48}+205 e^{52}\right )}{464908}\right ) x^3-945813 \left (1+\frac {e^4 \left (3115326+1757447 e^4-5561836 e^8-12168283 e^{12}-11709062 e^{16}-6140721 e^{20}-1057288 e^{24}+942951 e^{28}+871506 e^{32}+378717 e^{36}+106420 e^{40}+21087 e^{44}+2870 e^{48}+205 e^{52}\right )}{945813}\right ) x^4-48373 \left (1+\frac {e^4 \left (181420+170170 e^4-127988 e^8-415141 e^{12}-421352 e^{16}-237620 e^{20}-65416 e^{24}+10011 e^{28}+17212 e^{32}+7066 e^{36}+1404 e^{40}+117 e^{44}\right )}{48373}\right ) x^5\right )}{5 \left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2}+\frac {2 \left (961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\left (2135+2872 e^4-1100 e^8-4728 e^{12}-3622 e^{16}-1016 e^{20}+20 e^{24}+56 e^{28}+7 e^{32}\right ) x+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 x^4\right )}{5 \left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )}\right ) \, dx \\ & = \frac {2}{5} \int \frac {-19681280 \left (1+\frac {e^4 \left (-273856-1445592 e^4-2979112 e^8-3263831 e^{12}-1871478 e^{16}-165955 e^{20}+645616 e^{24}+615610 e^{28}+328964 e^{32}+122162 e^{36}+32904 e^{40}+6221 e^{44}+738 e^{48}+41 e^{52}\right )}{15376}\right )-50290688 \left (1+\frac {e^4 \left (-279636-3949012 e^4-10086545 e^8-12735510 e^{12}-8665919 e^{16}-2057411 e^{20}+1811630 e^{24}+2236024 e^{28}+1299558 e^{32}+506082 e^{36}+141683 e^{40}+27942 e^{44}+3485 e^{48}+205 e^{52}\right )}{196448}\right ) x-28823168 \left (1+\frac {e^4 \left (1336564-5790417 e^4-21316796 e^8-31233470 e^{12}-24535704 e^{16}-8734047 e^{20}+2364680 e^{24}+4851000 e^{28}+3124372 e^{32}+1274025 e^{36}+367956 e^{40}+75186 e^{44}+9840 e^{48}+615 e^{52}\right )}{900724}\right ) x^2-7438528 \left (1+\frac {e^4 \left (1231447-428651 e^4-5518414 e^8-9587746 e^{12}-8466299 e^{16}-3830109 e^{20}-28516 e^{24}+1182304 e^{28}+873985 e^{32}+371195 e^{36}+108626 e^{40}+22582 e^{44}+3075 e^{48}+205 e^{52}\right )}{464908}\right ) x^3-945813 \left (1+\frac {e^4 \left (3115326+1757447 e^4-5561836 e^8-12168283 e^{12}-11709062 e^{16}-6140721 e^{20}-1057288 e^{24}+942951 e^{28}+871506 e^{32}+378717 e^{36}+106420 e^{40}+21087 e^{44}+2870 e^{48}+205 e^{52}\right )}{945813}\right ) x^4-48373 \left (1+\frac {e^4 \left (181420+170170 e^4-127988 e^8-415141 e^{12}-421352 e^{16}-237620 e^{20}-65416 e^{24}+10011 e^{28}+17212 e^{32}+7066 e^{36}+1404 e^{40}+117 e^{44}\right )}{48373}\right ) x^5}{\left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2} \, dx+\frac {2}{5} \int \frac {961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\left (2135+2872 e^4-1100 e^8-4728 e^{12}-3622 e^{16}-1016 e^{20}+20 e^{24}+56 e^{28}+7 e^{32}\right ) x+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 x^4}{20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6} \, dx \\ & = \frac {48373+181420 e^4+170170 e^8-127988 e^{12}-415141 e^{16}-421352 e^{20}-237620 e^{24}-65416 e^{28}+10011 e^{32}+17212 e^{36}+7066 e^{40}+1404 e^{44}+117 e^{48}}{15 \left (1280 \left (2+e^4\right )^4+256 \left (2+e^4\right )^2 \left (12+15 e^4+5 e^8\right ) x+32 \left (116+236 e^4+211 e^8+90 e^{12}+15 e^{16}\right ) x^2+16 \left (52+71 e^4+57 e^8+25 e^{12}+5 e^{16}\right ) x^3+\left (149+100 e^4+62 e^8+20 e^{12}+5 e^{16}\right ) x^4+2 \left (9+2 e^4+e^8\right ) x^5+x^6\right )}+\frac {1}{15} \int \frac {256 \left (2+e^4\right )^2 \left (465156+5071875 e^4+13706735 e^8+15023294 e^{12}+3153188 e^{16}-10365919 e^{20}-13861085 e^{24}-9073852 e^{28}-3395068 e^{32}-437291 e^{36}+280197 e^{40}+191678 e^{44}+56564 e^{48}+8775 e^{52}+585 e^{56}\right )+64 \left (896516+39172012 e^4+167537831 e^8+310023782 e^{12}[phone] e^{16}[phone] e^{20}-174186249 e^{24}-235333478 e^{28}-162228091 e^{32}-68339060 e^{36}-14603699 e^{40}+1981530 e^{44}+2864479 e^{48}+1134336 e^{52}+252117 e^{56}+31590 e^{60}+1755 e^{64}\right ) x-48 \left (1087500-7522067 e^4-47648589 e^8-102244143 e^{12}-108736455 e^{16}-44623535 e^{20}[phone] e^{24}[phone] e^{28}[phone] e^{32}[phone] e^{36}+5759489 e^{40}-7149 e^{44}-688141 e^{48}-311685 e^{52}-74639 e^{56}-9945 e^{60}-585 e^{64}\right ) x^2-4 \left (3950215-2314152 e^4-56784080 e^8-142604224 e^{12}-169871900 e^{16}-95270872 e^{20}[phone] e^{24}[phone] e^{28}[phone] e^{32}[phone] e^{36}+8010384 e^{40}+750944 e^{44}-448252 e^{48}-252328 e^{52}-65744 e^{56}-9360 e^{60}-585 e^{64}\right ) x^3-4 \left (330327+349174 e^4-2220687 e^8-6767424 e^{12}-8697237 e^{16}-5687498 e^{20}-720019 e^{24}+2127408 e^{28}+2110309 e^{32}+1033474 e^{36}+298003 e^{40}+49680 e^{44}+4313 e^{48}+210 e^{52}+15 e^{56}\right ) x^4}{\left (20480 \left (1+2 e^4+\frac {1}{16} e^8 \left (24+8 e^4+e^8\right )\right )+12288 \left (1+\frac {1}{48} e^4 \left (108+92 e^4+35 e^8+5 e^{12}\right )\right ) x+3712 \left (1+\frac {1}{116} e^4 \left (236+211 e^4+90 e^8+15 e^{12}\right )\right ) x^2+832 \left (1+\frac {1}{52} e^4 \left (71+57 e^4+25 e^8+5 e^{12}\right )\right ) x^3+149 \left (1+\frac {1}{149} e^4 \left (100+62 e^4+20 e^8+5 e^{12}\right )\right ) x^4+18 \left (1+\frac {1}{9} e^4 \left (2+e^4\right )\right ) x^5+x^6\right )^2} \, dx+\frac {2}{5} \int \frac {961-19038 e^4-53715 e^8-50688 e^{12}-12582 e^{16}+12276 e^{20}+12650 e^{24}+6096 e^{28}+1957 e^{32}+410 e^{36}+41 e^{40}+\left (2135+2872 e^4-1100 e^8-4728 e^{12}-3622 e^{16}-1016 e^{20}+20 e^{24}+56 e^{28}+7 e^{32}\right ) x+\left (413+694 e^4+435 e^8+44 e^{12}-117 e^{16}-66 e^{20}-11 e^{24}\right ) x^2+\left (35+60 e^4+34 e^8+12 e^{12}+3 e^{16}\right ) x^3+\left (1+e^4\right )^2 x^4}{20480+12288 x+3712 x^2+832 x^3+149 x^4+18 x^5+x^6+5 e^{16} (4+x)^4+20 e^{12} (4+x)^3 (8+x)+2 e^8 (4+x)^2 \left (960+256 x+23 x^2+x^3\right )+4 e^4 \left (10240+6912 x+1888 x^2+284 x^3+25 x^4+x^5\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(158\) vs. \(2(34)=68\).

Time = 0.83 (sec) , antiderivative size = 158, normalized size of antiderivative = 4.65 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {\left (8+x+e^4 (4+x)\right )^2 \left (320+112 x+21 x^2+2 x^3+5 e^8 (4+x)^2+10 e^4 \left (32+12 x+x^2\right )\right )}{5 \left (20480+12288 x+3712 x^2+832 x^3+149 x^4+18 x^5+x^6+5 e^{16} (4+x)^4+20 e^{12} (4+x)^3 (8+x)+2 e^8 (4+x)^2 \left (960+256 x+23 x^2+x^3\right )+4 e^4 \left (10240+6912 x+1888 x^2+284 x^3+25 x^4+x^5\right )\right )} \]

[In]

Integrate[(10485760*x + 18874368*x^2 + 14155776*x^3 + 5914624*x^4 + 1545728*x^5 + 267520*x^6 + 31232*x^7 + 238
4*x^8 + 106*x^9 + 2*x^10 + E^16*(655360*x + 1310720*x^2 + 1146880*x^3 + 573440*x^4 + 179200*x^5 + 35840*x^6 +
4480*x^7 + 320*x^8 + 10*x^9) + E^12*(5242880*x + 10158080*x^2 + 8519680*x^3 + 4034560*x^4 + 1177600*x^5 + 2163
20*x^6 + 24320*x^7 + 1520*x^8 + 40*x^9) + E^8*(15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 29562
88*x^5 + 512000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + E^4*(20971520*x + 38535168*x^2 + 29884416*x^3
+ 12881920*x^4 + 3414016*x^5 + 581120*x^6 + 64512*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2097152000 + 251658240
0*x + 1515192320*x^2 + 626524160*x^3 + 201646080*x^4 + 52879360*x^5 + 11408640*x^6 + 2030720*x^7 + 297885*x^8
+ 35140*x^9 + 3110*x^10 + 180*x^11 + 5*x^12 + E^32*(8192000 + 16384000*x + 14336000*x^2 + 7168000*x^3 + 224000
0*x^4 + 448000*x^5 + 56000*x^6 + 4000*x^7 + 125*x^8) + E^28*(131072000 + 245760000*x + 200704000*x^2 + 9318400
0*x^3 + 26880000*x^4 + 4928000*x^5 + 560000*x^6 + 36000*x^7 + 1000*x^8) + E^24*(917504000 + 1612185600*x + 123
1667200*x^2 + 534732800*x^3 + 144614400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^7 + 6700*x^8 + 100*x^9) +
E^20*(3670016000 + 6042419200*x + 4333568000*x^2 + 1776230400*x^3 + 459110400*x^4 + 77952000*x^5 + 8780800*x^6
+ 644000*x^7 + 28600*x^8 + 600*x^9) + E^16*(9175040000 + 14155776000*x + 9581035520*x^2 + 3757015040*x^3 + 95
1324160*x^4 + 164334080*x^5 + 19918400*x^6 + 1702880*x^7 + 100110*x^8 + 3740*x^9 + 70*x^10) + E^12*(1468006400
0 + 21233664000*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 244779520*x^5 + 33366400*x^6 + 3407840
*x^7 + 251800*x^8 + 12080*x^9 + 280*x^10) + E^8*(14680064000 + 19922944000*x + 12332564480*x^2 + 4699586560*x^
3 + 1257328640*x^4 + 253757440*x^5 + 39852480*x^6 + 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060*x^10 + 20*x^11
) + E^4*(8388608000 + 10695475200*x + 6464471040*x^2 + 2527723520*x^3 + 731463680*x^4 + 166676480*x^5 + 302937
60*x^6 + 4308960*x^7 + 462280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11)),x]

[Out]

-1/5*((8 + x + E^4*(4 + x))^2*(320 + 112*x + 21*x^2 + 2*x^3 + 5*E^8*(4 + x)^2 + 10*E^4*(32 + 12*x + x^2)))/(20
480 + 12288*x + 3712*x^2 + 832*x^3 + 149*x^4 + 18*x^5 + x^6 + 5*E^16*(4 + x)^4 + 20*E^12*(4 + x)^3*(8 + x) + 2
*E^8*(4 + x)^2*(960 + 256*x + 23*x^2 + x^3) + 4*E^4*(10240 + 6912*x + 1888*x^2 + 284*x^3 + 25*x^4 + x^5))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(284\) vs. \(2(33)=66\).

Time = 3.82 (sec) , antiderivative size = 285, normalized size of antiderivative = 8.38

method	result	size
risch	\(\frac {\left (-\frac {2 \,{\mathrm e}^{8}}{25}-\frac {4 \,{\mathrm e}^{4}}{25}-\frac {2}{25}\right ) x^{5}+\left (-\frac {{\mathrm e}^{16}}{5}-\frac {4 \,{\mathrm e}^{12}}{5}-\frac {62 \,{\mathrm e}^{8}}{25}-4 \,{\mathrm e}^{4}-\frac {53}{25}\right ) x^{4}+\left (-\frac {16 \,{\mathrm e}^{16}}{5}-16 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{25}-\frac {1136 \,{\mathrm e}^{4}}{25}-\frac {576}{25}\right ) x^{3}+\left (-\frac {96 \,{\mathrm e}^{16}}{5}-\frac {576 \,{\mathrm e}^{12}}{5}-\frac {6752 \,{\mathrm e}^{8}}{25}-\frac {7552 \,{\mathrm e}^{4}}{25}-\frac {3456}{25}\right ) x^{2}+\left (-\frac {256 \,{\mathrm e}^{16}}{5}-\frac {1792 \,{\mathrm e}^{12}}{5}-\frac {23552 \,{\mathrm e}^{8}}{25}-\frac {27648 \,{\mathrm e}^{4}}{25}-\frac {12288}{25}\right ) x -\frac {256 \,{\mathrm e}^{16}}{5}-\frac {2048 \,{\mathrm e}^{12}}{5}-\frac {6144 \,{\mathrm e}^{8}}{5}-\frac {8192 \,{\mathrm e}^{4}}{5}-\frac {4096}{5}}{4096+\frac {12288 x}{5}+96 x^{2} {\mathrm e}^{16}+{\mathrm e}^{16} x^{4}+4 \,{\mathrm e}^{12} x^{4}+80 \,{\mathrm e}^{12} x^{3}+\frac {912 \,{\mathrm e}^{8} x^{3}}{5}+\frac {23552 x \,{\mathrm e}^{8}}{5}+256 x \,{\mathrm e}^{16}+\frac {1136 x^{3} {\mathrm e}^{4}}{5}+\frac {7552 x^{2} {\mathrm e}^{4}}{5}+2048 \,{\mathrm e}^{12}+20 x^{4} {\mathrm e}^{4}+\frac {4 x^{5} {\mathrm e}^{4}}{5}+6144 \,{\mathrm e}^{8}+256 \,{\mathrm e}^{16}+16 x^{3} {\mathrm e}^{16}+\frac {27648 x \,{\mathrm e}^{4}}{5}+8192 \,{\mathrm e}^{4}+\frac {149 x^{4}}{5}+\frac {832 x^{3}}{5}+\frac {3712 x^{2}}{5}+\frac {x^{6}}{5}+\frac {18 x^{5}}{5}+\frac {6752 x^{2} {\mathrm e}^{8}}{5}+\frac {62 x^{4} {\mathrm e}^{8}}{5}+\frac {2 x^{5} {\mathrm e}^{8}}{5}+1792 x \,{\mathrm e}^{12}+576 x^{2} {\mathrm e}^{12}}\)	\(285\)
gosper	\(-\frac {\left (5 \,{\mathrm e}^{12} x^{3}+60 x^{2} {\mathrm e}^{12}+15 \,{\mathrm e}^{8} x^{3}+2 x^{4} {\mathrm e}^{4}+240 x \,{\mathrm e}^{12}+240 x^{2} {\mathrm e}^{8}+39 x^{3} {\mathrm e}^{4}+2 x^{4}+320 \,{\mathrm e}^{12}+1200 x \,{\mathrm e}^{8}+396 x^{2} {\mathrm e}^{4}+37 x^{3}+1920 \,{\mathrm e}^{8}+2048 x \,{\mathrm e}^{4}+280 x^{2}+3840 \,{\mathrm e}^{4}+1216 x +2560\right ) \left (x \,{\mathrm e}^{4}+4 \,{\mathrm e}^{4}+x +8\right )}{5 \left (20480+12288 x +480 x^{2} {\mathrm e}^{16}+5 \,{\mathrm e}^{16} x^{4}+20 \,{\mathrm e}^{12} x^{4}+400 \,{\mathrm e}^{12} x^{3}+912 \,{\mathrm e}^{8} x^{3}+23552 x \,{\mathrm e}^{8}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+80 x^{3} {\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+62 x^{4} {\mathrm e}^{8}+2 x^{5} {\mathrm e}^{8}+8960 x \,{\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}\right )}\)	\(322\)
norman	\(\frac {\left (-\frac {2}{5}-\frac {4 \,{\mathrm e}^{4}}{5}-\frac {2 \,{\mathrm e}^{8}}{5}\right ) x^{5}+\left (-256 \,{\mathrm e}^{16}-1792 \,{\mathrm e}^{12}-\frac {23552 \,{\mathrm e}^{8}}{5}-\frac {27648 \,{\mathrm e}^{4}}{5}-\frac {12288}{5}\right ) x +\left (-96 \,{\mathrm e}^{16}-576 \,{\mathrm e}^{12}-\frac {6752 \,{\mathrm e}^{8}}{5}-\frac {7552 \,{\mathrm e}^{4}}{5}-\frac {3456}{5}\right ) x^{2}+\left (-16 \,{\mathrm e}^{16}-80 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{5}-\frac {1136 \,{\mathrm e}^{4}}{5}-\frac {576}{5}\right ) x^{3}+\left (-{\mathrm e}^{16}-4 \,{\mathrm e}^{12}-\frac {62 \,{\mathrm e}^{8}}{5}-20 \,{\mathrm e}^{4}-\frac {53}{5}\right ) x^{4}-256 \,{\mathrm e}^{16}-2048 \,{\mathrm e}^{12}-6144 \,{\mathrm e}^{8}-8192 \,{\mathrm e}^{4}-4096}{20480+12288 x +480 x^{2} {\mathrm e}^{16}+5 \,{\mathrm e}^{16} x^{4}+20 \,{\mathrm e}^{12} x^{4}+400 \,{\mathrm e}^{12} x^{3}+912 \,{\mathrm e}^{8} x^{3}+23552 x \,{\mathrm e}^{8}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+80 x^{3} {\mathrm e}^{16}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+149 x^{4}+832 x^{3}+3712 x^{2}+x^{6}+18 x^{5}+6752 x^{2} {\mathrm e}^{8}+62 x^{4} {\mathrm e}^{8}+2 x^{5} {\mathrm e}^{8}+8960 x \,{\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}}\)	\(348\)
parallelrisch	\(\frac {-20480-12288 x -480 x^{2} {\mathrm e}^{16}-5 \,{\mathrm e}^{16} x^{4}-20 \,{\mathrm e}^{12} x^{4}-400 \,{\mathrm e}^{12} x^{3}-912 \,{\mathrm e}^{8} x^{3}-23552 x \,{\mathrm e}^{8}-1280 x \,{\mathrm e}^{16}-1136 x^{3} {\mathrm e}^{4}-7552 x^{2} {\mathrm e}^{4}-10240 \,{\mathrm e}^{12}-100 x^{4} {\mathrm e}^{4}-4 x^{5} {\mathrm e}^{4}-30720 \,{\mathrm e}^{8}-1280 \,{\mathrm e}^{16}-80 x^{3} {\mathrm e}^{16}-27648 x \,{\mathrm e}^{4}-40960 \,{\mathrm e}^{4}-53 x^{4}-576 x^{3}-3456 x^{2}-2 x^{5}-6752 x^{2} {\mathrm e}^{8}-62 x^{4} {\mathrm e}^{8}-2 x^{5} {\mathrm e}^{8}-8960 x \,{\mathrm e}^{12}-2880 x^{2} {\mathrm e}^{12}}{102400+61440 x +2400 x^{2} {\mathrm e}^{16}+25 \,{\mathrm e}^{16} x^{4}+100 \,{\mathrm e}^{12} x^{4}+2000 \,{\mathrm e}^{12} x^{3}+4560 \,{\mathrm e}^{8} x^{3}+117760 x \,{\mathrm e}^{8}+6400 x \,{\mathrm e}^{16}+5680 x^{3} {\mathrm e}^{4}+37760 x^{2} {\mathrm e}^{4}+51200 \,{\mathrm e}^{12}+500 x^{4} {\mathrm e}^{4}+20 x^{5} {\mathrm e}^{4}+153600 \,{\mathrm e}^{8}+6400 \,{\mathrm e}^{16}+400 x^{3} {\mathrm e}^{16}+138240 x \,{\mathrm e}^{4}+204800 \,{\mathrm e}^{4}+745 x^{4}+4160 x^{3}+18560 x^{2}+5 x^{6}+90 x^{5}+33760 x^{2} {\mathrm e}^{8}+310 x^{4} {\mathrm e}^{8}+10 x^{5} {\mathrm e}^{8}+44800 x \,{\mathrm e}^{12}+14400 x^{2} {\mathrm e}^{12}}\)	\(390\)
default	\(\text {Expression too large to display}\)	\(1183\)

[In]

int(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+1310720*x^2+655360*x)*exp(4)^4+(40*x
^9+1520*x^8+24320*x^7+216320*x^6+1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x^10+
124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+29622272*x^2+15728640*x)*exp(4)^2+
(4*x^10+200*x^9+4624*x^8+64512*x^7+581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x)*e
xp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+14155776*x^3+18874368*x^2+10485760*
x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+(
1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^2+245760000*x+131072000)*exp(4
)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+161218560
0*x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459110400*x^4+1776230400*x^3+43
33568000*x^2+6042419200*x+3670016000)*exp(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080
*x^5+951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+(280*x^10+12080*x^9+251800
*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+146800
64000)*exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+253757440*x^5+1257328640*x^4+
4699586560*x^3+12332564480*x^2+19922944000*x+14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+430
8960*x^7+30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475200*x+8388608000)*exp(
4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+62652416
0*x^3+1515192320*x^2+2516582400*x+2097152000),x,method=_RETURNVERBOSE)

[Out]

((-2/25*exp(8)-4/25*exp(4)-2/25)*x^5+(-1/5*exp(16)-4/5*exp(12)-62/25*exp(8)-4*exp(4)-53/25)*x^4+(-16/5*exp(16)
-16*exp(12)-912/25*exp(8)-1136/25*exp(4)-576/25)*x^3+(-96/5*exp(16)-576/5*exp(12)-6752/25*exp(8)-7552/25*exp(4
)-3456/25)*x^2+(-256/5*exp(16)-1792/5*exp(12)-23552/25*exp(8)-27648/25*exp(4)-12288/25)*x-256/5*exp(16)-2048/5
*exp(12)-6144/5*exp(8)-8192/5*exp(4)-4096/5)/(4096+12288/5*x+96*x^2*exp(16)+exp(16)*x^4+4*exp(12)*x^4+80*exp(1
2)*x^3+912/5*exp(8)*x^3+23552/5*x*exp(8)+256*x*exp(16)+1136/5*x^3*exp(4)+7552/5*x^2*exp(4)+2048*exp(12)+20*x^4
*exp(4)+4/5*x^5*exp(4)+6144*exp(8)+256*exp(16)+16*x^3*exp(16)+27648/5*x*exp(4)+8192*exp(4)+149/5*x^4+832/5*x^3
+3712/5*x^2+1/5*x^6+18/5*x^5+6752/5*x^2*exp(8)+62/5*x^4*exp(8)+2/5*x^5*exp(8)+1792*x*exp(12)+576*x^2*exp(12))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 253 vs. \(2 (33) = 66\).

Time = 0.27 (sec) , antiderivative size = 253, normalized size of antiderivative = 7.44 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} + 53 \, x^{4} + 576 \, x^{3} + 3456 \, x^{2} + 5 \, {\left (x^{4} + 16 \, x^{3} + 96 \, x^{2} + 256 \, x + 256\right )} e^{16} + 20 \, {\left (x^{4} + 20 \, x^{3} + 144 \, x^{2} + 448 \, x + 512\right )} e^{12} + 2 \, {\left (x^{5} + 31 \, x^{4} + 456 \, x^{3} + 3376 \, x^{2} + 11776 \, x + 15360\right )} e^{8} + 4 \, {\left (x^{5} + 25 \, x^{4} + 284 \, x^{3} + 1888 \, x^{2} + 6912 \, x + 10240\right )} e^{4} + 12288 \, x + 20480}{5 \, {\left (x^{6} + 18 \, x^{5} + 149 \, x^{4} + 832 \, x^{3} + 3712 \, x^{2} + 5 \, {\left (x^{4} + 16 \, x^{3} + 96 \, x^{2} + 256 \, x + 256\right )} e^{16} + 20 \, {\left (x^{4} + 20 \, x^{3} + 144 \, x^{2} + 448 \, x + 512\right )} e^{12} + 2 \, {\left (x^{5} + 31 \, x^{4} + 456 \, x^{3} + 3376 \, x^{2} + 11776 \, x + 15360\right )} e^{8} + 4 \, {\left (x^{5} + 25 \, x^{4} + 284 \, x^{3} + 1888 \, x^{2} + 6912 \, x + 10240\right )} e^{4} + 12288 \, x + 20480\right )}} \]

[In]

integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+1310720*x^2+655360*x)*exp(4)^4
+(40*x^9+1520*x^8+24320*x^7+216320*x^6+1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2
*x^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+29622272*x^2+15728640*x)*exp
(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+2097152
0*x)*exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+14155776*x^3+18874368*x^2+104
85760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(
4)^8+(1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^2+245760000*x+131072000)
*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+161
2185600*x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459110400*x^4+1776230400*
x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164
334080*x^5+951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+(280*x^10+12080*x^9+
251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+
14680064000)*exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+253757440*x^5+125732864
0*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x
^8+4308960*x^7+30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475200*x+8388608000
)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+62
6524160*x^3+1515192320*x^2+2516582400*x+2097152000),x, algorithm="fricas")

[Out]

-1/5*(2*x^5 + 53*x^4 + 576*x^3 + 3456*x^2 + 5*(x^4 + 16*x^3 + 96*x^2 + 256*x + 256)*e^16 + 20*(x^4 + 20*x^3 +
144*x^2 + 448*x + 512)*e^12 + 2*(x^5 + 31*x^4 + 456*x^3 + 3376*x^2 + 11776*x + 15360)*e^8 + 4*(x^5 + 25*x^4 +
284*x^3 + 1888*x^2 + 6912*x + 10240)*e^4 + 12288*x + 20480)/(x^6 + 18*x^5 + 149*x^4 + 832*x^3 + 3712*x^2 + 5*(
x^4 + 16*x^3 + 96*x^2 + 256*x + 256)*e^16 + 20*(x^4 + 20*x^3 + 144*x^2 + 448*x + 512)*e^12 + 2*(x^5 + 31*x^4 +
456*x^3 + 3376*x^2 + 11776*x + 15360)*e^8 + 4*(x^5 + 25*x^4 + 284*x^3 + 1888*x^2 + 6912*x + 10240)*e^4 + 1228
8*x + 20480)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 287 vs. \(2 (26) = 52\).

Time = 76.41 (sec) , antiderivative size = 287, normalized size of antiderivative = 8.44 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=\frac {x^{5} \left (- 2 e^{8} - 4 e^{4} - 2\right ) + x^{4} \left (- 5 e^{16} - 20 e^{12} - 62 e^{8} - 100 e^{4} - 53\right ) + x^{3} \left (- 80 e^{16} - 400 e^{12} - 912 e^{8} - 1136 e^{4} - 576\right ) + x^{2} \left (- 480 e^{16} - 2880 e^{12} - 6752 e^{8} - 7552 e^{4} - 3456\right ) + x \left (- 1280 e^{16} - 8960 e^{12} - 23552 e^{8} - 27648 e^{4} - 12288\right ) - 1280 e^{16} - 10240 e^{12} - 30720 e^{8} - 40960 e^{4} - 20480}{5 x^{6} + x^{5} \cdot \left (90 + 20 e^{4} + 10 e^{8}\right ) + x^{4} \cdot \left (745 + 500 e^{4} + 310 e^{8} + 100 e^{12} + 25 e^{16}\right ) + x^{3} \cdot \left (4160 + 5680 e^{4} + 4560 e^{8} + 2000 e^{12} + 400 e^{16}\right ) + x^{2} \cdot \left (18560 + 37760 e^{4} + 33760 e^{8} + 14400 e^{12} + 2400 e^{16}\right ) + x \left (61440 + 138240 e^{4} + 117760 e^{8} + 44800 e^{12} + 6400 e^{16}\right ) + 102400 + 204800 e^{4} + 153600 e^{8} + 51200 e^{12} + 6400 e^{16}} \]

[In]

integrate(((10*x**9+320*x**8+4480*x**7+35840*x**6+179200*x**5+573440*x**4+1146880*x**3+1310720*x**2+655360*x)*
exp(4)**4+(40*x**9+1520*x**8+24320*x**7+216320*x**6+1177600*x**5+4034560*x**4+8519680*x**3+10158080*x**2+52428
80*x)*exp(4)**3+(2*x**10+124*x**9+3536*x**8+55168*x**7+512000*x**6+2956288*x**5+10735616*x**4+23855104*x**3+29
622272*x**2+15728640*x)*exp(4)**2+(4*x**10+200*x**9+4624*x**8+64512*x**7+581120*x**6+3414016*x**5+12881920*x**
4+29884416*x**3+38535168*x**2+20971520*x)*exp(4)+2*x**10+106*x**9+2384*x**8+31232*x**7+267520*x**6+1545728*x**
5+5914624*x**4+14155776*x**3+18874368*x**2+10485760*x)/((125*x**8+4000*x**7+56000*x**6+448000*x**5+2240000*x**
4+7168000*x**3+14336000*x**2+16384000*x+8192000)*exp(4)**8+(1000*x**8+36000*x**7+560000*x**6+4928000*x**5+2688
0000*x**4+93184000*x**3+200704000*x**2+245760000*x+131072000)*exp(4)**7+(100*x**9+6700*x**8+184800*x**7+276640
0*x**6+25088000*x**5+144614400*x**4+534732800*x**3+1231667200*x**2+1612185600*x+917504000)*exp(4)**6+(600*x**9
+28600*x**8+644000*x**7+8780800*x**6+77952000*x**5+459110400*x**4+1776230400*x**3+4333568000*x**2+6042419200*x
[phone])*exp(4)**5+(70*x**10+3740*x**9+100110*x**8+1702880*x**7+19918400*x**6+164334080*x**5+951324160*x**
4+3757015040*x**3+9581035520*x**2+14155776000*x+9175040000)*exp(4)**4+(280*x**10+12080*x**9+251800*x**8+340784
0*x**7+33366400*x**6+244779520*x**5+1335685120*x**4+5221580800*x**3+13668188160*x**2+21233664000*x+14680064000
)*exp(4)**3+(20*x**11+1060*x**10+27260*x**9+436140*x**8+4837920*x**7+39852480*x**6+253757440*x**5+1257328640*x
**4+4699586560*x**3+12332564480*x**2+19922944000*x+14680064000)*exp(4)**2+(40*x**11+1720*x**10+35320*x**9+4622
80*x**8+4308960*x**7+30293760*x**6+166676480*x**5+731463680*x**4+2527723520*x**3+6464471040*x**2+10695475200*x
[phone])*exp(4)+5*x**12+180*x**11+3110*x**10+35140*x**9+297885*x**8+2030720*x**7+11408640*x**6+52879360*x*
*5+201646080*x**4+626524160*x**3+1515192320*x**2+2516582400*x+2097152000),x)

[Out]

(x**5*(-2*exp(8) - 4*exp(4) - 2) + x**4*(-5*exp(16) - 20*exp(12) - 62*exp(8) - 100*exp(4) - 53) + x**3*(-80*ex
p(16) - 400*exp(12) - 912*exp(8) - 1136*exp(4) - 576) + x**2*(-480*exp(16) - 2880*exp(12) - 6752*exp(8) - 7552
*exp(4) - 3456) + x*(-1280*exp(16) - 8960*exp(12) - 23552*exp(8) - 27648*exp(4) - 12288) - 1280*exp(16) - 1024
0*exp(12) - 30720*exp(8) - 40960*exp(4) - 20480)/(5*x**6 + x**5*(90 + 20*exp(4) + 10*exp(8)) + x**4*(745 + 500
*exp(4) + 310*exp(8) + 100*exp(12) + 25*exp(16)) + x**3*(4160 + 5680*exp(4) + 4560*exp(8) + 2000*exp(12) + 400
*exp(16)) + x**2*(18560 + 37760*exp(4) + 33760*exp(8) + 14400*exp(12) + 2400*exp(16)) + x*(61440 + 138240*exp(
4) + 117760*exp(8) + 44800*exp(12) + 6400*exp(16)) + 102400 + 204800*exp(4) + 153600*exp(8) + 51200*exp(12) +
6400*exp(16))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (33) = 66\).

Time = 0.24 (sec) , antiderivative size = 247, normalized size of antiderivative = 7.26 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} {\left (e^{8} + 2 \, e^{4} + 1\right )} + x^{4} {\left (5 \, e^{16} + 20 \, e^{12} + 62 \, e^{8} + 100 \, e^{4} + 53\right )} + 16 \, x^{3} {\left (5 \, e^{16} + 25 \, e^{12} + 57 \, e^{8} + 71 \, e^{4} + 36\right )} + 32 \, x^{2} {\left (15 \, e^{16} + 90 \, e^{12} + 211 \, e^{8} + 236 \, e^{4} + 108\right )} + 256 \, x {\left (5 \, e^{16} + 35 \, e^{12} + 92 \, e^{8} + 108 \, e^{4} + 48\right )} + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480}{5 \, {\left (x^{6} + 2 \, x^{5} {\left (e^{8} + 2 \, e^{4} + 9\right )} + x^{4} {\left (5 \, e^{16} + 20 \, e^{12} + 62 \, e^{8} + 100 \, e^{4} + 149\right )} + 16 \, x^{3} {\left (5 \, e^{16} + 25 \, e^{12} + 57 \, e^{8} + 71 \, e^{4} + 52\right )} + 32 \, x^{2} {\left (15 \, e^{16} + 90 \, e^{12} + 211 \, e^{8} + 236 \, e^{4} + 116\right )} + 256 \, x {\left (5 \, e^{16} + 35 \, e^{12} + 92 \, e^{8} + 108 \, e^{4} + 48\right )} + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480\right )}} \]

[In]

integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+1310720*x^2+655360*x)*exp(4)^4
+(40*x^9+1520*x^8+24320*x^7+216320*x^6+1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2
*x^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+29622272*x^2+15728640*x)*exp
(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+2097152
0*x)*exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+14155776*x^3+18874368*x^2+104
85760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(
4)^8+(1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^2+245760000*x+131072000)
*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+161
2185600*x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459110400*x^4+1776230400*
x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164
334080*x^5+951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+(280*x^10+12080*x^9+
251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+
14680064000)*exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+253757440*x^5+125732864
0*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x
^8+4308960*x^7+30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475200*x+8388608000
)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+62
6524160*x^3+1515192320*x^2+2516582400*x+2097152000),x, algorithm="maxima")

[Out]

-1/5*(2*x^5*(e^8 + 2*e^4 + 1) + x^4*(5*e^16 + 20*e^12 + 62*e^8 + 100*e^4 + 53) + 16*x^3*(5*e^16 + 25*e^12 + 57
*e^8 + 71*e^4 + 36) + 32*x^2*(15*e^16 + 90*e^12 + 211*e^8 + 236*e^4 + 108) + 256*x*(5*e^16 + 35*e^12 + 92*e^8
+ 108*e^4 + 48) + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)/(x^6 + 2*x^5*(e^8 + 2*e^4 + 9) + x^4
*(5*e^16 + 20*e^12 + 62*e^8 + 100*e^4 + 149) + 16*x^3*(5*e^16 + 25*e^12 + 57*e^8 + 71*e^4 + 52) + 32*x^2*(15*e
^16 + 90*e^12 + 211*e^8 + 236*e^4 + 116) + 256*x*(5*e^16 + 35*e^12 + 92*e^8 + 108*e^4 + 48) + 1280*e^16 + 1024
0*e^12 + 30720*e^8 + 40960*e^4 + 20480)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 325 vs. \(2 (33) = 66\).

Time = 1.89 (sec) , antiderivative size = 325, normalized size of antiderivative = 9.56 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 2 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 53 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 576 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3456 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480}{5 \, {\left (x^{6} + 2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 18 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 149 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 832 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3712 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480\right )}} \]

[In]

integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+1310720*x^2+655360*x)*exp(4)^4
+(40*x^9+1520*x^8+24320*x^7+216320*x^6+1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2
*x^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+29622272*x^2+15728640*x)*exp
(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+2097152
0*x)*exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+14155776*x^3+18874368*x^2+104
85760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(
4)^8+(1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^2+245760000*x+131072000)
*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+161
2185600*x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459110400*x^4+1776230400*
x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164
334080*x^5+951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+(280*x^10+12080*x^9+
251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+
14680064000)*exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+253757440*x^5+125732864
0*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x
^8+4308960*x^7+30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475200*x+8388608000
)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+62
6524160*x^3+1515192320*x^2+2516582400*x+2097152000),x, algorithm="giac")

[Out]

-1/5*(2*x^5*e^8 + 4*x^5*e^4 + 2*x^5 + 5*x^4*e^16 + 20*x^4*e^12 + 62*x^4*e^8 + 100*x^4*e^4 + 53*x^4 + 80*x^3*e^
16 + 400*x^3*e^12 + 912*x^3*e^8 + 1136*x^3*e^4 + 576*x^3 + 480*x^2*e^16 + 2880*x^2*e^12 + 6752*x^2*e^8 + 7552*
x^2*e^4 + 3456*x^2 + 1280*x*e^16 + 8960*x*e^12 + 23552*x*e^8 + 27648*x*e^4 + 12288*x + 1280*e^16 + 10240*e^12
+ 30720*e^8 + 40960*e^4 + 20480)/(x^6 + 2*x^5*e^8 + 4*x^5*e^4 + 18*x^5 + 5*x^4*e^16 + 20*x^4*e^12 + 62*x^4*e^8
+ 100*x^4*e^4 + 149*x^4 + 80*x^3*e^16 + 400*x^3*e^12 + 912*x^3*e^8 + 1136*x^3*e^4 + 832*x^3 + 480*x^2*e^16 +
2880*x^2*e^12 + 6752*x^2*e^8 + 7552*x^2*e^4 + 3712*x^2 + 1280*x*e^16 + 8960*x*e^12 + 23552*x*e^8 + 27648*x*e^4
+ 12288*x + 1280*e^16 + 10240*e^12 + 30720*e^8 + 40960*e^4 + 20480)

Mupad [B] (verification not implemented)

Time = 11.71 (sec) , antiderivative size = 192, normalized size of antiderivative = 5.65 \[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx=-\frac {{\left (x+4\,{\mathrm {e}}^4+x\,{\mathrm {e}}^4+8\right )}^2\,\left (112\,x+320\,{\mathrm {e}}^4+80\,{\mathrm {e}}^8+120\,x\,{\mathrm {e}}^4+40\,x\,{\mathrm {e}}^8+10\,x^2\,{\mathrm {e}}^4+5\,x^2\,{\mathrm {e}}^8+21\,x^2+2\,x^3+320\right )}{5\,\left (x^6+\left (4\,{\mathrm {e}}^4+2\,{\mathrm {e}}^8+18\right )\,x^5+\left (100\,{\mathrm {e}}^4+62\,{\mathrm {e}}^8+20\,{\mathrm {e}}^{12}+5\,{\mathrm {e}}^{16}+149\right )\,x^4+\left (1136\,{\mathrm {e}}^4+912\,{\mathrm {e}}^8+400\,{\mathrm {e}}^{12}+80\,{\mathrm {e}}^{16}+832\right )\,x^3+\left (7552\,{\mathrm {e}}^4+6752\,{\mathrm {e}}^8+2880\,{\mathrm {e}}^{12}+480\,{\mathrm {e}}^{16}+3712\right )\,x^2+\left (27648\,{\mathrm {e}}^4+23552\,{\mathrm {e}}^8+8960\,{\mathrm {e}}^{12}+1280\,{\mathrm {e}}^{16}+12288\right )\,x+40960\,{\mathrm {e}}^4+30720\,{\mathrm {e}}^8+10240\,{\mathrm {e}}^{12}+1280\,{\mathrm {e}}^{16}+20480\right )} \]

[In]

int((10485760*x + exp(16)*(655360*x + 1310720*x^2 + 1146880*x^3 + 573440*x^4 + 179200*x^5 + 35840*x^6 + 4480*x
^7 + 320*x^8 + 10*x^9) + exp(12)*(5242880*x + 10158080*x^2 + 8519680*x^3 + 4034560*x^4 + 1177600*x^5 + 216320*
x^6 + 24320*x^7 + 1520*x^8 + 40*x^9) + 18874368*x^2 + 14155776*x^3 + 5914624*x^4 + 1545728*x^5 + 267520*x^6 +
31232*x^7 + 2384*x^8 + 106*x^9 + 2*x^10 + exp(8)*(15728640*x + 29622272*x^2 + 23855104*x^3 + 10735616*x^4 + 29
56288*x^5 + 512000*x^6 + 55168*x^7 + 3536*x^8 + 124*x^9 + 2*x^10) + exp(4)*(20971520*x + 38535168*x^2 + 298844
16*x^3 + 12881920*x^4 + 3414016*x^5 + 581120*x^6 + 64512*x^7 + 4624*x^8 + 200*x^9 + 4*x^10))/(2516582400*x + e
xp(12)*(21233664000*x + 13668188160*x^2 + 5221580800*x^3 + 1335685120*x^4 + 244779520*x^5 + 33366400*x^6 + 340
7840*x^7 + 251800*x^8 + 12080*x^9 + 280*x^10 + 14680064000) + exp(32)*(16384000*x + 14336000*x^2 + 7168000*x^3
+ 2240000*x^4 + 448000*x^5 + 56000*x^6 + 4000*x^7 + 125*x^8 + 8192000) + exp(20)*(6042419200*x + 4333568000*x
^2 + 1776230400*x^3 + 459110400*x^4 + 77952000*x^5 + 8780800*x^6 + 644000*x^7 + 28600*x^8 + 600*x^9 + 36700160
00) + exp(8)*(19922944000*x + 12332564480*x^2 + 4699586560*x^3 + 1257328640*x^4 + 253757440*x^5 + 39852480*x^6
+ 4837920*x^7 + 436140*x^8 + 27260*x^9 + 1060*x^10 + 20*x^11 + 14680064000) + exp(28)*(245760000*x + 20070400
0*x^2 + 93184000*x^3 + 26880000*x^4 + 4928000*x^5 + 560000*x^6 + 36000*x^7 + 1000*x^8 + 131072000) + exp(16)*(
14155776000*x + 9581035520*x^2 + 3757015040*x^3 + 951324160*x^4 + 164334080*x^5 + 19918400*x^6 + 1702880*x^7 +
100110*x^8 + 3740*x^9 + 70*x^10 + 9175040000) + exp(24)*(1612185600*x + 1231667200*x^2 + 534732800*x^3 + 1446
14400*x^4 + 25088000*x^5 + 2766400*x^6 + 184800*x^7 + 6700*x^8 + 100*x^9 + 917504000) + 1515192320*x^2 + 62652
4160*x^3 + 201646080*x^4 + 52879360*x^5 + 11408640*x^6 + 2030720*x^7 + 297885*x^8 + 35140*x^9 + 3110*x^10 + 18
0*x^11 + 5*x^12 + exp(4)*(10695475200*x + 6464471040*x^2 + 2527723520*x^3 + 731463680*x^4 + 166676480*x^5 + 30
293760*x^6 + 4308960*x^7 + 462280*x^8 + 35320*x^9 + 1720*x^10 + 40*x^11 + 8388608000) + 2097152000),x)

[Out]

-((x + 4*exp(4) + x*exp(4) + 8)^2*(112*x + 320*exp(4) + 80*exp(8) + 120*x*exp(4) + 40*x*exp(8) + 10*x^2*exp(4)
+ 5*x^2*exp(8) + 21*x^2 + 2*x^3 + 320))/(5*(40960*exp(4) + 30720*exp(8) + 10240*exp(12) + 1280*exp(16) + x^5*
(4*exp(4) + 2*exp(8) + 18) + x*(27648*exp(4) + 23552*exp(8) + 8960*exp(12) + 1280*exp(16) + 12288) + x^4*(100*
exp(4) + 62*exp(8) + 20*exp(12) + 5*exp(16) + 149) + x^3*(1136*exp(4) + 912*exp(8) + 400*exp(12) + 80*exp(16)
+ 832) + x^2*(7552*exp(4) + 6752*exp(8) + 2880*exp(12) + 480*exp(16) + 3712) + x^6 + 20480))