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

Optimal. Leaf size=34 \[ \frac {1}{4+\frac {\left (x+5 \left (e^4+\frac {x+\frac {4 x}{4+x}}{x}\right )^2\right )^2}{x^2}} \]

________________________________________________________________________________________

Rubi [F]  time = 21.96, 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*} \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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \text {integral} &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.75, size = 158, normalized size = 4.65 \begin {gather*} -\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 )} \end {gather*}

Antiderivative was successfully verified.

[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))

________________________________________________________________________________________

fricas [B]  time = 0.89, size = 253, normalized size = 7.44 \begin {gather*} -\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 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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]

Timed out

________________________________________________________________________________________

maple [B]  time = 6.04, size = 285, normalized size = 8.38

method	result	size
risch	\(\frac {x^{5} \left (-\frac {2 \,{\mathrm e}^{8}}{25}-\frac {4 \,{\mathrm e}^{4}}{25}-\frac {2}{25}\right )+x^{4} \left (-\frac {{\mathrm e}^{16}}{5}-\frac {4 \,{\mathrm e}^{12}}{5}-\frac {62 \,{\mathrm e}^{8}}{25}-4 \,{\mathrm e}^{4}-\frac {53}{25}\right )+x^{3} \left (-\frac {16 \,{\mathrm e}^{16}}{5}-16 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{25}-\frac {1136 \,{\mathrm e}^{4}}{25}-\frac {576}{25}\right )+x^{2} \left (-\frac {96 \,{\mathrm e}^{16}}{5}-\frac {576 \,{\mathrm e}^{12}}{5}-\frac {6752 \,{\mathrm e}^{8}}{25}-\frac {7552 \,{\mathrm e}^{4}}{25}-\frac {3456}{25}\right )+x \left (-\frac {256 \,{\mathrm e}^{16}}{5}-\frac {1792 \,{\mathrm e}^{12}}{5}-\frac {23552 \,{\mathrm e}^{8}}{25}-\frac {27648 \,{\mathrm e}^{4}}{25}-\frac {12288}{25}\right )-\frac {256 \,{\mathrm e}^{16}}{5}-\frac {2048 \,{\mathrm e}^{12}}{5}-\frac {6144 \,{\mathrm e}^{8}}{5}-\frac {8192 \,{\mathrm e}^{4}}{5}-\frac {4096}{5}}{4096+\frac {12288 x}{5}+\frac {23552 x \,{\mathrm e}^{8}}{5}+6144 \,{\mathrm e}^{8}+256 \,{\mathrm e}^{16}+\frac {6752 x^{2} {\mathrm e}^{8}}{5}+\frac {27648 x \,{\mathrm e}^{4}}{5}+8192 \,{\mathrm e}^{4}+\frac {x^{6}}{5}+\frac {18 x^{5}}{5}+\frac {149 x^{4}}{5}+\frac {832 x^{3}}{5}+\frac {3712 x^{2}}{5}+96 x^{2} {\mathrm e}^{16}+256 x \,{\mathrm e}^{16}+\frac {1136 x^{3} {\mathrm e}^{4}}{5}+\frac {7552 x^{2} {\mathrm e}^{4}}{5}+\frac {62 x^{4} {\mathrm e}^{8}}{5}+\frac {912 x^{3} {\mathrm e}^{8}}{5}+x^{4} {\mathrm e}^{16}+1792 x \,{\mathrm e}^{12}+80 x^{3} {\mathrm e}^{12}+\frac {2 x^{5} {\mathrm e}^{8}}{5}+4 x^{4} {\mathrm e}^{12}+576 x^{2} {\mathrm e}^{12}+2048 \,{\mathrm e}^{12}+20 x^{4} {\mathrm e}^{4}+\frac {4 x^{5} {\mathrm e}^{4}}{5}+16 x^{3} {\mathrm e}^{16}}\)	\(285\)
gosper	\(-\frac {\left (5 x^{3} {\mathrm e}^{12}+60 x^{2} {\mathrm e}^{12}+15 x^{3} {\mathrm e}^{8}+2 x^{4} {\mathrm e}^{4}+240 x \,{\mathrm e}^{12}+240 x^{2} {\mathrm e}^{8}+39 x^{3} {\mathrm e}^{4}+2 x^{4}+320 \,{\mathrm e}^{12}+1200 x \,{\mathrm e}^{8}+396 x^{2} {\mathrm e}^{4}+37 x^{3}+1920 \,{\mathrm e}^{8}+2048 x \,{\mathrm e}^{4}+280 x^{2}+3840 \,{\mathrm e}^{4}+1216 x +2560\right ) \left (x \,{\mathrm e}^{4}+4 \,{\mathrm e}^{4}+x +8\right )}{5 \left (20480+12288 x +23552 x \,{\mathrm e}^{8}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+6752 x^{2} {\mathrm e}^{8}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+x^{6}+18 x^{5}+149 x^{4}+832 x^{3}+3712 x^{2}+480 x^{2} {\mathrm e}^{16}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+62 x^{4} {\mathrm e}^{8}+912 x^{3} {\mathrm e}^{8}+5 x^{4} {\mathrm e}^{16}+8960 x \,{\mathrm e}^{12}+400 x^{3} {\mathrm e}^{12}+2 x^{5} {\mathrm e}^{8}+20 x^{4} {\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+80 x^{3} {\mathrm e}^{16}\right )}\)	\(322\)
norman	\(\frac {\left (-\frac {2}{5}-\frac {4 \,{\mathrm e}^{4}}{5}-\frac {2 \,{\mathrm e}^{8}}{5}\right ) x^{5}+\left (-256 \,{\mathrm e}^{16}-1792 \,{\mathrm e}^{12}-\frac {23552 \,{\mathrm e}^{8}}{5}-\frac {27648 \,{\mathrm e}^{4}}{5}-\frac {12288}{5}\right ) x +\left (-96 \,{\mathrm e}^{16}-576 \,{\mathrm e}^{12}-\frac {6752 \,{\mathrm e}^{8}}{5}-\frac {7552 \,{\mathrm e}^{4}}{5}-\frac {3456}{5}\right ) x^{2}+\left (-16 \,{\mathrm e}^{16}-80 \,{\mathrm e}^{12}-\frac {912 \,{\mathrm e}^{8}}{5}-\frac {1136 \,{\mathrm e}^{4}}{5}-\frac {576}{5}\right ) x^{3}+\left (-{\mathrm e}^{16}-4 \,{\mathrm e}^{12}-\frac {62 \,{\mathrm e}^{8}}{5}-20 \,{\mathrm e}^{4}-\frac {53}{5}\right ) x^{4}-256 \,{\mathrm e}^{16}-2048 \,{\mathrm e}^{12}-6144 \,{\mathrm e}^{8}-8192 \,{\mathrm e}^{4}-4096}{20480+12288 x +23552 x \,{\mathrm e}^{8}+30720 \,{\mathrm e}^{8}+1280 \,{\mathrm e}^{16}+6752 x^{2} {\mathrm e}^{8}+27648 x \,{\mathrm e}^{4}+40960 \,{\mathrm e}^{4}+x^{6}+18 x^{5}+149 x^{4}+832 x^{3}+3712 x^{2}+480 x^{2} {\mathrm e}^{16}+1280 x \,{\mathrm e}^{16}+1136 x^{3} {\mathrm e}^{4}+7552 x^{2} {\mathrm e}^{4}+62 x^{4} {\mathrm e}^{8}+912 x^{3} {\mathrm e}^{8}+5 x^{4} {\mathrm e}^{16}+8960 x \,{\mathrm e}^{12}+400 x^{3} {\mathrm e}^{12}+2 x^{5} {\mathrm e}^{8}+20 x^{4} {\mathrm e}^{12}+2880 x^{2} {\mathrm e}^{12}+10240 \,{\mathrm e}^{12}+100 x^{4} {\mathrm e}^{4}+4 x^{5} {\mathrm e}^{4}+80 x^{3} {\mathrm e}^{16}}\)	\(348\)
default	\(\frac {\left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{12}+\left (8 \,{\mathrm e}^{4}+4 \,{\mathrm e}^{8}+36\right ) \textit {\_Z}^{11}+\left (344 \,{\mathrm e}^{4}+212 \,{\mathrm e}^{8}+14 \,{\mathrm e}^{16}+56 \,{\mathrm e}^{12}+622\right ) \textit {\_Z}^{10}+\left (7064 \,{\mathrm e}^{4}+120 \,{\mathrm e}^{20}+5452 \,{\mathrm e}^{8}+748 \,{\mathrm e}^{16}+20 \,{\mathrm e}^{24}+2416 \,{\mathrm e}^{12}+7028\right ) \textit {\_Z}^{9}+\left (92456 \,{\mathrm e}^{4}+5720 \,{\mathrm e}^{20}+87228 \,{\mathrm e}^{8}+20022 \,{\mathrm e}^{16}+25 \,{\mathrm e}^{32}+200 \,{\mathrm e}^{28}+1340 \,{\mathrm e}^{24}+50360 \,{\mathrm e}^{12}+59577\right ) \textit {\_Z}^{8}+\left (861792 \,{\mathrm e}^{4}+128800 \,{\mathrm e}^{20}+967584 \,{\mathrm e}^{8}+340576 \,{\mathrm e}^{16}+800 \,{\mathrm e}^{32}+7200 \,{\mathrm e}^{28}+36960 \,{\mathrm e}^{24}+681568 \,{\mathrm e}^{12}+406144\right ) \textit {\_Z}^{7}+\left (6058752 \,{\mathrm e}^{4}+1756160 \,{\mathrm e}^{20}+7970496 \,{\mathrm e}^{8}+3983680 \,{\mathrm e}^{16}+11200 \,{\mathrm e}^{32}+112000 \,{\mathrm e}^{28}+553280 \,{\mathrm e}^{24}+6673280 \,{\mathrm e}^{12}+2281728\right ) \textit {\_Z}^{6}+\left (33335296 \,{\mathrm e}^{4}[phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}+89600 \,{\mathrm e}^{32}+985600 \,{\mathrm e}^{28}+5017600 \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{12}[phone]\right ) \textit {\_Z}^{5}+\left (146292736 \,{\mathrm e}^{4}[phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}+448000 \,{\mathrm e}^{32}+5376000 \,{\mathrm e}^{28}[phone] \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{12}[phone]\right ) \textit {\_Z}^{4}+\left (505544704 \,{\mathrm e}^{4}[phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}+1433600 \,{\mathrm e}^{32}[phone] \,{\mathrm e}^{28}[phone] \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{12}[phone]\right ) \textit {\_Z}^{3}+\left (1292894208 \,{\mathrm e}^{4}[phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}+2867200 \,{\mathrm e}^{32}[phone] \,{\mathrm e}^{28}[phone] \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{12}[phone]\right ) \textit {\_Z}^{2}+\left (2139095040 \,{\mathrm e}^{4}[phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}+3276800 \,{\mathrm e}^{32}[phone] \,{\mathrm e}^{28}[phone] \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{12}[phone]\right ) \textit {\_Z} [phone]+734003200 \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}[phone] \,{\mathrm e}^{4}+1638400 \,{\mathrm e}^{32}[phone] \,{\mathrm e}^{12}[phone] \,{\mathrm e}^{24}[phone] \,{\mathrm e}^{28}\right )}{\sum }\frac {\left (\left (2 \,{\mathrm e}^{4}+{\mathrm e}^{8}+1\right ) \textit {\_R}^{10}+\left (100 \,{\mathrm e}^{4}+62 \,{\mathrm e}^{8}+5 \,{\mathrm e}^{16}+20 \,{\mathrm e}^{12}+53\right ) \textit {\_R}^{9}+8 \left (149+289 \,{\mathrm e}^{4}+221 \,{\mathrm e}^{8}+20 \,{\mathrm e}^{16}+95 \,{\mathrm e}^{12}\right ) \textit {\_R}^{8}+64 \left (244+504 \,{\mathrm e}^{4}+431 \,{\mathrm e}^{8}+35 \,{\mathrm e}^{16}+190 \,{\mathrm e}^{12}\right ) \textit {\_R}^{7}+640 \left (209+454 \,{\mathrm e}^{4}+400 \,{\mathrm e}^{8}+28 \,{\mathrm e}^{16}+169 \,{\mathrm e}^{12}\right ) \textit {\_R}^{6}+256 \left (3019+6668 \,{\mathrm e}^{4}+5774 \,{\mathrm e}^{8}+350 \,{\mathrm e}^{16}+2300 \,{\mathrm e}^{12}\right ) \textit {\_R}^{5}+2048 \left (1444+3145 \,{\mathrm e}^{4}+2621 \,{\mathrm e}^{8}+140 \,{\mathrm e}^{16}+985 \,{\mathrm e}^{12}\right ) \textit {\_R}^{4}+16384 \left (432+912 \,{\mathrm e}^{4}+728 \,{\mathrm e}^{8}+35 \,{\mathrm e}^{16}+260 \,{\mathrm e}^{12}\right ) \textit {\_R}^{3}+32768 \left (288+588 \,{\mathrm e}^{4}+452 \,{\mathrm e}^{8}+20 \,{\mathrm e}^{16}+155 \,{\mathrm e}^{12}\right ) \textit {\_R}^{2}+327680 \left (16+24 \,{\mathrm e}^{8}+{\mathrm e}^{16}+32 \,{\mathrm e}^{4}+8 \,{\mathrm e}^{12}\right ) \textit {\_R} \right ) \ln \left (x -\textit {\_R} \right )}{125829120+151519232 \textit {\_R} [phone] \,{\mathrm e}^{20}[phone] \,{\mathrm e}^{8}[phone] \,{\mathrm e}^{16}[phone] \,{\mathrm e}^{4}[phone] \textit {\_R}^{4}[phone] \textit {\_R}^{3}+3422592 \textit {\_R}^{5}[phone] \textit {\_R}^{2}[phone] \textit {\_R} \,{\mathrm e}^{12}+819200 \,{\mathrm e}^{32}[phone] \,{\mathrm e}^{12}[phone] \,{\mathrm e}^{24}+50 \,{\mathrm e}^{32} \textit {\_R}^{7}+6272000 \,{\mathrm e}^{24} \textit {\_R}^{4}+2634240 \,{\mathrm e}^{20} \textit {\_R}^{5}+1433600 \,{\mathrm e}^{32} \textit {\_R} [phone] \,{\mathrm e}^{28} \textit {\_R}^{2}[phone] \,{\mathrm e}^{20} \textit {\_R}^{4}+225400 \,{\mathrm e}^{20} \textit {\_R}^{6}+1075200 \,{\mathrm e}^{32} \textit {\_R}^{2}+5376000 \,{\mathrm e}^{28} \textit {\_R}^{3}+140 \,{\mathrm e}^{12} \textit {\_R}^{9}+11 \,{\mathrm e}^{8} \textit {\_R}^{10}+448000 \,{\mathrm e}^{32} \textit {\_R}^{3}+1232000 \,{\mathrm e}^{28} \textit {\_R}^{4}+829920 \,{\mathrm e}^{24} \textit {\_R}^{5}[phone] \,{\mathrm e}^{24} \textit {\_R} +64680 \textit {\_R}^{6} {\mathrm e}^{24}[phone] \textit {\_R}^{3} {\mathrm e}^{24}+12267 \textit {\_R}^{8} {\mathrm e}^{8}+1683 \textit {\_R}^{8} {\mathrm e}^{16}[phone] \textit {\_R}^{4} {\mathrm e}^{8}+40044 \,{\mathrm e}^{16} \textit {\_R}^{7}+5436 \,{\mathrm e}^{12} \textit {\_R}^{8}+530 \,{\mathrm e}^{8} \textit {\_R}^{9}+596008 \,{\mathrm e}^{16} \textit {\_R}^{6}+100720 \,{\mathrm e}^{12} \textit {\_R}^{7}[phone] \,{\mathrm e}^{12} \textit {\_R}^{5}+1693272 \,{\mathrm e}^{8} \textit {\_R}^{6}[phone] \textit {\_R}^{3} {\mathrm e}^{8}[phone] \textit {\_R}^{4} {\mathrm e}^{16}[phone] \textit {\_R}^{3} {\mathrm e}^{12}[phone] \textit {\_R}^{5} {\mathrm e}^{8}[phone] \textit {\_R}^{4} {\mathrm e}^{12}+174456 \textit {\_R}^{7} {\mathrm e}^{8}+5975520 \textit {\_R}^{5} {\mathrm e}^{16}+1192744 \textit {\_R}^{6} {\mathrm e}^{12}[phone] \textit {\_R} \,{\mathrm e}^{20}+22 \,{\mathrm e}^{4} \textit {\_R}^{10}[phone] \textit {\_R}^{2} {\mathrm e}^{12}[phone] \textit {\_R}^{4} {\mathrm e}^{4}+9088128 \textit {\_R}^{5} {\mathrm e}^{4}+1508136 \textit {\_R}^{6} {\mathrm e}^{4}[phone] \textit {\_R}^{3} {\mathrm e}^{16}[phone] \,{\mathrm e}^{28}+3 \textit {\_R}^{11}+119154 \textit {\_R}^{7}+15813 \textit {\_R}^{8}+99 \textit {\_R}^{10}+1555 \textit {\_R}^{9}+710752 \textit {\_R}^{6}[phone] \textit {\_R}^{2} {\mathrm e}^{20}[phone] \textit {\_R} \,{\mathrm e}^{8}[phone] \textit {\_R}^{2} {\mathrm e}^{8}[phone] \textit {\_R} \,{\mathrm e}^{4}[phone] \textit {\_R}^{2} {\mathrm e}^{16}+184912 \textit {\_R}^{7} {\mathrm e}^{4}+15894 \textit {\_R}^{8} {\mathrm e}^{4}+860 \textit {\_R}^{9} {\mathrm e}^{4}[phone] \textit {\_R} \,{\mathrm e}^{16}[phone] \textit {\_R}^{3} {\mathrm e}^{4}[phone] \textit {\_R}^{2} {\mathrm e}^{4}+11440 \,{\mathrm e}^{20} \textit {\_R}^{7}+35 \textit {\_R}^{9} {\mathrm e}^{16}+16800 \,{\mathrm e}^{32} \textit {\_R}^{5}+12600 \,{\mathrm e}^{28} \textit {\_R}^{6}+2680 \,{\mathrm e}^{24} \textit {\_R}^{7}+270 \,{\mathrm e}^{20} \textit {\_R}^{8}+112000 \,{\mathrm e}^{32} \textit {\_R}^{4}+168000 \,{\mathrm e}^{28} \textit {\_R}^{5}+1400 \,{\mathrm e}^{32} \textit {\_R}^{6}+400 \,{\mathrm e}^{28} \textit {\_R}^{7}+45 \,{\mathrm e}^{24} \textit {\_R}^{8}[phone] \,{\mathrm e}^{28} \textit {\_R} [phone] \,{\mathrm e}^{24} \textit {\_R}^{2}[phone] \,{\mathrm e}^{20} \textit {\_R}^{3}}\right )}{10}\)	\(1183\)

Verification of antiderivative is not currently implemented for this CAS.

[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]

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

________________________________________________________________________________________

maxima [B]  time = 0.61, size = 247, normalized size = 7.26 \begin {gather*} -\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 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

________________________________________________________________________________________

mupad [B]  time = 2.77, size = 192, normalized size = 5.65 \begin {gather*} -\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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________

sympy [B]  time = 136.48, size = 287, normalized size = 8.44 \begin {gather*} \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} \left (90 + 20 e^{4} + 10 e^{8}\right ) + x^{4} \left (745 + 500 e^{4} + 310 e^{8} + 100 e^{12} + 25 e^{16}\right ) + x^{3} \left (4160 + 5680 e^{4} + 4560 e^{8} + 2000 e^{12} + 400 e^{16}\right ) + x^{2} \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}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

________________________________________________________________________________________