\(\int \frac {-337500+1012500 x-4 e^{16} x-1260000 x^2+872000 x^3-374200 x^4+104008 x^5-18816 x^6+2144 x^7-140 x^8+4 x^9+e^{12} (-100-40 x+52 x^2-8 x^3)+e^8 (-4500+6000 x-2760 x^2+528 x^3-36 x^4)+e^{5 x} (108-216 x+144 x^2-40 x^3+4 x^4)+e^4 (-67500+153000 x-137100 x^2+64440 x^3-17380 x^4+2712 x^5-228 x^6+8 x^7)+e^{4 x} (-2700+5940 x-4680 x^2+1720 x^3-300 x^4+20 x^5+e^4 (-108+288 x-192 x^2+48 x^3-4 x^4))+e^{3 x} (27000-64800 x+58680 x^2-26560 x^3+6440 x^4-800 x^5+40 x^6+e^8 (36-156 x+84 x^2-12 x^3)+e^4 (2160-5544 x+4236 x^2-1404 x^3+212 x^4-12 x^5))+e^{2 x} (-135000+351000 x-358200 x^2+191480 x^3-58760 x^4+10440 x^5-1000 x^6+40 x^7+e^{12} (-4+40 x-12 x^2)+e^8 (-540+1800 x-1188 x^2+288 x^3-24 x^4)+e^4 (-16200+39960 x-33444 x^2+13320 x^3-2760 x^4+288 x^5-12 x^6))+e^x (337500-945000 x-4 e^{16} x+1071000 x^2-657800 x^3+242640 x^4-55480 x^5+7720 x^6-600 x^7+20 x^8+e^{12} (40-192 x+92 x^2-12 x^3)+e^8 (2700-6300 x+4392 x^2-1368 x^3+204 x^4-12 x^5)+e^4 (54000-127800 x+112740 x^2-50388 x^3+12584 x^4-1776 x^5+132 x^6-4 x^7))+(-337500+900000 x-960000 x^2+552000 x^3-190200 x^4+40608 x^5-5280 x^6+384 x^7-12 x^8+e^{12} (-60 x+12 x^2)+e^{5 x} (108-180 x+84 x^2-12 x^3)+e^8 (-1500+600 x+240 x^2-120 x^3+12 x^4)+e^4 (-45000+82500 x-56700 x^2+19320 x^3-3504 x^4+324 x^5-12 x^6)+e^{4 x} (-2700+5040 x-3000 x^2+720 x^3-60 x^4+e^4 (-72+204 x-96 x^2+12 x^3))+e^{3 x} (27000-55800 x+40080 x^2-13200 x^3+2040 x^4-120 x^5+e^8 (12-84 x+24 x^2)+e^4 (1440-3720 x+2196 x^2-480 x^3+36 x^4))+e^{2 x} (-135000+306000 x+12 e^{12} x-256200 x^2+106080 x^3-23400 x^4+2640 x^5-120 x^6+e^8 (-180+864 x-396 x^2+48 x^3)+e^4 (-10800+25200 x-17028 x^2+5004 x^3-684 x^4+36 x^5))+e^x (337500-832500 x+793500 x^2-393300 x^3+111540 x^4-18300 x^5+1620 x^6-60 x^7+e^{12} (-48 x+12 x^2)+e^8 (900-2340 x+1332 x^2-300 x^3+24 x^4)+e^4 (36000-75000 x+53580 x^2-18384 x^3+3336 x^4-312 x^5+12 x^6))) \log (x)+(-112500+262500 x-232500 x^2+106500 x^3-27900 x^4+4236 x^5-348 x^6+12 x^7+e^{5 x} (36-48 x+12 x^2)+e^8 (-300 x+120 x^2-12 x^3)+e^4 (-7500+9000 x-3600 x^2+600 x^3-36 x^4)+e^{4 x} (-900+1380 x-540 x^2+60 x^3+e^4 (-12+48 x-12 x^2))+e^{3 x} (9000-15600 x-12 e^8 x+8160 x^2-1680 x^3+120 x^4+e^4 (240-792 x+324 x^2-36 x^3))+e^{2 x} (-45000+87000 x-56400 x^2+16560 x^3-2280 x^4+120 x^5+e^8 (108 x-24 x^2)+e^4 (-1800+4680 x-2484 x^2+504 x^3-36 x^4))+e^x (112500-240000 x+184500 x^2-69600 x^3+13980 x^4-1440 x^5+60 x^6+e^8 (-180 x+96 x^2-12 x^3)+e^4 (6000-11400 x+6540 x^2-1740 x^3+228 x^4-12 x^5))) \log ^2(x)+(-12500+e^{5 x} (4-4 x)+25000 x-17500 x^2+6000 x^3-1100 x^4+104 x^5-4 x^6+e^{4 x} (-100+120 x+4 e^4 x-20 x^2)+e^4 (-500 x+300 x^2-60 x^3+4 x^4)+e^{3 x} (1000-1400 x+440 x^2-40 x^3+e^4 (-56 x+12 x^2))+e^{2 x} (-5000+8000 x-3600 x^2+640 x^3-40 x^4+e^4 (240 x-108 x^2+12 x^3))+e^x (12500-22500 x+13000 x^2-3400 x^3+420 x^4-20 x^5+e^4 (-200 x+180 x^2-48 x^3+4 x^4))) \log ^3(x)}{-3125 x+e^{5 x} x+3125 x^2-1250 x^3+250 x^4-25 x^5+x^6+e^{4 x} (-25 x+5 x^2)+e^{3 x} (250 x-100 x^2+10 x^3)+e^{2 x} (-1250 x+750 x^2-150 x^3+10 x^4)+e^x (3125 x-2500 x^2+750 x^3-100 x^4+5 x^5)} \, dx\) [5449]
Optimal result
Integrand size = 1676, antiderivative size = 21 \[
\text {the integral} =\left (-3+x+\frac {e^4}{-5+e^x+x}-\log (x)\right )^4
\]
[Out]
(x+exp(4)/(exp(x)+x-5)-3-ln(x))^4
Rubi [F]
\[
\text {the integral} =\text {Too large to display}
\]
[In]
Int[(-337500 + 1012500*x - 4*E^16*x - 1260000*x^2 + 872000*x^3 - 374200*x^4 + 104008*x^5 - 18816*x^6 + 2144*x^
7 - 140*x^8 + 4*x^9 + E^12*(-100 - 40*x + 52*x^2 - 8*x^3) + E^8*(-4500 + 6000*x - 2760*x^2 + 528*x^3 - 36*x^4)
+ E^(5*x)*(108 - 216*x + 144*x^2 - 40*x^3 + 4*x^4) + E^4*(-67500 + 153000*x - 137100*x^2 + 64440*x^3 - 17380*
x^4 + 2712*x^5 - 228*x^6 + 8*x^7) + E^(4*x)*(-2700 + 5940*x - 4680*x^2 + 1720*x^3 - 300*x^4 + 20*x^5 + E^4*(-1
08 + 288*x - 192*x^2 + 48*x^3 - 4*x^4)) + E^(3*x)*(27000 - 64800*x + 58680*x^2 - 26560*x^3 + 6440*x^4 - 800*x^
5 + 40*x^6 + E^8*(36 - 156*x + 84*x^2 - 12*x^3) + E^4*(2160 - 5544*x + 4236*x^2 - 1404*x^3 + 212*x^4 - 12*x^5)
) + E^(2*x)*(-135000 + 351000*x - 358200*x^2 + 191480*x^3 - 58760*x^4 + 10440*x^5 - 1000*x^6 + 40*x^7 + E^12*(
-4 + 40*x - 12*x^2) + E^8*(-540 + 1800*x - 1188*x^2 + 288*x^3 - 24*x^4) + E^4*(-16200 + 39960*x - 33444*x^2 +
13320*x^3 - 2760*x^4 + 288*x^5 - 12*x^6)) + E^x*(337500 - 945000*x - 4*E^16*x + 1071000*x^2 - 657800*x^3 + 242
640*x^4 - 55480*x^5 + 7720*x^6 - 600*x^7 + 20*x^8 + E^12*(40 - 192*x + 92*x^2 - 12*x^3) + E^8*(2700 - 6300*x +
4392*x^2 - 1368*x^3 + 204*x^4 - 12*x^5) + E^4*(54000 - 127800*x + 112740*x^2 - 50388*x^3 + 12584*x^4 - 1776*x
^5 + 132*x^6 - 4*x^7)) + (-337500 + 900000*x - 960000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 + 3
84*x^7 - 12*x^8 + E^12*(-60*x + 12*x^2) + E^(5*x)*(108 - 180*x + 84*x^2 - 12*x^3) + E^8*(-1500 + 600*x + 240*x
^2 - 120*x^3 + 12*x^4) + E^4*(-45000 + 82500*x - 56700*x^2 + 19320*x^3 - 3504*x^4 + 324*x^5 - 12*x^6) + E^(4*x
)*(-2700 + 5040*x - 3000*x^2 + 720*x^3 - 60*x^4 + E^4*(-72 + 204*x - 96*x^2 + 12*x^3)) + E^(3*x)*(27000 - 5580
0*x + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + E^8*(12 - 84*x + 24*x^2) + E^4*(1440 - 3720*x + 2196*x^2 -
480*x^3 + 36*x^4)) + E^(2*x)*(-135000 + 306000*x + 12*E^12*x - 256200*x^2 + 106080*x^3 - 23400*x^4 + 2640*x^5
- 120*x^6 + E^8*(-180 + 864*x - 396*x^2 + 48*x^3) + E^4*(-10800 + 25200*x - 17028*x^2 + 5004*x^3 - 684*x^4 + 3
6*x^5)) + E^x*(337500 - 832500*x + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^7 + E^12
*(-48*x + 12*x^2) + E^8*(900 - 2340*x + 1332*x^2 - 300*x^3 + 24*x^4) + E^4*(36000 - 75000*x + 53580*x^2 - 1838
4*x^3 + 3336*x^4 - 312*x^5 + 12*x^6)))*Log[x] + (-112500 + 262500*x - 232500*x^2 + 106500*x^3 - 27900*x^4 + 42
36*x^5 - 348*x^6 + 12*x^7 + E^(5*x)*(36 - 48*x + 12*x^2) + E^8*(-300*x + 120*x^2 - 12*x^3) + E^4*(-7500 + 9000
*x - 3600*x^2 + 600*x^3 - 36*x^4) + E^(4*x)*(-900 + 1380*x - 540*x^2 + 60*x^3 + E^4*(-12 + 48*x - 12*x^2)) + E
^(3*x)*(9000 - 15600*x - 12*E^8*x + 8160*x^2 - 1680*x^3 + 120*x^4 + E^4*(240 - 792*x + 324*x^2 - 36*x^3)) + E^
(2*x)*(-45000 + 87000*x - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 + E^8*(108*x - 24*x^2) + E^4*(-1800 + 468
0*x - 2484*x^2 + 504*x^3 - 36*x^4)) + E^x*(112500 - 240000*x + 184500*x^2 - 69600*x^3 + 13980*x^4 - 1440*x^5 +
60*x^6 + E^8*(-180*x + 96*x^2 - 12*x^3) + E^4*(6000 - 11400*x + 6540*x^2 - 1740*x^3 + 228*x^4 - 12*x^5)))*Log
[x]^2 + (-12500 + E^(5*x)*(4 - 4*x) + 25000*x - 17500*x^2 + 6000*x^3 - 1100*x^4 + 104*x^5 - 4*x^6 + E^(4*x)*(-
100 + 120*x + 4*E^4*x - 20*x^2) + E^4*(-500*x + 300*x^2 - 60*x^3 + 4*x^4) + E^(3*x)*(1000 - 1400*x + 440*x^2 -
40*x^3 + E^4*(-56*x + 12*x^2)) + E^(2*x)*(-5000 + 8000*x - 3600*x^2 + 640*x^3 - 40*x^4 + E^4*(240*x - 108*x^2
+ 12*x^3)) + E^x*(12500 - 22500*x + 13000*x^2 - 3400*x^3 + 420*x^4 - 20*x^5 + E^4*(-200*x + 180*x^2 - 48*x^3
+ 4*x^4)))*Log[x]^3)/(-3125*x + E^(5*x)*x + 3125*x^2 - 1250*x^3 + 250*x^4 - 25*x^5 + x^6 + E^(4*x)*(-25*x + 5*
x^2) + E^(3*x)*(250*x - 100*x^2 + 10*x^3) + E^(2*x)*(-1250*x + 750*x^2 - 150*x^3 + 10*x^4) + E^x*(3125*x - 250
0*x^2 + 750*x^3 - 100*x^4 + 5*x^5)),x]
[Out]
(3 - x + Log[x])^4 - 24*E^16*Defer[Int][(-5 + E^x + x)^(-5), x] + 4*E^16*Defer[Int][x/(-5 + E^x + x)^5, x] + 4
*E^12*(54 - E^4)*Defer[Int][(-5 + E^x + x)^(-4), x] + 72*E^12*Log[x]*Defer[Int][(-5 + E^x + x)^(-4), x] - 108*
E^12*Defer[Int][x/(-5 + E^x + x)^4, x] - 12*E^12*Log[x]*Defer[Int][x/(-5 + E^x + x)^4, x] + 12*E^12*Defer[Int]
[x^2/(-5 + E^x + x)^4, x] - 8*E^8*(81 - 5*E^4)*Defer[Int][(-5 + E^x + x)^(-3), x] - 12*E^8*(36 - E^4)*Log[x]*D
efer[Int][(-5 + E^x + x)^(-3), x] - 4*E^12*Defer[Int][1/(x*(-5 + E^x + x)^3), x] + 12*E^8*(45 - E^4)*Defer[Int
][x/(-5 + E^x + x)^3, x] + 216*E^8*Log[x]*Defer[Int][x/(-5 + E^x + x)^3, x] - 144*E^8*Defer[Int][x^2/(-5 + E^x
+ x)^3, x] - 24*E^8*Log[x]*Defer[Int][x^2/(-5 + E^x + x)^3, x] + 12*E^8*Defer[Int][x^3/(-5 + E^x + x)^3, x] +
12*E^4*(54 - 13*E^4)*Defer[Int][(-5 + E^x + x)^(-2), x] + 12*E^4*(54 - 7*E^4)*Log[x]*Defer[Int][(-5 + E^x + x
)^(-2), x] + 36*E^8*Defer[Int][1/(x*(-5 + E^x + x)^2), x] + 12*E^8*Log[x]*Defer[Int][1/(x*(-5 + E^x + x)^2), x
] - 84*E^4*(9 - E^4)*Defer[Int][x/(-5 + E^x + x)^2, x] - 12*E^4*(45 - 2*E^4)*Log[x]*Defer[Int][x/(-5 + E^x + x
)^2, x] + 12*E^4*(27 - E^4)*Defer[Int][x^2/(-5 + E^x + x)^2, x] + 144*E^4*Log[x]*Defer[Int][x^2/(-5 + E^x + x)
^2, x] - 60*E^4*Defer[Int][x^3/(-5 + E^x + x)^2, x] - 12*E^4*Log[x]*Defer[Int][x^3/(-5 + E^x + x)^2, x] + 4*E^
4*Defer[Int][x^4/(-5 + E^x + x)^2, x] + 288*E^4*Defer[Int][(-5 + E^x + x)^(-1), x] + 204*E^4*Log[x]*Defer[Int]
[(-5 + E^x + x)^(-1), x] - 108*E^4*Defer[Int][1/(x*(-5 + E^x + x)), x] - 72*E^4*Log[x]*Defer[Int][1/(x*(-5 + E
^x + x)), x] - 192*E^4*Defer[Int][x/(-5 + E^x + x), x] - 96*E^4*Log[x]*Defer[Int][x/(-5 + E^x + x), x] + 48*E^
4*Defer[Int][x^2/(-5 + E^x + x), x] + 12*E^4*Log[x]*Defer[Int][x^2/(-5 + E^x + x), x] - 4*E^4*Defer[Int][x^3/(
-5 + E^x + x), x] - 72*E^8*Defer[Int][Log[x]^2/(-5 + E^x + x)^3, x] + 12*E^8*Defer[Int][(x*Log[x]^2)/(-5 + E^x
+ x)^3, x] + 12*E^4*(18 - E^4)*Defer[Int][Log[x]^2/(-5 + E^x + x)^2, x] - 108*E^4*Defer[Int][(x*Log[x]^2)/(-5
+ E^x + x)^2, x] + 12*E^4*Defer[Int][(x^2*Log[x]^2)/(-5 + E^x + x)^2, x] + 48*E^4*Defer[Int][Log[x]^2/(-5 + E
^x + x), x] - 12*E^4*Defer[Int][Log[x]^2/(x*(-5 + E^x + x)), x] - 12*E^4*Defer[Int][(x*Log[x]^2)/(-5 + E^x + x
), x] + 24*E^4*Defer[Int][Log[x]^3/(-5 + E^x + x)^2, x] - 4*E^4*Defer[Int][(x*Log[x]^3)/(-5 + E^x + x)^2, x] +
4*E^4*Defer[Int][Log[x]^3/(-5 + E^x + x), x] - 72*E^12*Defer[Int][Defer[Int][(-5 + E^x + x)^(-4), x]/x, x] +
12*E^12*Defer[Int][Defer[Int][x/(-5 + E^x + x)^4, x]/x, x] + 12*E^8*(36 - E^4)*Defer[Int][Defer[Int][(-5 + E^x
+ x)^(-3), x]/x, x] - 216*E^8*Defer[Int][Defer[Int][x/(-5 + E^x + x)^3, x]/x, x] + 24*E^8*Defer[Int][Defer[In
t][x^2/(-5 + E^x + x)^3, x]/x, x] - 12*E^4*(54 - 7*E^4)*Defer[Int][Defer[Int][(-5 + E^x + x)^(-2), x]/x, x] -
12*E^8*Defer[Int][Defer[Int][1/(x*(-5 + E^x + x)^2), x]/x, x] + 12*E^4*(45 - 2*E^4)*Defer[Int][Defer[Int][x/(-
5 + E^x + x)^2, x]/x, x] - 144*E^4*Defer[Int][Defer[Int][x^2/(-5 + E^x + x)^2, x]/x, x] + 12*E^4*Defer[Int][De
fer[Int][x^3/(-5 + E^x + x)^2, x]/x, x] - 204*E^4*Defer[Int][Defer[Int][(-5 + E^x + x)^(-1), x]/x, x] + 72*E^4
*Defer[Int][Defer[Int][1/(x*(-5 + E^x + x)), x]/x, x] + 96*E^4*Defer[Int][Defer[Int][x/(-5 + E^x + x), x]/x, x
] - 12*E^4*Defer[Int][Defer[Int][x^2/(-5 + E^x + x), x]/x, x]
Rubi steps \begin{align*}
\text {integral}& = \text {Too large to display} \\
\end{align*}
Mathematica [B] (verified)
Leaf count is larger than twice the leaf count of optimal. \(308\) vs. \(2(21)=42\).
Time = 0.70 (sec) , antiderivative size = 308, normalized size of antiderivative = 14.67
\[
\text {the integral} =-108 x+54 x^2-12 x^3+x^4+\frac {e^{16}}{\left (-5+e^x+x\right )^4}+\frac {4 e^{12} (-3+x)}{\left (-5+e^x+x\right )^3}+\frac {6 e^8 (-3+x)^2}{\left (-5+e^x+x\right )^2}+\frac {4 e^4 (-3+x)^3}{-5+e^x+x}+108 \log (x)-\frac {4 \left (e^{12}+3 e^{8+x} (-3+x)+3 e^{4+2 x} (-3+x)^2+6 e^{4+x} (-5+x) (-3+x)^2+e^{3 x} x \left (27-9 x+x^2\right )+3 e^x (-5+x)^2 x \left (27-9 x+x^2\right )+(-5+x)^3 x \left (27-9 x+x^2\right )+3 e^8 \left (15-8 x+x^2\right )+3 e^4 \left (15-8 x+x^2\right )^2+3 e^{2 x} x \left (-135+72 x-14 x^2+x^3\right )\right ) \log (x)}{\left (-5+e^x+x\right )^3}+\frac {6 \left (15+e^4+e^x (-3+x)-8 x+x^2\right )^2 \log ^2(x)}{\left (-5+e^x+x\right )^2}-\frac {4 \left (15+e^4+e^x (-3+x)-8 x+x^2\right ) \log ^3(x)}{-5+e^x+x}+\log ^4(x)
\]
[In]
Integrate[(-337500 + 1012500*x - 4*E^16*x - 1260000*x^2 + 872000*x^3 - 374200*x^4 + 104008*x^5 - 18816*x^6 + 2
144*x^7 - 140*x^8 + 4*x^9 + E^12*(-100 - 40*x + 52*x^2 - 8*x^3) + E^8*(-4500 + 6000*x - 2760*x^2 + 528*x^3 - 3
6*x^4) + E^(5*x)*(108 - 216*x + 144*x^2 - 40*x^3 + 4*x^4) + E^4*(-67500 + 153000*x - 137100*x^2 + 64440*x^3 -
17380*x^4 + 2712*x^5 - 228*x^6 + 8*x^7) + E^(4*x)*(-2700 + 5940*x - 4680*x^2 + 1720*x^3 - 300*x^4 + 20*x^5 + E
^4*(-108 + 288*x - 192*x^2 + 48*x^3 - 4*x^4)) + E^(3*x)*(27000 - 64800*x + 58680*x^2 - 26560*x^3 + 6440*x^4 -
800*x^5 + 40*x^6 + E^8*(36 - 156*x + 84*x^2 - 12*x^3) + E^4*(2160 - 5544*x + 4236*x^2 - 1404*x^3 + 212*x^4 - 1
2*x^5)) + E^(2*x)*(-135000 + 351000*x - 358200*x^2 + 191480*x^3 - 58760*x^4 + 10440*x^5 - 1000*x^6 + 40*x^7 +
E^12*(-4 + 40*x - 12*x^2) + E^8*(-540 + 1800*x - 1188*x^2 + 288*x^3 - 24*x^4) + E^4*(-16200 + 39960*x - 33444*
x^2 + 13320*x^3 - 2760*x^4 + 288*x^5 - 12*x^6)) + E^x*(337500 - 945000*x - 4*E^16*x + 1071000*x^2 - 657800*x^3
+ 242640*x^4 - 55480*x^5 + 7720*x^6 - 600*x^7 + 20*x^8 + E^12*(40 - 192*x + 92*x^2 - 12*x^3) + E^8*(2700 - 63
00*x + 4392*x^2 - 1368*x^3 + 204*x^4 - 12*x^5) + E^4*(54000 - 127800*x + 112740*x^2 - 50388*x^3 + 12584*x^4 -
1776*x^5 + 132*x^6 - 4*x^7)) + (-337500 + 900000*x - 960000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x
^6 + 384*x^7 - 12*x^8 + E^12*(-60*x + 12*x^2) + E^(5*x)*(108 - 180*x + 84*x^2 - 12*x^3) + E^8*(-1500 + 600*x +
240*x^2 - 120*x^3 + 12*x^4) + E^4*(-45000 + 82500*x - 56700*x^2 + 19320*x^3 - 3504*x^4 + 324*x^5 - 12*x^6) +
E^(4*x)*(-2700 + 5040*x - 3000*x^2 + 720*x^3 - 60*x^4 + E^4*(-72 + 204*x - 96*x^2 + 12*x^3)) + E^(3*x)*(27000
- 55800*x + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + E^8*(12 - 84*x + 24*x^2) + E^4*(1440 - 3720*x + 2196*
x^2 - 480*x^3 + 36*x^4)) + E^(2*x)*(-135000 + 306000*x + 12*E^12*x - 256200*x^2 + 106080*x^3 - 23400*x^4 + 264
0*x^5 - 120*x^6 + E^8*(-180 + 864*x - 396*x^2 + 48*x^3) + E^4*(-10800 + 25200*x - 17028*x^2 + 5004*x^3 - 684*x
^4 + 36*x^5)) + E^x*(337500 - 832500*x + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^7
+ E^12*(-48*x + 12*x^2) + E^8*(900 - 2340*x + 1332*x^2 - 300*x^3 + 24*x^4) + E^4*(36000 - 75000*x + 53580*x^2
- 18384*x^3 + 3336*x^4 - 312*x^5 + 12*x^6)))*Log[x] + (-112500 + 262500*x - 232500*x^2 + 106500*x^3 - 27900*x^
4 + 4236*x^5 - 348*x^6 + 12*x^7 + E^(5*x)*(36 - 48*x + 12*x^2) + E^8*(-300*x + 120*x^2 - 12*x^3) + E^4*(-7500
+ 9000*x - 3600*x^2 + 600*x^3 - 36*x^4) + E^(4*x)*(-900 + 1380*x - 540*x^2 + 60*x^3 + E^4*(-12 + 48*x - 12*x^2
)) + E^(3*x)*(9000 - 15600*x - 12*E^8*x + 8160*x^2 - 1680*x^3 + 120*x^4 + E^4*(240 - 792*x + 324*x^2 - 36*x^3)
) + E^(2*x)*(-45000 + 87000*x - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 + E^8*(108*x - 24*x^2) + E^4*(-1800
+ 4680*x - 2484*x^2 + 504*x^3 - 36*x^4)) + E^x*(112500 - 240000*x + 184500*x^2 - 69600*x^3 + 13980*x^4 - 1440
*x^5 + 60*x^6 + E^8*(-180*x + 96*x^2 - 12*x^3) + E^4*(6000 - 11400*x + 6540*x^2 - 1740*x^3 + 228*x^4 - 12*x^5)
))*Log[x]^2 + (-12500 + E^(5*x)*(4 - 4*x) + 25000*x - 17500*x^2 + 6000*x^3 - 1100*x^4 + 104*x^5 - 4*x^6 + E^(4
*x)*(-100 + 120*x + 4*E^4*x - 20*x^2) + E^4*(-500*x + 300*x^2 - 60*x^3 + 4*x^4) + E^(3*x)*(1000 - 1400*x + 440
*x^2 - 40*x^3 + E^4*(-56*x + 12*x^2)) + E^(2*x)*(-5000 + 8000*x - 3600*x^2 + 640*x^3 - 40*x^4 + E^4*(240*x - 1
08*x^2 + 12*x^3)) + E^x*(12500 - 22500*x + 13000*x^2 - 3400*x^3 + 420*x^4 - 20*x^5 + E^4*(-200*x + 180*x^2 - 4
8*x^3 + 4*x^4)))*Log[x]^3)/(-3125*x + E^(5*x)*x + 3125*x^2 - 1250*x^3 + 250*x^4 - 25*x^5 + x^6 + E^(4*x)*(-25*
x + 5*x^2) + E^(3*x)*(250*x - 100*x^2 + 10*x^3) + E^(2*x)*(-1250*x + 750*x^2 - 150*x^3 + 10*x^4) + E^x*(3125*x
- 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5)),x]
[Out]
-108*x + 54*x^2 - 12*x^3 + x^4 + E^16/(-5 + E^x + x)^4 + (4*E^12*(-3 + x))/(-5 + E^x + x)^3 + (6*E^8*(-3 + x)^
2)/(-5 + E^x + x)^2 + (4*E^4*(-3 + x)^3)/(-5 + E^x + x) + 108*Log[x] - (4*(E^12 + 3*E^(8 + x)*(-3 + x) + 3*E^(
4 + 2*x)*(-3 + x)^2 + 6*E^(4 + x)*(-5 + x)*(-3 + x)^2 + E^(3*x)*x*(27 - 9*x + x^2) + 3*E^x*(-5 + x)^2*x*(27 -
9*x + x^2) + (-5 + x)^3*x*(27 - 9*x + x^2) + 3*E^8*(15 - 8*x + x^2) + 3*E^4*(15 - 8*x + x^2)^2 + 3*E^(2*x)*x*(
-135 + 72*x - 14*x^2 + x^3))*Log[x])/(-5 + E^x + x)^3 + (6*(15 + E^4 + E^x*(-3 + x) - 8*x + x^2)^2*Log[x]^2)/(
-5 + E^x + x)^2 - (4*(15 + E^4 + E^x*(-3 + x) - 8*x + x^2)*Log[x]^3)/(-5 + E^x + x) + Log[x]^4
Maple [B] (verified)
Leaf count of result is larger than twice the leaf count of optimal. \(953\) vs. \(2(19)=38\).
Time = 4.23 (sec) , antiderivative size = 954, normalized size of antiderivative = 45.43
| | |
| method | result | size |
| | |
| risch |
\(\text {Expression too large to display}\) |
\(954\) |
| parallelrisch |
\(\text {Expression too large to display}\) |
\(2146\) |
| | |
|
|
|
|
[In]
int((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x^2-56*x)*exp(4)-40*x^3+440*x^2-1400*x+1000
)*exp(x)^3+((12*x^3-108*x^2+240*x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+180*x^2
-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x)+(4*x^4-60*x^3+300*x^2-500*x)*exp(4)-4*x
^6+104*x^5-1100*x^4+6000*x^3-17500*x^2+25000*x-12500)*ln(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x-12)*ex
p(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x^2-792*x+240)*exp(4)+120*x^4-1680*x^3+8
160*x^2-15600*x+9000)*exp(x)^3+((-24*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+120*x^5
-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-180*x)*exp(4)^2+(-12*x^5+228*x^4-1740*x
^3+6540*x^2-11400*x+6000)*exp(4)+60*x^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)+(-12*x
^3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12*x^7-348*x^6+4236*x^5-27900*x^4+106
500*x^3-232500*x^2+262500*x-112500)*ln(x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x-72)*exp
(4)-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2+(36*x^4-480*x^3+2196*x^2-3720*x+1
440)*exp(4)-120*x^5+2040*x^4-13200*x^3+40080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^2+864*x-
180)*exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6+2640*x^5-23400*x^4+106080*x^3-2
56200*x^2+306000*x-135000)*exp(x)^2+((12*x^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4)^2+(12*
x^6-312*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-18300*x^5+111540*x^4-393300*x^3
+793500*x^2-832500*x+337500)*exp(x)+(12*x^2-60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^2+(-12*x
^6+324*x^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280*x^6+40608*x^5-190200*x^4+552
000*x^3-960000*x^2+900000*x-337500)*ln(x)+(4*x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-192*x^2+28
8*x-108)*exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84*x^2-156*x+36)*exp(4)^2+(-1
2*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*exp(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800*x+27000)
*exp(x)^3+((-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+(-12*x^6+288*x^5-2760*x^4+
13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7-1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+351000*x-1
35000)*exp(x)^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368*x^3+4392*x^2-6300*x+27
00)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-50388*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-600*x^7+772
0*x^6-55480*x^5+242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(-8*x^3+52*x^2-40*x-100
)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp(4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^3-137100*
x^2+153000*x-67500)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^3-1260000*x^2+10125
00*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3-100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^2-1250*x)
*exp(x)^2+(5*x^5-100*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2-3125*x),x,method
=_RETURNVERBOSE)
[Out]
ln(x)^4-4*(x^2+exp(x)*x+exp(4)-8*x-3*exp(x)+15)/(exp(x)+x-5)*ln(x)^3+6*(x^4+2*exp(x)*x^3+exp(2*x)*x^2+2*x^2*ex
p(4)+2*x*exp(4+x)-16*x^3-22*exp(x)*x^2-6*x*exp(2*x)+exp(8)-16*x*exp(4)-6*exp(4+x)+94*x^2+78*exp(x)*x+9*exp(2*x
)+30*exp(4)-240*x-90*exp(x)+225)/(exp(x)+x-5)^2*ln(x)^2-4*(3375+3*x*exp(x+8)-5400*x+3*exp(2*x)*x^4-66*x^2*exp(
4+x)-24*x*exp(8)-9*x^2*exp(3*x)-42*exp(2*x)*x^3-48*x^3*exp(4)+27*x*exp(3*x)+216*exp(2*x)*x^2-486*x*exp(2*x)+28
2*x^2*exp(4)-57*exp(x)*x^4-1566*exp(x)*x^2+426*exp(x)*x^3+2835*exp(x)*x-9*exp(x+8)+exp(12)+27*exp(4+2*x)+234*x
*exp(4+x)-270*exp(4+x)+3*x^4*exp(4)+45*exp(8)+3*x^5*exp(x)+x^3*exp(3*x)-720*x*exp(4)+6*x^3*exp(4+x)-27*exp(3*x
)+405*exp(2*x)+675*exp(4)+x^6-24*x^5+237*x^4-1232*x^3+3555*x^2-2025*exp(x)+3*x^2*exp(8)-18*x*exp(4+2*x)+3*x^2*
exp(4+2*x))/(exp(x)+x-5)^3*ln(x)+(50625-96*x^3*exp(8)+468*x*exp(x+8)-12*exp(x+12)+6*x^2*exp(2*x+8)+x^4*exp(4*x
)-108000*x+1194*exp(2*x)*x^4-6264*x^2*exp(4+x)-1440*x*exp(8)+4*x^7*exp(x)+108*x*exp(4+3*x)-1512*x^2*exp(3*x)-5
688*exp(2*x)*x^3-12*x^3*exp(4*x)-132*x^5*exp(2*x)-4928*x^3*exp(4)+2484*x*exp(3*x)+15066*exp(2*x)*x^2-21060*x*e
xp(2*x)-108*x^6*exp(x)+14220*x^2*exp(4)-7772*exp(x)*x^4-64260*exp(x)*x^2+29004*exp(x)*x^3+78300*exp(x)*x+6*x^4
*exp(8)-32*x*exp(12)+54*exp(2*x+8)-108*exp(4+3*x)-540*exp(x+8)+60*exp(12)-108*x*exp(4*x)+1620*exp(4+2*x)+11340
*x*exp(4+x)-8100*exp(4+x)+81*exp(4*x)+948*x^4*exp(4)-96*x^5*exp(4)+1350*exp(8)+exp(16)+4*x^6*exp(4)+1236*x^5*e
xp(x)+54*x^2*exp(4*x)+456*x^3*exp(3*x)-21600*x*exp(4)+1704*x^3*exp(4+x)-1620*exp(3*x)+12150*exp(2*x)+13500*exp
(4)-32*x^7+x^8+444*x^6-3488*x^5+16966*x^4-52320*x^3+99900*x^2-40500*exp(x)+564*x^2*exp(8)+4*exp(12)*x^2-68*x^4
*exp(3*x)-36*x*exp(2*x+8)-132*x^2*exp(x+8)+6*exp(2*x)*x^6+4*exp(3*x)*x^5-1944*x*exp(4+2*x)-228*x^4*exp(4+x)-16
8*x^3*exp(4+2*x)-36*x^2*exp(4+3*x)+864*x^2*exp(4+2*x)+4*x*exp(x+12)+12*x^3*exp(x+8)+12*x^4*exp(4+2*x)+4*x^3*ex
p(4+3*x)+12*x^5*exp(4+x))/(exp(x)+x-5)^4
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1050 vs. \(2 (19) = 38\).
Time = 0.29 (sec) , antiderivative size = 1050, normalized size of antiderivative = 50.00
\[
\text {the integral} =\text {Too large to display}
\]
[In]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x^2-56*x)*exp(4)-40*x^3+440*x^2-1400*
x+1000)*exp(x)^3+((12*x^3-108*x^2+240*x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+1
80*x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x)+(4*x^4-60*x^3+300*x^2-500*x)*exp(
4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500*x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x
-12)*exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x^2-792*x+240)*exp(4)+120*x^4-168
0*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-24*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+
120*x^5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-180*x)*exp(4)^2+(-12*x^5+228*x^4
-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)
+(-12*x^3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12*x^7-348*x^6+4236*x^5-27900*
x^4+106500*x^3-232500*x^2+262500*x-112500)*log(x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x
-72)*exp(4)-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2+(36*x^4-480*x^3+2196*x^2-
3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+40080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^
2+864*x-180)*exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6+2640*x^5-23400*x^4+1060
80*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4
)^2+(12*x^6-312*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-18300*x^5+111540*x^4-39
3300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2-60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^
2+(-12*x^6+324*x^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280*x^6+40608*x^5-190200
*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4*x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-1
92*x^2+288*x-108)*exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84*x^2-156*x+36)*exp
(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*exp(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800
*x+27000)*exp(x)^3+((-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+(-12*x^6+288*x^5-
2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7-1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+3
51000*x-135000)*exp(x)^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368*x^3+4392*x^2-
6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-50388*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-60
0*x^7+7720*x^6-55480*x^5+242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(-8*x^3+52*x^2
-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp(4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^
3-137100*x^2+153000*x-67500)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^3-1260000*
x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3-100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^
2-1250*x)*exp(x)^2+(5*x^5-100*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2-3125*x)
,x, algorithm="fricas")
[Out]
(x^8 - 32*x^7 + 444*x^6 - 3488*x^5 + (x^4 - 20*x^3 + 150*x^2 + 4*(x - 5)*e^(3*x) + 6*(x^2 - 10*x + 25)*e^(2*x)
+ 4*(x^3 - 15*x^2 + 75*x - 125)*e^x - 500*x + e^(4*x) + 625)*log(x)^4 + 16885*x^4 - 4*(x^5 - 23*x^4 + 210*x^3
- 950*x^2 + (x^3 - 15*x^2 + 75*x - 125)*e^4 + (x - 3)*e^(4*x) + (4*x^2 - 32*x + e^4 + 60)*e^(3*x) + 3*(2*x^3
- 26*x^2 + (x - 5)*e^4 + 110*x - 150)*e^(2*x) + (4*x^4 - 72*x^3 + 480*x^2 + 3*(x^2 - 10*x + 25)*e^4 - 1400*x +
1500)*e^x + 2125*x - 1875)*log(x)^3 - 50700*x^3 + 6*(x^6 - 26*x^5 + 279*x^4 - 1580*x^3 + 4975*x^2 + (x^2 - 10
*x + 25)*e^8 + 2*(x^4 - 18*x^3 + 120*x^2 - 350*x + 375)*e^4 + (x^2 - 6*x + 9)*e^(4*x) + 2*(2*x^3 - 22*x^2 + (x
- 3)*e^4 + 78*x - 90)*e^(3*x) + (6*x^4 - 96*x^3 + 564*x^2 + 6*(x^2 - 8*x + 15)*e^4 - 1440*x + e^8 + 1350)*e^(
2*x) + 2*(2*x^5 - 42*x^4 + 348*x^3 - 1420*x^2 + (x - 5)*e^8 + 3*(x^3 - 13*x^2 + 55*x - 75)*e^4 + 2850*x - 2250
)*e^x - 8250*x + 5625)*log(x)^2 + 87750*x^2 + 4*(x^2 - 8*x + 15)*e^12 + 6*(x^4 - 16*x^3 + 94*x^2 - 240*x + 225
)*e^8 + 4*(x^6 - 24*x^5 + 237*x^4 - 1232*x^3 + 3555*x^2 - 5400*x + 3375)*e^4 + (x^4 - 12*x^3 + 54*x^2 - 108*x)
*e^(4*x) + 4*(x^5 - 17*x^4 + 114*x^3 - 378*x^2 + (x^3 - 9*x^2 + 27*x - 27)*e^4 + 540*x)*e^(3*x) + 6*(x^6 - 22*
x^5 + 199*x^4 - 948*x^3 + 2430*x^2 + (x^2 - 6*x + 9)*e^8 + 2*(x^4 - 14*x^3 + 72*x^2 - 162*x + 135)*e^4 - 2700*
x)*e^(2*x) + 4*(x^7 - 27*x^6 + 309*x^5 - 1943*x^4 + 7170*x^3 - 14850*x^2 + (x - 3)*e^12 + 3*(x^3 - 11*x^2 + 39
*x - 45)*e^8 + 3*(x^5 - 19*x^4 + 142*x^3 - 522*x^2 + 945*x - 675)*e^4 + 13500*x)*e^x - 4*(x^7 - 29*x^6 + 357*x
^5 - 2417*x^4 + 9715*x^3 - 23175*x^2 + (x - 5)*e^12 + 3*(x^3 - 13*x^2 + 55*x - 75)*e^8 + 3*(x^5 - 21*x^4 + 174
*x^3 - 710*x^2 + 1425*x - 1125)*e^4 + (x^3 - 9*x^2 + 27*x - 27)*e^(4*x) + (4*x^4 - 56*x^3 + 288*x^2 + 3*(x^2 -
6*x + 9)*e^4 - 648*x + 540)*e^(3*x) + 3*(2*x^5 - 38*x^4 + 284*x^3 - 1044*x^2 + (x - 3)*e^8 + 3*(x^3 - 11*x^2
+ 39*x - 45)*e^4 + 1890*x - 1350)*e^(2*x) + (4*x^6 - 96*x^5 + 948*x^4 - 4928*x^3 + 14220*x^2 + 6*(x^2 - 8*x +
15)*e^8 + 9*(x^4 - 16*x^3 + 94*x^2 - 240*x + 225)*e^4 - 21600*x + e^12 + 13500)*e^x + 30375*x - 16875)*log(x)
- 67500*x + e^16)/(x^4 - 20*x^3 + 150*x^2 + 4*(x - 5)*e^(3*x) + 6*(x^2 - 10*x + 25)*e^(2*x) + 4*(x^3 - 15*x^2
+ 75*x - 125)*e^x - 500*x + e^(4*x) + 625)
Sympy [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1107 vs. \(2 (17) = 34\).
Time = 1.49 (sec) , antiderivative size = 1107, normalized size of antiderivative = 52.71
\[
\text {the integral} =\text {Too large to display}
\]
[In]
integrate((((4-4*x)*exp(x)**5+(4*x*exp(4)-20*x**2+120*x-100)*exp(x)**4+((12*x**2-56*x)*exp(4)-40*x**3+440*x**2
-1400*x+1000)*exp(x)**3+((12*x**3-108*x**2+240*x)*exp(4)-40*x**4+640*x**3-3600*x**2+8000*x-5000)*exp(x)**2+((4
*x**4-48*x**3+180*x**2-200*x)*exp(4)-20*x**5+420*x**4-3400*x**3+13000*x**2-22500*x+12500)*exp(x)+(4*x**4-60*x*
*3+300*x**2-500*x)*exp(4)-4*x**6+104*x**5-1100*x**4+6000*x**3-17500*x**2+25000*x-12500)*ln(x)**3+((12*x**2-48*
x+36)*exp(x)**5+((-12*x**2+48*x-12)*exp(4)+60*x**3-540*x**2+1380*x-900)*exp(x)**4+(-12*x*exp(4)**2+(-36*x**3+3
24*x**2-792*x+240)*exp(4)+120*x**4-1680*x**3+8160*x**2-15600*x+9000)*exp(x)**3+((-24*x**2+108*x)*exp(4)**2+(-3
6*x**4+504*x**3-2484*x**2+4680*x-1800)*exp(4)+120*x**5-2280*x**4+16560*x**3-56400*x**2+87000*x-45000)*exp(x)**
2+((-12*x**3+96*x**2-180*x)*exp(4)**2+(-12*x**5+228*x**4-1740*x**3+6540*x**2-11400*x+6000)*exp(4)+60*x**6-1440
*x**5+13980*x**4-69600*x**3+184500*x**2-240000*x+112500)*exp(x)+(-12*x**3+120*x**2-300*x)*exp(4)**2+(-36*x**4+
600*x**3-3600*x**2+9000*x-7500)*exp(4)+12*x**7-348*x**6+4236*x**5-27900*x**4+106500*x**3-232500*x**2+262500*x-
112500)*ln(x)**2+((-12*x**3+84*x**2-180*x+108)*exp(x)**5+((12*x**3-96*x**2+204*x-72)*exp(4)-60*x**4+720*x**3-3
000*x**2+5040*x-2700)*exp(x)**4+((24*x**2-84*x+12)*exp(4)**2+(36*x**4-480*x**3+2196*x**2-3720*x+1440)*exp(4)-1
20*x**5+2040*x**4-13200*x**3+40080*x**2-55800*x+27000)*exp(x)**3+(12*x*exp(4)**3+(48*x**3-396*x**2+864*x-180)*
exp(4)**2+(36*x**5-684*x**4+5004*x**3-17028*x**2+25200*x-10800)*exp(4)-120*x**6+2640*x**5-23400*x**4+106080*x*
*3-256200*x**2+306000*x-135000)*exp(x)**2+((12*x**2-48*x)*exp(4)**3+(24*x**4-300*x**3+1332*x**2-2340*x+900)*ex
p(4)**2+(12*x**6-312*x**5+3336*x**4-18384*x**3+53580*x**2-75000*x+36000)*exp(4)-60*x**7+1620*x**6-18300*x**5+1
11540*x**4-393300*x**3+793500*x**2-832500*x+337500)*exp(x)+(12*x**2-60*x)*exp(4)**3+(12*x**4-120*x**3+240*x**2
+600*x-1500)*exp(4)**2+(-12*x**6+324*x**5-3504*x**4+19320*x**3-56700*x**2+82500*x-45000)*exp(4)-12*x**8+384*x*
*7-5280*x**6+40608*x**5-190200*x**4+552000*x**3-960000*x**2+900000*x-337500)*ln(x)+(4*x**4-40*x**3+144*x**2-21
6*x+108)*exp(x)**5+((-4*x**4+48*x**3-192*x**2+288*x-108)*exp(4)+20*x**5-300*x**4+1720*x**3-4680*x**2+5940*x-27
00)*exp(x)**4+((-12*x**3+84*x**2-156*x+36)*exp(4)**2+(-12*x**5+212*x**4-1404*x**3+4236*x**2-5544*x+2160)*exp(4
)+40*x**6-800*x**5+6440*x**4-26560*x**3+58680*x**2-64800*x+27000)*exp(x)**3+((-12*x**2+40*x-4)*exp(4)**3+(-24*
x**4+288*x**3-1188*x**2+1800*x-540)*exp(4)**2+(-12*x**6+288*x**5-2760*x**4+13320*x**3-33444*x**2+39960*x-16200
)*exp(4)+40*x**7-1000*x**6+10440*x**5-58760*x**4+191480*x**3-358200*x**2+351000*x-135000)*exp(x)**2+(-4*x*exp(
4)**4+(-12*x**3+92*x**2-192*x+40)*exp(4)**3+(-12*x**5+204*x**4-1368*x**3+4392*x**2-6300*x+2700)*exp(4)**2+(-4*
x**7+132*x**6-1776*x**5+12584*x**4-50388*x**3+112740*x**2-127800*x+54000)*exp(4)+20*x**8-600*x**7+7720*x**6-55
480*x**5+242640*x**4-657800*x**3+1071000*x**2-945000*x+337500)*exp(x)-4*x*exp(4)**4+(-8*x**3+52*x**2-40*x-100)
*exp(4)**3+(-36*x**4+528*x**3-2760*x**2+6000*x-4500)*exp(4)**2+(8*x**7-228*x**6+2712*x**5-17380*x**4+64440*x**
3-137100*x**2+153000*x-67500)*exp(4)+4*x**9-140*x**8+2144*x**7-18816*x**6+104008*x**5-374200*x**4+872000*x**3-
1260000*x**2+1012500*x-337500)/(x*exp(x)**5+(5*x**2-25*x)*exp(x)**4+(10*x**3-100*x**2+250*x)*exp(x)**3+(10*x**
4-150*x**3+750*x**2-1250*x)*exp(x)**2+(5*x**5-100*x**4+750*x**3-2500*x**2+3125*x)*exp(x)+x**6-25*x**5+250*x**4
-1250*x**3+3125*x**2-3125*x),x)
[Out]
x**4 - 12*x**3 + 54*x**2 - 108*x + (12 - 4*x)*log(x)**3 + (6*x**2 - 36*x + 54)*log(x)**2 + (-4*x**3 + 36*x**2
- 108*x)*log(x) + log(x)**4 + 108*log(x) + (4*x**6*exp(4) - 12*x**5*exp(4)*log(x) - 96*x**5*exp(4) + 12*x**4*e
xp(4)*log(x)**2 + 252*x**4*exp(4)*log(x) + 6*x**4*exp(8) + 948*x**4*exp(4) - 4*x**3*exp(4)*log(x)**3 - 216*x**
3*exp(4)*log(x)**2 - 2088*x**3*exp(4)*log(x) - 12*x**3*exp(8)*log(x) - 96*x**3*exp(8) - 4928*x**3*exp(4) + 60*
x**2*exp(4)*log(x)**3 + 6*x**2*exp(8)*log(x)**2 + 1440*x**2*exp(4)*log(x)**2 + 156*x**2*exp(8)*log(x) + 8520*x
**2*exp(4)*log(x) + 4*x**2*exp(12) + 14220*x**2*exp(4) + 564*x**2*exp(8) - 300*x*exp(4)*log(x)**3 - 4200*x*exp
(4)*log(x)**2 - 60*x*exp(8)*log(x)**2 - 660*x*exp(8)*log(x) - 17100*x*exp(4)*log(x) - 4*x*exp(12)*log(x) - 32*
x*exp(12) - 1440*x*exp(8) - 21600*x*exp(4) + (4*x**3*exp(4) - 12*x**2*exp(4)*log(x) - 36*x**2*exp(4) + 12*x*ex
p(4)*log(x)**2 + 72*x*exp(4)*log(x) + 108*x*exp(4) - 4*exp(4)*log(x)**3 - 36*exp(4)*log(x)**2 - 108*exp(4)*log
(x) - 108*exp(4))*exp(3*x) + (12*x**4*exp(4) - 36*x**3*exp(4)*log(x) - 168*x**3*exp(4) + 36*x**2*exp(4)*log(x)
**2 + 396*x**2*exp(4)*log(x) + 6*x**2*exp(8) + 864*x**2*exp(4) - 12*x*exp(4)*log(x)**3 - 288*x*exp(4)*log(x)**
2 - 1404*x*exp(4)*log(x) - 12*x*exp(8)*log(x) - 36*x*exp(8) - 1944*x*exp(4) + 60*exp(4)*log(x)**3 + 6*exp(8)*l
og(x)**2 + 540*exp(4)*log(x)**2 + 1620*exp(4)*log(x) + 36*exp(8)*log(x) + 1620*exp(4) + 54*exp(8))*exp(2*x) +
(12*x**5*exp(4) - 36*x**4*exp(4)*log(x) - 228*x**4*exp(4) + 36*x**3*exp(4)*log(x)**2 + 576*x**3*exp(4)*log(x)
+ 12*x**3*exp(8) + 1704*x**3*exp(4) - 12*x**2*exp(4)*log(x)**3 - 468*x**2*exp(4)*log(x)**2 - 3384*x**2*exp(4)*
log(x) - 24*x**2*exp(8)*log(x) - 132*x**2*exp(8) - 6264*x**2*exp(4) + 120*x*exp(4)*log(x)**3 + 12*x*exp(8)*log
(x)**2 + 1980*x*exp(4)*log(x)**2 + 8640*x*exp(4)*log(x) + 192*x*exp(8)*log(x) + 11340*x*exp(4) + 4*x*exp(12) +
468*x*exp(8) - 300*exp(4)*log(x)**3 - 60*exp(8)*log(x)**2 - 2700*exp(4)*log(x)**2 - 360*exp(8)*log(x) - 4*exp
(12)*log(x) - 8100*exp(4)*log(x) - 12*exp(12) - 540*exp(8) - 8100*exp(4))*exp(x) + 500*exp(4)*log(x)**3 + 4500
*exp(4)*log(x)**2 + 150*exp(8)*log(x)**2 + 13500*exp(4)*log(x) + 900*exp(8)*log(x) + 20*exp(12)*log(x) + 13500
*exp(4) + 1350*exp(8) + exp(16) + 60*exp(12))/(x**4 - 20*x**3 + 150*x**2 - 500*x + (4*x - 20)*exp(3*x) + (6*x*
*2 - 60*x + 150)*exp(2*x) + (4*x**3 - 60*x**2 + 300*x - 500)*exp(x) + exp(4*x) + 625)
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1075 vs. \(2 (19) = 38\).
Time = 0.74 (sec) , antiderivative size = 1075, normalized size of antiderivative = 51.19
\[
\text {the integral} =\text {Too large to display}
\]
[In]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x^2-56*x)*exp(4)-40*x^3+440*x^2-1400*
x+1000)*exp(x)^3+((12*x^3-108*x^2+240*x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+1
80*x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x)+(4*x^4-60*x^3+300*x^2-500*x)*exp(
4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500*x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x
-12)*exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x^2-792*x+240)*exp(4)+120*x^4-168
0*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-24*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+
120*x^5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-180*x)*exp(4)^2+(-12*x^5+228*x^4
-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)
+(-12*x^3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12*x^7-348*x^6+4236*x^5-27900*
x^4+106500*x^3-232500*x^2+262500*x-112500)*log(x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x
-72)*exp(4)-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2+(36*x^4-480*x^3+2196*x^2-
3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+40080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^
2+864*x-180)*exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6+2640*x^5-23400*x^4+1060
80*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4
)^2+(12*x^6-312*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-18300*x^5+111540*x^4-39
3300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2-60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^
2+(-12*x^6+324*x^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280*x^6+40608*x^5-190200
*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4*x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-1
92*x^2+288*x-108)*exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84*x^2-156*x+36)*exp
(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*exp(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800
*x+27000)*exp(x)^3+((-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+(-12*x^6+288*x^5-
2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7-1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+3
51000*x-135000)*exp(x)^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368*x^3+4392*x^2-
6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-50388*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-60
0*x^7+7720*x^6-55480*x^5+242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(-8*x^3+52*x^2
-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp(4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^
3-137100*x^2+153000*x-67500)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^3-1260000*
x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3-100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^
2-1250*x)*exp(x)^2+(5*x^5-100*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2-3125*x)
,x, algorithm="maxima")
[Out]
(x^8 - 32*x^7 + 4*x^6*(e^4 + 111) - 32*x^5*(3*e^4 + 109) + x^4*(6*e^8 + 948*e^4 + 16885) + (x^4 - 20*x^3 + 150
*x^2 - 500*x + 625)*log(x)^4 - 4*x^3*(24*e^8 + 1232*e^4 + 12675) - 4*(x^5 - 23*x^4 + x^3*(e^4 + 210) - 5*x^2*(
3*e^4 + 190) + 25*x*(3*e^4 + 85) - 125*e^4 - 1875)*log(x)^3 + 2*x^2*(2*e^12 + 282*e^8 + 7110*e^4 + 43875) + 6*
(x^6 - 26*x^5 + x^4*(2*e^4 + 279) - 4*x^3*(9*e^4 + 395) + x^2*(e^8 + 240*e^4 + 4975) - 10*x*(e^8 + 70*e^4 + 82
5) + 25*e^8 + 750*e^4 + 5625)*log(x)^2 - 4*x*(8*e^12 + 360*e^8 + 5400*e^4 + 16875) + (x^4 - 4*(x - 3)*log(x)^3
+ log(x)^4 - 12*x^3 + 6*(x^2 - 6*x + 9)*log(x)^2 + 54*x^2 - 4*(x^3 - 9*x^2 + 27*x - 27)*log(x) - 108*x)*e^(4*
x) + 4*(x^5 + (x - 5)*log(x)^4 - 17*x^4 + x^3*(e^4 + 114) - (4*x^2 - 32*x + e^4 + 60)*log(x)^3 - 9*x^2*(e^4 +
42) + 3*(2*x^3 - 22*x^2 + x*(e^4 + 78) - 3*e^4 - 90)*log(x)^2 + 27*x*(e^4 + 20) - (4*x^4 - 56*x^3 + 3*x^2*(e^4
+ 96) - 18*x*(e^4 + 36) + 27*e^4 + 540)*log(x) - 27*e^4)*e^(3*x) + 6*(x^6 - 22*x^5 + x^4*(2*e^4 + 199) + (x^2
- 10*x + 25)*log(x)^4 - 4*x^3*(7*e^4 + 237) - 2*(2*x^3 - 26*x^2 + x*(e^4 + 110) - 5*e^4 - 150)*log(x)^3 + x^2
*(e^8 + 144*e^4 + 2430) + (6*x^4 - 96*x^3 + 6*x^2*(e^4 + 94) - 48*x*(e^4 + 30) + e^8 + 90*e^4 + 1350)*log(x)^2
- 6*x*(e^8 + 54*e^4 + 450) - 2*(2*x^5 - 38*x^4 + x^3*(3*e^4 + 284) - 3*x^2*(11*e^4 + 348) + x*(e^8 + 117*e^4
+ 1890) - 3*e^8 - 135*e^4 - 1350)*log(x) + 9*e^8 + 270*e^4)*e^(2*x) + 4*(x^7 - 27*x^6 + 3*x^5*(e^4 + 103) - x^
4*(57*e^4 + 1943) + (x^3 - 15*x^2 + 75*x - 125)*log(x)^4 + 3*x^3*(e^8 + 142*e^4 + 2390) - (4*x^4 - 72*x^3 + 3*
x^2*(e^4 + 160) - 10*x*(3*e^4 + 140) + 75*e^4 + 1500)*log(x)^3 - 3*x^2*(11*e^8 + 522*e^4 + 4950) + 3*(2*x^5 -
42*x^4 + 3*x^3*(e^4 + 116) - x^2*(39*e^4 + 1420) + x*(e^8 + 165*e^4 + 2850) - 5*e^8 - 225*e^4 - 2250)*log(x)^2
+ x*(e^12 + 117*e^8 + 2835*e^4 + 13500) - (4*x^6 - 96*x^5 + 3*x^4*(3*e^4 + 316) - 16*x^3*(9*e^4 + 308) + 6*x^
2*(e^8 + 141*e^4 + 2370) - 48*x*(e^8 + 45*e^4 + 450) + e^12 + 90*e^8 + 2025*e^4 + 13500)*log(x) - 3*e^12 - 135
*e^8 - 2025*e^4)*e^x - 4*(x^7 - 29*x^6 + 3*x^5*(e^4 + 119) - x^4*(63*e^4 + 2417) + x^3*(3*e^8 + 522*e^4 + 9715
) - 3*x^2*(13*e^8 + 710*e^4 + 7725) + x*(e^12 + 165*e^8 + 4275*e^4 + 30375) - 5*e^12 - 225*e^8 - 3375*e^4 - 16
875)*log(x) + e^16 + 60*e^12 + 1350*e^8 + 13500*e^4)/(x^4 - 20*x^3 + 150*x^2 + 4*(x - 5)*e^(3*x) + 6*(x^2 - 10
*x + 25)*e^(2*x) + 4*(x^3 - 15*x^2 + 75*x - 125)*e^x - 500*x + e^(4*x) + 625)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 6815 vs. \(2 (19) = 38\).
Time = 0.99 (sec) , antiderivative size = 6815, normalized size of antiderivative = 324.52
\[
\text {the integral} =\text {Too large to display}
\]
[In]
integrate((((4-4*x)*exp(x)^5+(4*x*exp(4)-20*x^2+120*x-100)*exp(x)^4+((12*x^2-56*x)*exp(4)-40*x^3+440*x^2-1400*
x+1000)*exp(x)^3+((12*x^3-108*x^2+240*x)*exp(4)-40*x^4+640*x^3-3600*x^2+8000*x-5000)*exp(x)^2+((4*x^4-48*x^3+1
80*x^2-200*x)*exp(4)-20*x^5+420*x^4-3400*x^3+13000*x^2-22500*x+12500)*exp(x)+(4*x^4-60*x^3+300*x^2-500*x)*exp(
4)-4*x^6+104*x^5-1100*x^4+6000*x^3-17500*x^2+25000*x-12500)*log(x)^3+((12*x^2-48*x+36)*exp(x)^5+((-12*x^2+48*x
-12)*exp(4)+60*x^3-540*x^2+1380*x-900)*exp(x)^4+(-12*x*exp(4)^2+(-36*x^3+324*x^2-792*x+240)*exp(4)+120*x^4-168
0*x^3+8160*x^2-15600*x+9000)*exp(x)^3+((-24*x^2+108*x)*exp(4)^2+(-36*x^4+504*x^3-2484*x^2+4680*x-1800)*exp(4)+
120*x^5-2280*x^4+16560*x^3-56400*x^2+87000*x-45000)*exp(x)^2+((-12*x^3+96*x^2-180*x)*exp(4)^2+(-12*x^5+228*x^4
-1740*x^3+6540*x^2-11400*x+6000)*exp(4)+60*x^6-1440*x^5+13980*x^4-69600*x^3+184500*x^2-240000*x+112500)*exp(x)
+(-12*x^3+120*x^2-300*x)*exp(4)^2+(-36*x^4+600*x^3-3600*x^2+9000*x-7500)*exp(4)+12*x^7-348*x^6+4236*x^5-27900*
x^4+106500*x^3-232500*x^2+262500*x-112500)*log(x)^2+((-12*x^3+84*x^2-180*x+108)*exp(x)^5+((12*x^3-96*x^2+204*x
-72)*exp(4)-60*x^4+720*x^3-3000*x^2+5040*x-2700)*exp(x)^4+((24*x^2-84*x+12)*exp(4)^2+(36*x^4-480*x^3+2196*x^2-
3720*x+1440)*exp(4)-120*x^5+2040*x^4-13200*x^3+40080*x^2-55800*x+27000)*exp(x)^3+(12*x*exp(4)^3+(48*x^3-396*x^
2+864*x-180)*exp(4)^2+(36*x^5-684*x^4+5004*x^3-17028*x^2+25200*x-10800)*exp(4)-120*x^6+2640*x^5-23400*x^4+1060
80*x^3-256200*x^2+306000*x-135000)*exp(x)^2+((12*x^2-48*x)*exp(4)^3+(24*x^4-300*x^3+1332*x^2-2340*x+900)*exp(4
)^2+(12*x^6-312*x^5+3336*x^4-18384*x^3+53580*x^2-75000*x+36000)*exp(4)-60*x^7+1620*x^6-18300*x^5+111540*x^4-39
3300*x^3+793500*x^2-832500*x+337500)*exp(x)+(12*x^2-60*x)*exp(4)^3+(12*x^4-120*x^3+240*x^2+600*x-1500)*exp(4)^
2+(-12*x^6+324*x^5-3504*x^4+19320*x^3-56700*x^2+82500*x-45000)*exp(4)-12*x^8+384*x^7-5280*x^6+40608*x^5-190200
*x^4+552000*x^3-960000*x^2+900000*x-337500)*log(x)+(4*x^4-40*x^3+144*x^2-216*x+108)*exp(x)^5+((-4*x^4+48*x^3-1
92*x^2+288*x-108)*exp(4)+20*x^5-300*x^4+1720*x^3-4680*x^2+5940*x-2700)*exp(x)^4+((-12*x^3+84*x^2-156*x+36)*exp
(4)^2+(-12*x^5+212*x^4-1404*x^3+4236*x^2-5544*x+2160)*exp(4)+40*x^6-800*x^5+6440*x^4-26560*x^3+58680*x^2-64800
*x+27000)*exp(x)^3+((-12*x^2+40*x-4)*exp(4)^3+(-24*x^4+288*x^3-1188*x^2+1800*x-540)*exp(4)^2+(-12*x^6+288*x^5-
2760*x^4+13320*x^3-33444*x^2+39960*x-16200)*exp(4)+40*x^7-1000*x^6+10440*x^5-58760*x^4+191480*x^3-358200*x^2+3
51000*x-135000)*exp(x)^2+(-4*x*exp(4)^4+(-12*x^3+92*x^2-192*x+40)*exp(4)^3+(-12*x^5+204*x^4-1368*x^3+4392*x^2-
6300*x+2700)*exp(4)^2+(-4*x^7+132*x^6-1776*x^5+12584*x^4-50388*x^3+112740*x^2-127800*x+54000)*exp(4)+20*x^8-60
0*x^7+7720*x^6-55480*x^5+242640*x^4-657800*x^3+1071000*x^2-945000*x+337500)*exp(x)-4*x*exp(4)^4+(-8*x^3+52*x^2
-40*x-100)*exp(4)^3+(-36*x^4+528*x^3-2760*x^2+6000*x-4500)*exp(4)^2+(8*x^7-228*x^6+2712*x^5-17380*x^4+64440*x^
3-137100*x^2+153000*x-67500)*exp(4)+4*x^9-140*x^8+2144*x^7-18816*x^6+104008*x^5-374200*x^4+872000*x^3-1260000*
x^2+1012500*x-337500)/(x*exp(x)^5+(5*x^2-25*x)*exp(x)^4+(10*x^3-100*x^2+250*x)*exp(x)^3+(10*x^4-150*x^3+750*x^
2-1250*x)*exp(x)^2+(5*x^5-100*x^4+750*x^3-2500*x^2+3125*x)*exp(x)+x^6-25*x^5+250*x^4-1250*x^3+3125*x^2-3125*x)
,x, algorithm="giac")
[Out]
(x^19 + 4*x^18*e^x - 4*x^18*log(x) - 16*x^17*e^x*log(x) + 6*x^17*log(x)^2 + 24*x^16*e^x*log(x)^2 - 4*x^16*log(
x)^3 - 16*x^15*e^x*log(x)^3 + x^15*log(x)^4 + 4*x^14*e^x*log(x)^4 - 74*x^18 + 4*x^17*e^4 + 6*x^17*e^(2*x) - 27
6*x^17*e^x + 284*x^17*log(x) - 12*x^16*e^4*log(x) - 24*x^16*e^(2*x)*log(x) + 1056*x^16*e^x*log(x) - 408*x^16*l
og(x)^2 + 12*x^15*e^4*log(x)^2 + 36*x^15*e^(2*x)*log(x)^2 - 1512*x^15*e^x*log(x)^2 + 260*x^15*log(x)^3 - 4*x^1
4*e^4*log(x)^3 - 24*x^14*e^(2*x)*log(x)^3 + 960*x^14*e^x*log(x)^3 - 62*x^14*log(x)^4 + 6*x^13*e^(2*x)*log(x)^4
- 228*x^13*e^x*log(x)^4 + 2544*x^17 - 264*x^16*e^4 + 4*x^16*e^(3*x) - 384*x^16*e^(2*x) + 12*x^16*e^(x + 4) +
8796*x^16*e^x - 9324*x^16*log(x) + 756*x^15*e^4*log(x) - 16*x^15*e^(3*x)*log(x) + 1464*x^15*e^(2*x)*log(x) - 3
6*x^15*e^(x + 4)*log(x) - 32016*x^15*e^x*log(x) + 12762*x^15*log(x)^2 - 720*x^14*e^4*log(x)^2 + 24*x^14*e^(3*x
)*log(x)^2 - 2088*x^14*e^(2*x)*log(x)^2 + 36*x^14*e^(x + 4)*log(x)^2 + 43488*x^14*e^x*log(x)^2 - 7728*x^14*log
(x)^3 + 228*x^13*e^4*log(x)^3 - 16*x^13*e^(3*x)*log(x)^3 + 1320*x^13*e^(2*x)*log(x)^3 - 12*x^13*e^(x + 4)*log(
x)^3 - 26112*x^13*e^x*log(x)^3 + 1746*x^13*log(x)^4 + 4*x^12*e^(3*x)*log(x)^4 - 312*x^12*e^(2*x)*log(x)^4 + 58
44*x^12*e^x*log(x)^4 - 53888*x^16 + 6*x^15*e^8 + 8004*x^15*e^4 + x^15*e^(4*x) - 236*x^15*e^(3*x) + 11274*x^15*
e^(2*x) + 12*x^15*e^(2*x + 4) - 732*x^15*e^(x + 4) - 171572*x^15*e^x + 187580*x^15*log(x) - 12*x^14*e^8*log(x)
- 21744*x^14*e^4*log(x) - 4*x^14*e^(4*x)*log(x) + 896*x^14*e^(3*x)*log(x) - 40704*x^14*e^(2*x)*log(x) - 36*x^
14*e^(2*x + 4)*log(x) + 2088*x^14*e^(x + 4)*log(x) + 590240*x^14*e^x*log(x) - 243084*x^14*log(x)^2 + 6*x^13*e^
8*log(x)^2 + 19584*x^13*e^4*log(x)^2 + 6*x^13*e^(4*x)*log(x)^2 - 1272*x^13*e^(3*x)*log(x)^2 + 54792*x^13*e^(2*
x)*log(x)^2 + 36*x^13*e^(2*x + 4)*log(x)^2 - 1980*x^13*e^(x + 4)*log(x)^2 - 754896*x^13*e^x*log(x)^2 + 138872*
x^13*log(x)^3 - 5844*x^12*e^4*log(x)^3 - 4*x^12*e^(4*x)*log(x)^3 + 800*x^12*e^(3*x)*log(x)^3 - 32568*x^12*e^(2
*x)*log(x)^3 - 12*x^12*e^(2*x + 4)*log(x)^3 + 624*x^12*e^(x + 4)*log(x)^3 + 424928*x^12*e^x*log(x)^3 - 29480*x
^12*log(x)^4 + x^11*e^(4*x)*log(x)^4 - 188*x^11*e^(3*x)*log(x)^4 + 7206*x^11*e^(2*x)*log(x)^4 - 88700*x^11*e^x
*log(x)^4 + 786325*x^15 - 348*x^14*e^8 - 147560*x^14*e^4 - 54*x^14*e^(4*x) + 6336*x^14*e^(3*x) - 200988*x^14*e
^(2*x) + 4*x^14*e^(3*x + 4) - 672*x^14*e^(2*x + 4) + 12*x^14*e^(x + 8) + 20352*x^14*e^(x + 4) + 2287440*x^14*e
^x - 2582884*x^14*log(x) + 660*x^13*e^8*log(x) + 377448*x^13*e^4*log(x) + 204*x^13*e^(4*x)*log(x) - 22656*x^13
*e^(3*x)*log(x) + 681840*x^13*e^(2*x)*log(x) - 12*x^13*e^(3*x + 4)*log(x) + 1908*x^13*e^(2*x + 4)*log(x) - 24*
x^13*e^(x + 8)*log(x) - 54792*x^13*e^(x + 4)*log(x) - 7380336*x^13*e^x*log(x) + 3145074*x^13*log(x)^2 - 312*x^
12*e^8*log(x)^2 - 318696*x^12*e^4*log(x)^2 - 288*x^12*e^(4*x)*log(x)^2 + 30168*x^12*e^(3*x)*log(x)^2 - 858384*
x^12*e^(2*x)*log(x)^2 + 12*x^12*e^(3*x + 4)*log(x)^2 - 1800*x^12*e^(2*x + 4)*log(x)^2 + 12*x^12*e^(x + 8)*log(
x)^2 + 48852*x^12*e^(x + 4)*log(x)^2 + 8805816*x^12*e^x*log(x)^2 - 1680100*x^12*log(x)^3 + 88700*x^11*e^4*log(
x)^3 + 180*x^11*e^(4*x)*log(x)^3 - 17712*x^11*e^(3*x)*log(x)^3 + 474552*x^11*e^(2*x)*log(x)^3 - 4*x^11*e^(3*x
+ 4)*log(x)^3 + 564*x^11*e^(2*x + 4)*log(x)^3 - 14412*x^11*e^(x + 4)*log(x)^3 - 4595760*x^11*e^x*log(x)^3 + 33
1585*x^11*log(x)^4 - 42*x^10*e^(4*x)*log(x)^4 + 3864*x^10*e^(3*x)*log(x)^4 - 97020*x^10*e^(2*x)*log(x)^4 + 882
840*x^10*e^x*log(x)^4 - 8368254*x^14 + 4*x^13*e^12 + 9132*x^13*e^8 + 1845084*x^13*e^4 + 1314*x^13*e^(4*x) - 10
2312*x^13*e^(3*x) + 2426220*x^13*e^(2*x) - 204*x^13*e^(3*x + 4) + 6*x^13*e^(2*x + 8) + 16992*x^13*e^(2*x + 4)
- 636*x^13*e^(x + 8) - 340920*x^13*e^(x + 4) - 22035816*x^13*e^x + 25744452*x^13*log(x) - 4*x^12*e^12*log(x) -
16284*x^12*e^8*log(x) - 4402908*x^12*e^4*log(x) - 4644*x^12*e^(4*x)*log(x) + 341280*x^12*e^(3*x)*log(x) - 766
1304*x^12*e^(2*x)*log(x) + 576*x^12*e^(3*x + 4)*log(x) - 12*x^12*e^(2*x + 8)*log(x) - 45252*x^12*e^(2*x + 4)*l
og(x) + 1200*x^12*e^(x + 8)*log(x) + 858384*x^12*e^(x + 4)*log(x) + 66076128*x^12*e^x*log(x) - 29181456*x^12*l
og(x)^2 + 7206*x^11*e^8*log(x)^2 + 3446820*x^11*e^4*log(x)^2 + 6102*x^11*e^(4*x)*log(x)^2 - 421416*x^11*e^(3*x
)*log(x)^2 + 8916804*x^11*e^(2*x)*log(x)^2 - 540*x^11*e^(3*x + 4)*log(x)^2 + 6*x^11*e^(2*x + 8)*log(x)^2 + 398
52*x^11*e^(2*x + 4)*log(x)^2 - 564*x^11*e^(x + 8)*log(x)^2 - 711828*x^11*e^(x + 4)*log(x)^2 - 72696744*x^11*e^
x*log(x)^2 + 14414004*x^11*log(x)^3 - 882840*x^10*e^4*log(x)^3 - 3528*x^10*e^(4*x)*log(x)^3 + 227808*x^10*e^(3
*x)*log(x)^3 - 4520880*x^10*e^(2*x)*log(x)^3 + 168*x^10*e^(3*x + 4)*log(x)^3 - 11592*x^10*e^(2*x + 4)*log(x)^3
+ 194040*x^10*e^(x + 4)*log(x)^3 + 34677216*x^10*e^x*log(x)^3 - 2608746*x^10*log(x)^4 + 756*x^9*e^(4*x)*log(x
)^4 - 45360*x^9*e^(3*x)*log(x)^4 + 839160*x^9*e^(2*x)*log(x)^4 - 6020784*x^9*e^x*log(x)^4 + 67043394*x^13 - 20
0*x^12*e^12 - 143064*x^12*e^8 - 16519032*x^12*e^4 - 19008*x^12*e^(4*x) + 1105920*x^12*e^(3*x) - 20922624*x^12*
e^(2*x) + 4644*x^12*e^(3*x + 4) - 288*x^12*e^(2*x + 8) - 255960*x^12*e^(2*x + 4) + 4*x^12*e^(x + 12) + 15084*x
^12*e^(x + 8) + 3830652*x^12*e^(x + 4) + 157994496*x^12*e^x - 191505924*x^12*log(x) + 188*x^11*e^12*log(x) + 2
37276*x^11*e^8*log(x) + 36348372*x^11*e^4*log(x) + 62100*x^11*e^(4*x)*log(x) - 3401136*x^11*e^(3*x)*log(x) + 6
0807672*x^11*e^(2*x)*log(x) - 12204*x^11*e^(3*x + 4)*log(x) + 540*x^11*e^(2*x + 8)*log(x) + 632124*x^11*e^(2*x
+ 4)*log(x) - 4*x^11*e^(x + 12)*log(x) - 26568*x^11*e^(x + 8)*log(x) - 8916804*x^11*e^(x + 4)*log(x) - 435643
056*x^11*e^x*log(x) + 199714518*x^11*log(x)^2 - 97020*x^10*e^8*log(x)^2 - 26007912*x^10*e^4*log(x)^2 - 74844*x
^10*e^(4*x)*log(x)^2 + 3837456*x^10*e^(3*x)*log(x)^2 - 64461096*x^10*e^(2*x)*log(x)^2 + 10584*x^10*e^(3*x + 4)
*log(x)^2 - 252*x^10*e^(2*x + 8)*log(x)^2 - 512568*x^10*e^(2*x + 4)*log(x)^2 + 11592*x^10*e^(x + 8)*log(x)^2 +
6781320*x^10*e^(x + 4)*log(x)^2 + 435374352*x^10*e^x*log(x)^2 - 89901000*x^10*log(x)^3 + 6020784*x^9*e^4*log(
x)^3 + 39312*x^9*e^(4*x)*log(x)^3 - 1874880*x^9*e^(3*x)*log(x)^3 + 29411424*x^9*e^(2*x)*log(x)^3 - 3024*x^9*e^
(3*x + 4)*log(x)^3 + 136080*x^9*e^(2*x + 4)*log(x)^3 - 1678320*x^9*e^(x + 4)*log(x)^3 - 186217920*x^9*e^x*log(
x)^3 + 14649012*x^9*log(x)^4 - 7560*x^8*e^(4*x)*log(x)^4 + 332640*x^8*e^(3*x)*log(x)^4 - 4835376*x^8*e^(2*x)*l
og(x)^4 + 28492128*x^8*e^x*log(x)^4 - 411182784*x^12 + x^11*e^16 + 4428*x^11*e^12 + 1486134*x^11*e^8 + 1089107
64*x^11*e^4 + 181440*x^11*e^(4*x) - 8418816*x^11*e^(3*x) + 132378624*x^11*e^(2*x) - 62100*x^11*e^(3*x + 4) + 6
102*x^11*e^(2*x + 8) + 2550852*x^11*e^(2*x + 4) - 180*x^11*e^(x + 12) - 210708*x^11*e^(x + 8) - 30403836*x^11*
e^(x + 4) - 854758656*x^11*e^x + 1079764884*x^11*log(x) - 3864*x^10*e^12*log(x) - 2260440*x^10*e^8*log(x) - 21
7687176*x^10*e^4*log(x) - 539784*x^10*e^(4*x)*log(x) + 23532768*x^10*e^(3*x)*log(x) - 349426224*x^10*e^(2*x)*l
og(x) + 149688*x^10*e^(3*x + 4)*log(x) - 10584*x^10*e^(2*x + 8)*log(x) - 5756184*x^10*e^(2*x + 4)*log(x) + 168
*x^10*e^(x + 12)*log(x) + 341712*x^10*e^(x + 8)*log(x) + 64461096*x^10*e^(x + 4)*log(x) + 2140844256*x^10*e^x*
log(x) - 1020503772*x^10*log(x)^2 + 839160*x^9*e^8*log(x)^2 + 139663440*x^9*e^4*log(x)^2 + 585144*x^9*e^(4*x)*
log(x)^2 - 23786784*x^9*e^(3*x)*log(x)^2 + 330756048*x^9*e^(2*x)*log(x)^2 - 117936*x^9*e^(3*x + 4)*log(x)^2 +
4536*x^9*e^(2*x + 8)*log(x)^2 + 4218480*x^9*e^(2*x + 4)*log(x)^2 - 136080*x^9*e^(x + 8)*log(x)^2 - 44117136*x^
9*e^(x + 4)*log(x)^2 - 1905143328*x^9*e^x*log(x)^2 + 410632848*x^9*log(x)^3 - 28492128*x^8*e^4*log(x)^3 - 2721
60*x^8*e^(4*x)*log(x)^3 + 10233216*x^8*e^(3*x)*log(x)^3 - 132269760*x^8*e^(2*x)*log(x)^3 + 30240*x^8*e^(3*x +
4)*log(x)^3 - 997920*x^8*e^(2*x + 4)*log(x)^3 + 9670752*x^8*e^(x + 4)*log(x)^3 + 711441792*x^8*e^x*log(x)^3 -
58711176*x^8*log(x)^4 + 45360*x^7*e^(4*x)*log(x)^4 - 1560384*x^7*e^(3*x)*log(x)^4 + 18561312*x^7*e^(2*x)*log(x
)^4 - 92384064*x^7*e^x*log(x)^4 + 1941910848*x^11 - 42*x^10*e^16 - 56952*x^10*e^12 - 10743516*x^10*e^8 - 53521
1064*x^10*e^4 - 1197504*x^10*e^(4*x) + 46158336*x^10*e^(3*x) - 620244864*x^10*e^(2*x) + 539784*x^10*e^(3*x + 4
) - 74844*x^10*e^(2*x + 8) - 17649576*x^10*e^(2*x + 4) + 3528*x^10*e^(x + 12) + 1918728*x^10*e^(x + 8) + 17471
3112*x^10*e^(x + 4) + 3493850112*x^10*e^x - 4635782280*x^10*log(x) + 45360*x^9*e^12*log(x) + 14705712*x^9*e^8*
log(x) + 952571664*x^9*e^4*log(x) + 3184272*x^9*e^(4*x)*log(x) - 115286976*x^9*e^(3*x)*log(x) + 1464135264*x^9
*e^(2*x)*log(x) - 1170288*x^9*e^(3*x + 4)*log(x) + 117936*x^9*e^(2*x + 8)*log(x) + 35680176*x^9*e^(2*x + 4)*lo
g(x) - 3024*x^9*e^(x + 12)*log(x) - 2812320*x^9*e^(x + 8)*log(x) - 330756048*x^9*e^(x + 4)*log(x) - 7838907840
*x^9*e^x*log(x) + 3892162104*x^9*log(x)^2 - 4835376*x^8*e^8*log(x)^2 - 533581344*x^8*e^4*log(x)^2 - 3020976*x^
8*e^(4*x)*log(x)^2 + 101570112*x^8*e^(3*x)*log(x)^2 - 1203934752*x^8*e^(2*x)*log(x)^2 + 816480*x^8*e^(3*x + 4)
*log(x)^2 - 45360*x^8*e^(2*x + 8)*log(x)^2 - 23024736*x^8*e^(2*x + 4)*log(x)^2 + 997920*x^8*e^(x + 8)*log(x)^2
+ 198404640*x^8*e^(x + 4)*log(x)^2 + 6042931776*x^8*e^x*log(x)^2 - 1362876192*x^8*log(x)^3 + 92384064*x^7*e^4
*log(x)^3 + 1197504*x^7*e^(4*x)*log(x)^3 - 37013760*x^7*e^(3*x)*log(x)^3 + 405813888*x^7*e^(2*x)*log(x)^3 - 18
1440*x^7*e^(3*x + 4)*log(x)^3 + 4681152*x^7*e^(2*x + 4)*log(x)^3 - 37122624*x^7*e^(x + 4)*log(x)^3 - 189429580
8*x^7*e^x*log(x)^3 + 164585520*x^7*log(x)^4 - 163296*x^6*e^(4*x)*log(x)^4 + 4572288*x^6*e^(3*x)*log(x)^4 - 457
69536*x^6*e^(2*x)*log(x)^4 + 196421760*x^6*e^x*log(x)^4 - 7034869440*x^10 + 756*x^9*e^16 + 468720*x^9*e^12 + 5
5126008*x^9*e^8 + 1959726960*x^9*e^4 + 5552064*x^9*e^(4*x) - 182704896*x^9*e^(3*x) + 2139550848*x^9*e^(2*x) -
3184272*x^9*e^(3*x + 4) + 585144*x^9*e^(2*x + 8) + 86465232*x^9*e^(2*x + 4) - 39312*x^9*e^(x + 12) - 11893392*
x^9*e^(x + 8) - 732067632*x^9*e^(x + 4) - 10670227200*x^9*e^x + 15077364624*x^9*log(x) - 332640*x^8*e^12*log(x
) - 66134880*x^8*e^8*log(x) - 3021465888*x^8*e^4*log(x) - 12900384*x^8*e^(4*x)*log(x) + 399655296*x^8*e^(3*x)*
log(x) - 4437685440*x^8*e^(2*x)*log(x) + 6041952*x^8*e^(3*x + 4)*log(x) - 816480*x^8*e^(2*x + 8)*log(x) - 1523
55168*x^8*e^(2*x + 4)*log(x) + 30240*x^8*e^(x + 12)*log(x) + 15349824*x^8*e^(x + 8)*log(x) + 1203934752*x^8*e^
(x + 4)*log(x) + 21114919296*x^8*e^x*log(x) - 10939560624*x^8*log(x)^2 + 18561312*x^7*e^8*log(x)^2 + 142072185
6*x^7*e^4*log(x)^2 + 10287648*x^7*e^(4*x)*log(x)^2 - 294772608*x^7*e^(3*x)*log(x)^2 + 3044723904*x^7*e^(2*x)*l
og(x)^2 - 3592512*x^7*e^(3*x + 4)*log(x)^2 + 272160*x^7*e^(2*x + 8)*log(x)^2 + 83280960*x^7*e^(2*x + 4)*log(x)
^2 - 4681152*x^7*e^(x + 8)*log(x)^2 - 608720832*x^7*e^(x + 4)*log(x)^2 - 13543583616*x^7*e^x*log(x)^2 + 320441
1840*x^7*log(x)^3 - 196421760*x^6*e^4*log(x)^3 - 3265920*x^6*e^(4*x)*log(x)^3 + 85473792*x^6*e^(3*x)*log(x)^3
- 812374272*x^6*e^(2*x)*log(x)^3 + 653184*x^6*e^(3*x + 4)*log(x)^3 - 13716864*x^6*e^(2*x + 4)*log(x)^3 + 91539
072*x^6*e^(x + 4)*log(x)^3 + 3346168320*x^6*e^x*log(x)^3 - 307346400*x^6*log(x)^4 + 326592*x^5*e^(4*x)*log(x)^
4 - 7651584*x^5*e^(3*x)*log(x)^4 + 65784960*x^5*e^(2*x)*log(x)^4 - 247276800*x^5*e^x*log(x)^4 + 19260669888*x^
9 - 7560*x^8*e^16 - 2558304*x^8*e^12 - 200655792*x^8*e^8 - 5278729824*x^8*e^4 - 17915904*x^8*e^(4*x) + 5128427
52*x^8*e^(3*x) - 5307586560*x^8*e^(2*x) + 12900384*x^8*e^(3*x + 4) - 3020976*x^8*e^(2*x + 8) - 299741472*x^8*e
^(2*x + 4) + 272160*x^8*e^(x + 12) + 50785056*x^8*e^(x + 8) + 2218842720*x^8*e^(x + 4) + 23691543552*x^8*e^x -
36556865568*x^8*log(x) + 1560384*x^7*e^12*log(x) + 202906944*x^7*e^8*log(x) + 6771791808*x^7*e^4*log(x) + 354
11904*x^7*e^(4*x)*log(x) - 960180480*x^7*e^(3*x)*log(x) + 9483951744*x^7*e^(2*x)*log(x) - 20575296*x^7*e^(3*x
+ 4)*log(x) + 3592512*x^7*e^(2*x + 8)*log(x) + 442158912*x^7*e^(2*x + 4)*log(x) - 181440*x^7*e^(x + 12)*log(x)
- 55520640*x^7*e^(x + 8)*log(x) - 3044723904*x^7*e^(x + 4)*log(x) - 40652865792*x^7*e^x*log(x) + 22016616480*
x^7*log(x)^2 - 45769536*x^6*e^8*log(x)^2 - 2509626240*x^6*e^4*log(x)^2 - 22254912*x^6*e^(4*x)*log(x)^2 + 55595
2896*x^6*e^(3*x)*log(x)^2 - 5091755904*x^6*e^(2*x)*log(x)^2 + 9797760*x^6*e^(3*x + 4)*log(x)^2 - 979776*x^6*e^
(2*x + 8)*log(x)^2 - 192316032*x^6*e^(2*x + 4)*log(x)^2 + 13716864*x^6*e^(x + 8)*log(x)^2 + 1218561408*x^6*e^(
x + 4)*log(x)^2 + 20348547840*x^6*e^x*log(x)^2 - 5064508800*x^6*log(x)^3 + 247276800*x^5*e^4*log(x)^3 + 503884
8*x^5*e^(4*x)*log(x)^3 - 114213888*x^5*e^(3*x)*log(x)^3 + 957381120*x^5*e^(2*x)*log(x)^3 - 1306368*x^5*e^(3*x
+ 4)*log(x)^3 + 22954752*x^5*e^(2*x + 4)*log(x)^3 - 131569920*x^5*e^(x + 4)*log(x)^3 - 3527193600*x^5*e^x*log(
x)^3 + 344088000*x^5*log(x)^4 - 279936*x^4*e^(4*x)*log(x)^4 + 5598720*x^4*e^(3*x)*log(x)^4 - 41990400*x^4*e^(2
*x)*log(x)^4 + 139968000*x^4*e^x*log(x)^4 - 38675957760*x^8 + 45360*x^7*e^16 + 9253440*x^7*e^12 + 507453984*x^
7*e^8 + 10163216448*x^7*e^4 + 38631168*x^7*e^(4*x) - 974177280*x^7*e^(3*x) + 8999382528*x^7*e^(2*x) - 35411904
*x^7*e^(3*x + 4) + 10287648*x^7*e^(2*x + 8) + 720135360*x^7*e^(2*x + 4) - 1197504*x^7*e^(x + 12) - 147386304*x
^7*e^(x + 8) - 4741975872*x^7*e^(x + 4) - 36246113280*x^7*e^x + 64055655360*x^7*log(x) - 4572288*x^6*e^12*log(
x) - 406187136*x^6*e^8*log(x) - 10174273920*x^6*e^4*log(x) - 62985600*x^6*e^(4*x)*log(x) + 1521732096*x^6*e^(3
*x)*log(x) - 13559539968*x^6*e^(2*x)*log(x) + 44509824*x^6*e^(3*x + 4)*log(x) - 9797760*x^6*e^(2*x + 8)*log(x)
- 833929344*x^6*e^(2*x + 4)*log(x) + 653184*x^6*e^(x + 12)*log(x) + 128210688*x^6*e^(x + 8)*log(x) + 50917559
04*x^6*e^(x + 4)*log(x) + 52958292480*x^6*e^x*log(x) - 30033633600*x^6*log(x)^2 + 65784960*x^5*e^8*log(x)^2 +
2645395200*x^5*e^4*log(x)^2 + 27713664*x^5*e^(4*x)*log(x)^2 - 614739456*x^5*e^(3*x)*log(x)^2 + 5064042240*x^5*
e^(2*x)*log(x)^2 - 15116544*x^5*e^(3*x + 4)*log(x)^2 + 1959552*x^5*e^(2*x + 8)*log(x)^2 + 256981248*x^5*e^(2*x
+ 4)*log(x)^2 - 22954752*x^5*e^(x + 8)*log(x)^2 - 1436071680*x^5*e^(x + 4)*log(x)^2 - 18391795200*x^5*e^x*log
(x)^2 + 4828896000*x^5*log(x)^3 - 139968000*x^4*e^4*log(x)^3 - 3359232*x^4*e^(4*x)*log(x)^3 + 67184640*x^4*e^(
3*x)*log(x)^3 - 503884800*x^4*e^(2*x)*log(x)^3 + 1119744*x^4*e^(3*x + 4)*log(x)^3 - 16796160*x^4*e^(2*x + 4)*l
og(x)^3 + 83980800*x^4*e^(x + 4)*log(x)^3 + 1679616000*x^4*e^x*log(x)^3 - 174960000*x^4*log(x)^4 + 53873683200
*x^7 - 163296*x^6*e^16 - 21368448*x^6*e^12 - 848625984*x^6*e^8 - 13239573120*x^6*e^4 - 50388480*x^6*e^(4*x) +
1128701952*x^6*e^(3*x) - 9372257280*x^6*e^(2*x) + 62985600*x^6*e^(3*x + 4) - 22254912*x^6*e^(2*x + 8) - 114129
9072*x^6*e^(2*x + 4) + 3265920*x^6*e^(x + 12) + 277976448*x^6*e^(x + 8) + 6779769984*x^6*e^(x + 4) + 342641664
00*x^6*e^x - 76653475200*x^6*log(x) + 7651584*x^5*e^12*log(x) + 478690560*x^5*e^8*log(x) + 9195897600*x^5*e^4*
log(x) + 65505024*x^5*e^(4*x)*log(x) - 1431032832*x^5*e^(3*x)*log(x) + 11639738880*x^5*e^(2*x)*log(x) - 554273
28*x^5*e^(3*x + 4)*log(x) + 15116544*x^5*e^(2*x + 8)*log(x) + 922109184*x^5*e^(2*x + 4)*log(x) - 1306368*x^5*e
^(x + 12)*log(x) - 171320832*x^5*e^(x + 8)*log(x) - 5064042240*x^5*e^(x + 4)*log(x) - 41822438400*x^5*e^x*log(
x) + 24879312000*x^5*log(x)^2 - 41990400*x^4*e^8*log(x)^2 - 1259712000*x^4*e^4*log(x)^2 - 15116544*x^4*e^(4*x)
*log(x)^2 + 302330880*x^4*e^(3*x)*log(x)^2 - 2267481600*x^4*e^(2*x)*log(x)^2 + 10077696*x^4*e^(3*x + 4)*log(x)
^2 - 1679616*x^4*e^(2*x + 8)*log(x)^2 - 151165440*x^4*e^(2*x + 4)*log(x)^2 + 16796160*x^4*e^(x + 8)*log(x)^2 +
755827200*x^4*e^(x + 4)*log(x)^2 + 7558272000*x^4*e^x*log(x)^2 - 2099520000*x^4*log(x)^3 - 46609344000*x^6 +
326592*x^5*e^16 + 28553472*x^5*e^12 + 844007040*x^5*e^8 + 10455609600*x^5*e^4 + 30233088*x^5*e^(4*x) - 6046617
60*x^5*e^(3*x) + 4534963200*x^5*e^(2*x) - 65505024*x^5*e^(3*x + 4) + 27713664*x^5*e^(2*x + 8) + 1073274624*x^5
*e^(2*x + 4) - 5038848*x^5*e^(x + 12) - 307369728*x^5*e^(x + 8) - 5819869440*x^5*e^(x + 4) - 15116544000*x^5*e
^x + 56057184000*x^5*log(x) - 5598720*x^4*e^12*log(x) - 251942400*x^4*e^8*log(x) - 3779136000*x^4*e^4*log(x) -
30233088*x^4*e^(4*x)*log(x) + 604661760*x^4*e^(3*x)*log(x) - 4534963200*x^4*e^(2*x)*log(x) + 30233088*x^4*e^(
3*x + 4)*log(x) - 10077696*x^4*e^(2*x + 8)*log(x) - 453496320*x^4*e^(2*x + 4)*log(x) + 1119744*x^4*e^(x + 12)*
log(x) + 100776960*x^4*e^(x + 8)*log(x) + 2267481600*x^4*e^(x + 4)*log(x) + 15116544000*x^4*e^x*log(x) - 94478
40000*x^4*log(x)^2 + 18895680000*x^5 - 279936*x^4*e^16 - 16796160*x^4*e^12 - 377913600*x^4*e^8 - 3779136000*x^
4*e^4 + 30233088*x^4*e^(3*x + 4) - 15116544*x^4*e^(2*x + 8) - 453496320*x^4*e^(2*x + 4) + 3359232*x^4*e^(x + 1
2) + 151165440*x^4*e^(x + 8) + 2267481600*x^4*e^(x + 4) - 18895680000*x^4*log(x))/(x^15 + 4*x^14*e^x - 62*x^14
+ 6*x^13*e^(2*x) - 228*x^13*e^x + 1746*x^13 + 4*x^12*e^(3*x) - 312*x^12*e^(2*x) + 5844*x^12*e^x - 29480*x^12
+ x^11*e^(4*x) - 188*x^11*e^(3*x) + 7206*x^11*e^(2*x) - 88700*x^11*e^x + 331585*x^11 - 42*x^10*e^(4*x) + 3864*
x^10*e^(3*x) - 97020*x^10*e^(2*x) + 882840*x^10*e^x - 2608746*x^10 + 756*x^9*e^(4*x) - 45360*x^9*e^(3*x) + 839
160*x^9*e^(2*x) - 6020784*x^9*e^x + 14649012*x^9 - 7560*x^8*e^(4*x) + 332640*x^8*e^(3*x) - 4835376*x^8*e^(2*x)
+ 28492128*x^8*e^x - 58711176*x^8 + 45360*x^7*e^(4*x) - 1560384*x^7*e^(3*x) + 18561312*x^7*e^(2*x) - 92384064
*x^7*e^x + 164585520*x^7 - 163296*x^6*e^(4*x) + 4572288*x^6*e^(3*x) - 45769536*x^6*e^(2*x) + 196421760*x^6*e^x
- 307346400*x^6 + 326592*x^5*e^(4*x) - 7651584*x^5*e^(3*x) + 65784960*x^5*e^(2*x) - 247276800*x^5*e^x + 34408
8000*x^5 - 279936*x^4*e^(4*x) + 5598720*x^4*e^(3*x) - 41990400*x^4*e^(2*x) + 139968000*x^4*e^x - 174960000*x^4
)
Mupad [F(-1)]
Timed out. \[
\text {the integral} =\text {Too large to display}
\]
[In]
int(-(log(x)^2*(exp(3*x)*(15600*x + 12*x*exp(8) + exp(4)*(792*x - 324*x^2 + 36*x^3 - 240) - 8160*x^2 + 1680*x^
3 - 120*x^4 - 9000) - exp(5*x)*(12*x^2 - 48*x + 36) - 262500*x + exp(8)*(300*x - 120*x^2 + 12*x^3) + exp(4*x)*
(exp(4)*(12*x^2 - 48*x + 12) - 1380*x + 540*x^2 - 60*x^3 + 900) - exp(2*x)*(87000*x + exp(8)*(108*x - 24*x^2)
- exp(4)*(2484*x^2 - 4680*x - 504*x^3 + 36*x^4 + 1800) - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 - 45000) +
exp(4)*(3600*x^2 - 9000*x - 600*x^3 + 36*x^4 + 7500) + exp(x)*(240000*x + exp(8)*(180*x - 96*x^2 + 12*x^3) +
exp(4)*(11400*x - 6540*x^2 + 1740*x^3 - 228*x^4 + 12*x^5 - 6000) - 184500*x^2 + 69600*x^3 - 13980*x^4 + 1440*x
^5 - 60*x^6 - 112500) + 232500*x^2 - 106500*x^3 + 27900*x^4 - 4236*x^5 + 348*x^6 - 12*x^7 + 112500) - 1012500*
x + exp(3*x)*(64800*x + exp(8)*(156*x - 84*x^2 + 12*x^3 - 36) + exp(4)*(5544*x - 4236*x^2 + 1404*x^3 - 212*x^4
+ 12*x^5 - 2160) - 58680*x^2 + 26560*x^3 - 6440*x^4 + 800*x^5 - 40*x^6 - 27000) + 4*x*exp(16) - exp(4)*(15300
0*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 2712*x^5 - 228*x^6 + 8*x^7 - 67500) + exp(4*x)*(exp(4)*(192*x^2 - 2
88*x - 48*x^3 + 4*x^4 + 108) - 5940*x + 4680*x^2 - 1720*x^3 + 300*x^4 - 20*x^5 + 2700) + exp(12)*(40*x - 52*x^
2 + 8*x^3 + 100) - exp(5*x)*(144*x^2 - 216*x - 40*x^3 + 4*x^4 + 108) - log(x)*(900000*x - exp(4)*(56700*x^2 -
82500*x - 19320*x^3 + 3504*x^4 - 324*x^5 + 12*x^6 + 45000) - exp(12)*(60*x - 12*x^2) - exp(5*x)*(180*x - 84*x^
2 + 12*x^3 - 108) + exp(2*x)*(306000*x + 12*x*exp(12) + exp(8)*(864*x - 396*x^2 + 48*x^3 - 180) + exp(4)*(2520
0*x - 17028*x^2 + 5004*x^3 - 684*x^4 + 36*x^5 - 10800) - 256200*x^2 + 106080*x^3 - 23400*x^4 + 2640*x^5 - 120*
x^6 - 135000) + exp(3*x)*(exp(8)*(24*x^2 - 84*x + 12) - 55800*x + exp(4)*(2196*x^2 - 3720*x - 480*x^3 + 36*x^4
+ 1440) + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + 27000) + exp(x)*(exp(4)*(53580*x^2 - 75000*x - 18384*x
^3 + 3336*x^4 - 312*x^5 + 12*x^6 + 36000) - 832500*x - exp(12)*(48*x - 12*x^2) + exp(8)*(1332*x^2 - 2340*x - 3
00*x^3 + 24*x^4 + 900) + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^7 + 337500) + exp(
8)*(600*x + 240*x^2 - 120*x^3 + 12*x^4 - 1500) - 960000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 +
384*x^7 - 12*x^8 + exp(4*x)*(5040*x + exp(4)*(204*x - 96*x^2 + 12*x^3 - 72) - 3000*x^2 + 720*x^3 - 60*x^4 - 2
700) - 337500) + exp(8)*(2760*x^2 - 6000*x - 528*x^3 + 36*x^4 + 4500) + exp(x)*(945000*x + 4*x*exp(16) + exp(4
)*(127800*x - 112740*x^2 + 50388*x^3 - 12584*x^4 + 1776*x^5 - 132*x^6 + 4*x^7 - 54000) + exp(12)*(192*x - 92*x
^2 + 12*x^3 - 40) + exp(8)*(6300*x - 4392*x^2 + 1368*x^3 - 204*x^4 + 12*x^5 - 2700) - 1071000*x^2 + 657800*x^3
- 242640*x^4 + 55480*x^5 - 7720*x^6 + 600*x^7 - 20*x^8 - 337500) + 1260000*x^2 - 872000*x^3 + 374200*x^4 - 10
4008*x^5 + 18816*x^6 - 2144*x^7 + 140*x^8 - 4*x^9 + log(x)^3*(exp(3*x)*(1400*x + exp(4)*(56*x - 12*x^2) - 440*
x^2 + 40*x^3 - 1000) - exp(4*x)*(120*x + 4*x*exp(4) - 20*x^2 - 100) - 25000*x + exp(4)*(500*x - 300*x^2 + 60*x
^3 - 4*x^4) + exp(5*x)*(4*x - 4) + 17500*x^2 - 6000*x^3 + 1100*x^4 - 104*x^5 + 4*x^6 - exp(2*x)*(8000*x + exp(
4)*(240*x - 108*x^2 + 12*x^3) - 3600*x^2 + 640*x^3 - 40*x^4 - 5000) + exp(x)*(22500*x + exp(4)*(200*x - 180*x^
2 + 48*x^3 - 4*x^4) - 13000*x^2 + 3400*x^3 - 420*x^4 + 20*x^5 - 12500) + 12500) + exp(2*x)*(exp(4)*(33444*x^2
- 39960*x - 13320*x^3 + 2760*x^4 - 288*x^5 + 12*x^6 + 16200) - 351000*x + exp(12)*(12*x^2 - 40*x + 4) + exp(8)
*(1188*x^2 - 1800*x - 288*x^3 + 24*x^4 + 540) + 358200*x^2 - 191480*x^3 + 58760*x^4 - 10440*x^5 + 1000*x^6 - 4
0*x^7 + 135000) + 337500)/(x*exp(5*x) - exp(4*x)*(25*x - 5*x^2) - 3125*x + exp(3*x)*(250*x - 100*x^2 + 10*x^3)
+ exp(x)*(3125*x - 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5) - exp(2*x)*(1250*x - 750*x^2 + 150*x^3 - 10*x^4) + 3
125*x^2 - 1250*x^3 + 250*x^4 - 25*x^5 + x^6),x)
[Out]
int(-(log(x)^2*(exp(3*x)*(15600*x + 12*x*exp(8) + exp(4)*(792*x - 324*x^2 + 36*x^3 - 240) - 8160*x^2 + 1680*x^
3 - 120*x^4 - 9000) - exp(5*x)*(12*x^2 - 48*x + 36) - 262500*x + exp(8)*(300*x - 120*x^2 + 12*x^3) + exp(4*x)*
(exp(4)*(12*x^2 - 48*x + 12) - 1380*x + 540*x^2 - 60*x^3 + 900) - exp(2*x)*(87000*x + exp(8)*(108*x - 24*x^2)
- exp(4)*(2484*x^2 - 4680*x - 504*x^3 + 36*x^4 + 1800) - 56400*x^2 + 16560*x^3 - 2280*x^4 + 120*x^5 - 45000) +
exp(4)*(3600*x^2 - 9000*x - 600*x^3 + 36*x^4 + 7500) + exp(x)*(240000*x + exp(8)*(180*x - 96*x^2 + 12*x^3) +
exp(4)*(11400*x - 6540*x^2 + 1740*x^3 - 228*x^4 + 12*x^5 - 6000) - 184500*x^2 + 69600*x^3 - 13980*x^4 + 1440*x
^5 - 60*x^6 - 112500) + 232500*x^2 - 106500*x^3 + 27900*x^4 - 4236*x^5 + 348*x^6 - 12*x^7 + 112500) - 1012500*
x + exp(3*x)*(64800*x + exp(8)*(156*x - 84*x^2 + 12*x^3 - 36) + exp(4)*(5544*x - 4236*x^2 + 1404*x^3 - 212*x^4
+ 12*x^5 - 2160) - 58680*x^2 + 26560*x^3 - 6440*x^4 + 800*x^5 - 40*x^6 - 27000) + 4*x*exp(16) - exp(4)*(15300
0*x - 137100*x^2 + 64440*x^3 - 17380*x^4 + 2712*x^5 - 228*x^6 + 8*x^7 - 67500) + exp(4*x)*(exp(4)*(192*x^2 - 2
88*x - 48*x^3 + 4*x^4 + 108) - 5940*x + 4680*x^2 - 1720*x^3 + 300*x^4 - 20*x^5 + 2700) + exp(12)*(40*x - 52*x^
2 + 8*x^3 + 100) - exp(5*x)*(144*x^2 - 216*x - 40*x^3 + 4*x^4 + 108) - log(x)*(900000*x - exp(4)*(56700*x^2 -
82500*x - 19320*x^3 + 3504*x^4 - 324*x^5 + 12*x^6 + 45000) - exp(12)*(60*x - 12*x^2) - exp(5*x)*(180*x - 84*x^
2 + 12*x^3 - 108) + exp(2*x)*(306000*x + 12*x*exp(12) + exp(8)*(864*x - 396*x^2 + 48*x^3 - 180) + exp(4)*(2520
0*x - 17028*x^2 + 5004*x^3 - 684*x^4 + 36*x^5 - 10800) - 256200*x^2 + 106080*x^3 - 23400*x^4 + 2640*x^5 - 120*
x^6 - 135000) + exp(3*x)*(exp(8)*(24*x^2 - 84*x + 12) - 55800*x + exp(4)*(2196*x^2 - 3720*x - 480*x^3 + 36*x^4
+ 1440) + 40080*x^2 - 13200*x^3 + 2040*x^4 - 120*x^5 + 27000) + exp(x)*(exp(4)*(53580*x^2 - 75000*x - 18384*x
^3 + 3336*x^4 - 312*x^5 + 12*x^6 + 36000) - 832500*x - exp(12)*(48*x - 12*x^2) + exp(8)*(1332*x^2 - 2340*x - 3
00*x^3 + 24*x^4 + 900) + 793500*x^2 - 393300*x^3 + 111540*x^4 - 18300*x^5 + 1620*x^6 - 60*x^7 + 337500) + exp(
8)*(600*x + 240*x^2 - 120*x^3 + 12*x^4 - 1500) - 960000*x^2 + 552000*x^3 - 190200*x^4 + 40608*x^5 - 5280*x^6 +
384*x^7 - 12*x^8 + exp(4*x)*(5040*x + exp(4)*(204*x - 96*x^2 + 12*x^3 - 72) - 3000*x^2 + 720*x^3 - 60*x^4 - 2
700) - 337500) + exp(8)*(2760*x^2 - 6000*x - 528*x^3 + 36*x^4 + 4500) + exp(x)*(945000*x + 4*x*exp(16) + exp(4
)*(127800*x - 112740*x^2 + 50388*x^3 - 12584*x^4 + 1776*x^5 - 132*x^6 + 4*x^7 - 54000) + exp(12)*(192*x - 92*x
^2 + 12*x^3 - 40) + exp(8)*(6300*x - 4392*x^2 + 1368*x^3 - 204*x^4 + 12*x^5 - 2700) - 1071000*x^2 + 657800*x^3
- 242640*x^4 + 55480*x^5 - 7720*x^6 + 600*x^7 - 20*x^8 - 337500) + 1260000*x^2 - 872000*x^3 + 374200*x^4 - 10
4008*x^5 + 18816*x^6 - 2144*x^7 + 140*x^8 - 4*x^9 + log(x)^3*(exp(3*x)*(1400*x + exp(4)*(56*x - 12*x^2) - 440*
x^2 + 40*x^3 - 1000) - exp(4*x)*(120*x + 4*x*exp(4) - 20*x^2 - 100) - 25000*x + exp(4)*(500*x - 300*x^2 + 60*x
^3 - 4*x^4) + exp(5*x)*(4*x - 4) + 17500*x^2 - 6000*x^3 + 1100*x^4 - 104*x^5 + 4*x^6 - exp(2*x)*(8000*x + exp(
4)*(240*x - 108*x^2 + 12*x^3) - 3600*x^2 + 640*x^3 - 40*x^4 - 5000) + exp(x)*(22500*x + exp(4)*(200*x - 180*x^
2 + 48*x^3 - 4*x^4) - 13000*x^2 + 3400*x^3 - 420*x^4 + 20*x^5 - 12500) + 12500) + exp(2*x)*(exp(4)*(33444*x^2
- 39960*x - 13320*x^3 + 2760*x^4 - 288*x^5 + 12*x^6 + 16200) - 351000*x + exp(12)*(12*x^2 - 40*x + 4) + exp(8)
*(1188*x^2 - 1800*x - 288*x^3 + 24*x^4 + 540) + 358200*x^2 - 191480*x^3 + 58760*x^4 - 10440*x^5 + 1000*x^6 - 4
0*x^7 + 135000) + 337500)/(x*exp(5*x) - exp(4*x)*(25*x - 5*x^2) - 3125*x + exp(3*x)*(250*x - 100*x^2 + 10*x^3)
+ exp(x)*(3125*x - 2500*x^2 + 750*x^3 - 100*x^4 + 5*x^5) - exp(2*x)*(1250*x - 750*x^2 + 150*x^3 - 10*x^4) + 3
125*x^2 - 1250*x^3 + 250*x^4 - 25*x^5 + x^6), x)