3.8.3 \(\int \frac {-288 x+4416 x^2-28803 x^3+104206 x^4-229260 x^5+318269 x^6-283473 x^7+164104 x^8-61968 x^9+15115 x^{10}-2343 x^{11}+236 x^{12}-18 x^{13}+x^{14}+e^{20} (x^4-x^6)+e^{15} (3 x^3-22 x^4+48 x^5-29 x^6+2 x^8)+e^{10} (96 x^2-585 x^3+1047 x^4-315 x^5-435 x^6+171 x^7+45 x^8-18 x^9)+e^5 (288 x-3648 x^2+18729 x^3-49936 x^4+74007 x^5-61691 x^6+29295 x^7-8121 x^8+1494 x^9-253 x^{10}+36 x^{11}-2 x^{12})+(864-13248 x+86427 x^2-312894 x^3+689580 x^4-961317 x^5+864729 x^6-512136 x^7+203472 x^8-55395 x^9+10719 x^{10}-1548 x^{11}+162 x^{12}-9 x^{13}+e^{15} (9 x^3-27 x^4+27 x^6-9 x^7)+e^{10} (27 x^2-270 x^3+999 x^4-1665 x^5+1215 x^6-333 x^7+9 x^9)+e^5 (288 x-2646 x^2+9027 x^3-13797 x^4+9081 x^5-3078 x^6+2934 x^7-2808 x^8+1143 x^9-189 x^{10}+9 x^{11})) \log (x)+(-81 x+1242 x^2-8100 x^3+29295 x^4-64395 x^5+89208 x^6-79056 x^7+45225 x^8-16605 x^9+3780 x^{10}-486 x^{11}+27 x^{12}+e^{10} (27 x^2-162 x^3+270 x^4-270 x^6+162 x^7-27 x^8)+e^5 (81 x-1026 x^2+5265 x^3-14013 x^4+20655 x^5-16929 x^6+7614 x^7-1755 x^8+162 x^9)) \log ^2(x)+(81-1242 x+8100 x^2-29295 x^3+64395 x^4-89208 x^5+79056 x^6-45225 x^7+16605 x^8-3780 x^9+486 x^{10}-27 x^{11}+e^5 (27 x-243 x^2+783 x^3-972 x^4+972 x^6-783 x^7+243 x^8-27 x^9)) \log ^3(x)}{64 x-960 x^2+6080 x^3-21120 x^4+43840 x^5-55872 x^6+43840 x^7-21120 x^8+6080 x^9-960 x^{10}+64 x^{11}} \, dx\)
Optimal. Leaf size=30 \[ \left (6+\frac {1}{16} \left (-x+\frac {e^5}{-3+\frac {1}{x}+x}+3 \log (x)\right )^2\right )^2 \]
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Rubi [C] time = 33.57, antiderivative size = 6883, normalized size of antiderivative =
229.43, number of steps used = 288, number of rules used = 27, integrand size = 716, \(\frac {\text {number of rules}}{\text {integrand size}}\)
= 0.038, Rules used = {6688, 12, 6742, 1660, 1657, 632, 31, 2357, 2295, 2301, 2304,
2319, 44, 2314, 2316, 2315, 2296, 2305, 2347, 2344, 2318, 2317, 2374, 6589, 2302, 30,
2383}
result too large to display
Antiderivative was successfully verified.
[In]
Int[(-288*x + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283473*x^7 + 164104*x^8 - 61968*x^
9 + 15115*x^10 - 2343*x^11 + 236*x^12 - 18*x^13 + x^14 + E^20*(x^4 - x^6) + E^15*(3*x^3 - 22*x^4 + 48*x^5 - 29
*x^6 + 2*x^8) + E^10*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171*x^7 + 45*x^8 - 18*x^9) + E^5*(288*
x - 3648*x^2 + 18729*x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^10 + 36
*x^11 - 2*x^12) + (864 - 13248*x + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961317*x^5 + 864729*x^6 - 512136*x^7
+ 203472*x^8 - 55395*x^9 + 10719*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + E^15*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7)
+ E^10*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^9) + E^5*(288*x - 2646*x^2 + 9027*x^
3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x^9 - 189*x^10 + 9*x^11))*Log[x] + (-81*x + 1
242*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 - 486*x
^11 + 27*x^12 + E^10*(27*x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 162*x^7 - 27*x^8) + E^5*(81*x - 1026*x^2 + 5265*x
^3 - 14013*x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9))*Log[x]^2 + (81 - 1242*x + 8100*x^2 -
29295*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 + E^5*(2
7*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9))*Log[x]^3)/(64*x - 960*x^2 + 6080*x^
3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^10 + 64*x^11),x]
[Out]
(27*E^15)/(400*(3 - Sqrt[5] - 2*x)^2) - (21*E^15)/(400*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)^2) - (21*E^15)/(200*(
3 - Sqrt[5])^2*(3 - Sqrt[5] - 2*x)) + (27*E^15)/(200*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (63*E^15)/(200*Sqrt[
5]*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (81*(5 - 6*Sqrt[5])*E^15)/(2000*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) - (
27*E^10*(6 - E^5))/(160*Sqrt[5]*(3 - Sqrt[5] - 2*x)) + (9*E^10*(7 + 3*E^5))/(80*Sqrt[5]*(3 - Sqrt[5])*(3 - Sqr
t[5] - 2*x)) + (27*E^15)/(400*(3 + Sqrt[5] - 2*x)^2) - (21*E^15)/(400*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)^2) - (
21*E^15)/(200*(3 + Sqrt[5])^2*(3 + Sqrt[5] - 2*x)) + (27*E^15)/(200*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) - (63*E
^15)/(200*Sqrt[5]*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (81*(5 + 6*Sqrt[5])*E^15)/(2000*(3 + Sqrt[5])*(3 + Sqrt
[5] - 2*x)) + (27*E^10*(6 - E^5))/(160*Sqrt[5]*(3 + Sqrt[5] - 2*x)) - (9*E^10*(7 + 3*E^5))/(80*Sqrt[5]*(3 + Sq
rt[5])*(3 + Sqrt[5] - 2*x)) + (9*(32 - E^5)*x)/64 - (3*(48 - E^5)*x)/32 + ((48 - E^5)*x^2)/64 + x^4/256 - (E^2
0*(8 - 21*x))/(256*(1 - 3*x + x^2)^4) + (E^15*(32 + 7*E^5 - 6*(14 - E^5)*x))/(256*(1 - 3*x + x^2)^3) - (E^10*(
1200 + 122*E^5 - 5*E^10 - 54*(65 - 3*E^5)*x))/(1280*(1 - 3*x + x^2)^2) + (E^5*(5200 + 2655*E^5 - 149*E^10 - 6*
(2575 - 180*E^5 - 11*E^10)*x))/(3200*(1 - 3*x + x^2)) - (81*E^10*Log[3 - Sqrt[5] - 2*x])/(80*Sqrt[5]*(3 - Sqrt
[5])^2) + (189*E^10*Log[3 - Sqrt[5] - 2*x])/(160*Sqrt[5]*(3 - Sqrt[5])) + (21*E^15*Log[3 - Sqrt[5] - 2*x])/(20
0*(3 - Sqrt[5])^3) - (27*E^15*Log[3 - Sqrt[5] - 2*x])/(200*(3 - Sqrt[5])^2) + (63*E^15*Log[3 - Sqrt[5] - 2*x])
/(400*(3 - Sqrt[5])) - (81*(15 - Sqrt[5])*E^15*Log[3 - Sqrt[5] - 2*x])/(2000*(3 - Sqrt[5])) - (27*E^5*(19 - 2*
E^5)*Log[3 - Sqrt[5] - 2*x])/160 - (27*(9 - Sqrt[5])*E^10*(6 - E^5)*Log[3 - Sqrt[5] - 2*x])/(800*(3 - Sqrt[5])
) + (27*E^10*(7 + 3*E^5)*Log[3 - Sqrt[5] - 2*x])/(400*(3 - Sqrt[5])) + (9*E^5*(71 + 13*E^5 - E^10)*Log[3 - Sqr
t[5] - 2*x])/(160*(3 - Sqrt[5])) + (3*E^5*(1125 - Sqrt[5]*(5325 + 60*E^5 + 22*E^10))*Log[3 - Sqrt[5] - 2*x])/1
6000 + (81*E^10*Log[3 + Sqrt[5] - 2*x])/(80*Sqrt[5]*(3 + Sqrt[5])^2) - (189*E^10*Log[3 + Sqrt[5] - 2*x])/(160*
Sqrt[5]*(3 + Sqrt[5])) + (21*E^15*Log[3 + Sqrt[5] - 2*x])/(200*(3 + Sqrt[5])^3) - (27*E^15*Log[3 + Sqrt[5] - 2
*x])/(200*(3 + Sqrt[5])^2) + (63*E^15*Log[3 + Sqrt[5] - 2*x])/(200*Sqrt[5]*(3 + Sqrt[5])^2) + (63*E^15*Log[3 +
Sqrt[5] - 2*x])/(400*(3 + Sqrt[5])) - (81*(15 + Sqrt[5])*E^15*Log[3 + Sqrt[5] - 2*x])/(2000*(3 + Sqrt[5])) -
(81*(5 + 6*Sqrt[5])*E^15*Log[3 + Sqrt[5] - 2*x])/(2000*(3 + Sqrt[5])^2) - (27*E^5*(19 - 2*E^5)*Log[3 + Sqrt[5]
- 2*x])/160 - (27*E^10*(6 - E^5)*Log[3 + Sqrt[5] - 2*x])/(160*Sqrt[5]*(3 + Sqrt[5])) - (27*(9 + Sqrt[5])*E^10
*(6 - E^5)*Log[3 + Sqrt[5] - 2*x])/(800*(3 + Sqrt[5])) + (9*E^10*(7 + 3*E^5)*Log[3 + Sqrt[5] - 2*x])/(80*Sqrt[
5]*(3 + Sqrt[5])^2) + (27*E^10*(7 + 3*E^5)*Log[3 + Sqrt[5] - 2*x])/(400*(3 + Sqrt[5])) + (9*E^5*(71 + 13*E^5 -
E^10)*Log[3 + Sqrt[5] - 2*x])/(160*(3 + Sqrt[5])) + (3*E^5*(1125 + Sqrt[5]*(5325 + 60*E^5 + 22*E^10))*Log[3 +
Sqrt[5] - 2*x])/16000 - (81*E^10*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(80*Sqrt[5]*(3 + Sqrt[5])^2) -
(243*E^10*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(400*(3 + Sqrt[5])) + (189*E^10*Log[(3 + Sqrt[5])/2]*Lo
g[3 + Sqrt[5] - 2*x])/(160*Sqrt[5]*(3 + Sqrt[5])) + (189*(9 + Sqrt[5])*E^10*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[
5] - 2*x])/(800*(3 + Sqrt[5])) + (9*E^15*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(20*Sqrt[5]) + (81*E^5*(
19 - 2*E^5)*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(160*Sqrt[5]) + (243*E^10*(6 - E^5)*Log[(3 + Sqrt[5])
/2]*Log[3 + Sqrt[5] - 2*x])/(800*Sqrt[5]) + (27*E^5*(7 - E^5)*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/160
- (81*E^5*(1 + E^5)*Log[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(80*(3 + Sqrt[5])) - (27*E^10*(7 + 3*E^5)*Lo
g[(3 + Sqrt[5])/2]*Log[3 + Sqrt[5] - 2*x])/(400*Sqrt[5]) - (9*E^5*(71 + 13*E^5 - E^10)*Log[(3 + Sqrt[5])/2]*Lo
g[3 + Sqrt[5] - 2*x])/(160*Sqrt[5]) - (21*E^15*Log[x])/(200*(3 - Sqrt[5])^3) + (27*E^15*Log[x])/(200*(3 - Sqrt
[5])^2) + (63*E^15*Log[x])/(200*Sqrt[5]*(3 - Sqrt[5])^2) + (81*(5 - 6*Sqrt[5])*E^15*Log[x])/(2000*(3 - Sqrt[5]
)^2) - (21*E^15*Log[x])/(200*(3 + Sqrt[5])^3) + (27*E^15*Log[x])/(200*(3 + Sqrt[5])^2) - (63*E^15*Log[x])/(200
*Sqrt[5]*(3 + Sqrt[5])^2) + (81*(5 + 6*Sqrt[5])*E^15*Log[x])/(2000*(3 + Sqrt[5])^2) - (27*E^10*(6 - E^5)*Log[x
])/(160*Sqrt[5]*(3 - Sqrt[5])) + (27*E^10*(6 - E^5)*Log[x])/(160*Sqrt[5]*(3 + Sqrt[5])) + (9*E^10*(7 + 3*E^5)*
Log[x])/(80*Sqrt[5]*(3 - Sqrt[5])^2) - (9*E^10*(7 + 3*E^5)*Log[x])/(80*Sqrt[5]*(3 + Sqrt[5])^2) + (21*E^15*Log
[x])/(200*(3 - Sqrt[5] - 2*x)^3) - (27*(3 - Sqrt[5])*E^15*Log[x])/(200*(3 - Sqrt[5] - 2*x)^3) - (63*E^15*Log[x
])/(200*Sqrt[5]*(3 - Sqrt[5] - 2*x)^2) - (81*(5 - 6*Sqrt[5])*E^15*Log[x])/(2000*(3 - Sqrt[5] - 2*x)^2) - (27*(
5 - 3*Sqrt[5])*E^10*(6 - E^5)*Log[x])/(800*(3 - Sqrt[5] - 2*x)^2) - (9*E^10*(7 + 3*E^5)*Log[x])/(80*Sqrt[5]*(3
- Sqrt[5] - 2*x)^2) + (21*E^15*Log[x])/(200*(3 + Sqrt[5] - 2*x)^3) - (27*(3 + Sqrt[5])*E^15*Log[x])/(200*(3 +
Sqrt[5] - 2*x)^3) + (63*E^15*Log[x])/(200*Sqrt[5]*(3 + Sqrt[5] - 2*x)^2) - (81*(5 + 6*Sqrt[5])*E^15*Log[x])/(
2000*(3 + Sqrt[5] - 2*x)^2) - (27*(5 + 3*Sqrt[5])*E^10*(6 - E^5)*Log[x])/(800*(3 + Sqrt[5] - 2*x)^2) + (9*E^10
*(7 + 3*E^5)*Log[x])/(80*Sqrt[5]*(3 + Sqrt[5] - 2*x)^2) - (9*(32 - E^5)*x*Log[x])/64 - (81*E^10*x*Log[x])/(40*
Sqrt[5]*(3 - Sqrt[5])^2*(3 - Sqrt[5] - 2*x)) + (189*E^10*x*Log[x])/(80*Sqrt[5]*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*
x)) + (63*E^15*x*Log[x])/(200*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) - (81*(15 - Sqrt[5])*E^15*x*Log[x])/(1000*(3
- Sqrt[5])*(3 - Sqrt[5] - 2*x)) - (27*E^5*(19 - 2*E^5)*x*Log[x])/(80*(3 - Sqrt[5] - 2*x)) - (27*(9 - Sqrt[5])*
E^10*(6 - E^5)*x*Log[x])/(400*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (27*E^10*(7 + 3*E^5)*x*Log[x])/(200*(3 - Sq
rt[5])*(3 - Sqrt[5] - 2*x)) + (9*E^5*(71 + 13*E^5 - E^10)*x*Log[x])/(80*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (
81*E^10*x*Log[x])/(40*Sqrt[5]*(3 + Sqrt[5])^2*(3 + Sqrt[5] - 2*x)) - (189*E^10*x*Log[x])/(80*Sqrt[5]*(3 + Sqrt
[5])*(3 + Sqrt[5] - 2*x)) + (63*E^15*x*Log[x])/(200*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) - (81*(15 + Sqrt[5])*E^
15*x*Log[x])/(1000*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) - (27*E^5*(19 - 2*E^5)*x*Log[x])/(80*(3 + Sqrt[5] - 2*x)
) - (27*(9 + Sqrt[5])*E^10*(6 - E^5)*x*Log[x])/(400*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (27*E^10*(7 + 3*E^5)*
x*Log[x])/(200*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (9*E^5*(71 + 13*E^5 - E^10)*x*Log[x])/(80*(3 + Sqrt[5])*(3
+ Sqrt[5] - 2*x)) - (3*x^3*Log[x])/64 + (27*Log[x]^2)/4 - (81*E^10*Log[x]^2)/(160*Sqrt[5]*(3 - Sqrt[5])^2) +
(189*E^10*Log[x]^2)/(320*Sqrt[5]*(3 - Sqrt[5])) + (81*E^10*Log[x]^2)/(160*Sqrt[5]*(3 + Sqrt[5])^2) - (189*E^10
*Log[x]^2)/(320*Sqrt[5]*(3 + Sqrt[5])) + (81*E^10*Log[x]^2)/(160*Sqrt[5]*(3 - Sqrt[5] - 2*x)^2) + (189*(5 - 3*
Sqrt[5])*E^10*Log[x]^2)/(1600*(3 - Sqrt[5] - 2*x)^2) - (81*E^10*Log[x]^2)/(160*Sqrt[5]*(3 + Sqrt[5] - 2*x)^2)
+ (189*(5 + 3*Sqrt[5])*E^10*Log[x]^2)/(1600*(3 + Sqrt[5] - 2*x)^2) - (243*E^10*x*Log[x]^2)/(400*(3 - Sqrt[5])*
(3 - Sqrt[5] - 2*x)) + (189*(9 - Sqrt[5])*E^10*x*Log[x]^2)/(800*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) + (27*E^5*(
7 - E^5)*x*Log[x]^2)/(160*(3 - Sqrt[5] - 2*x)) - (81*E^5*(1 + E^5)*x*Log[x]^2)/(80*(3 - Sqrt[5])*(3 - Sqrt[5]
- 2*x)) - (243*E^10*x*Log[x]^2)/(400*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (189*(9 + Sqrt[5])*E^10*x*Log[x]^2)/
(800*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (27*E^5*(7 - E^5)*x*Log[x]^2)/(160*(3 + Sqrt[5] - 2*x)) - (81*E^5*(1
+ E^5)*x*Log[x]^2)/(80*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (27*x^2*Log[x]^2)/128 - (27*x*Log[x]^3)/64 - (81*
E^5*x*Log[x]^3)/(160*(3 - Sqrt[5] - 2*x)) + (27*E^5*x*Log[x]^3)/(40*(3 - Sqrt[5])*(3 - Sqrt[5] - 2*x)) - (81*E
^5*x*Log[x]^3)/(160*(3 + Sqrt[5] - 2*x)) + (27*E^5*x*Log[x]^3)/(40*(3 + Sqrt[5])*(3 + Sqrt[5] - 2*x)) + (81*Lo
g[x]^4)/256 - (9*E^5*(15 + Sqrt[5]*(49 - E^5))*Log[(3 + Sqrt[5])/2]*Log[-3 - Sqrt[5] + 2*x])/320 + (81*E^10*Lo
g[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(80*Sqrt[5]*(3 - Sqrt[5])^2) - (243*E^10*Log[(3 - Sqrt[5])/2]*Log[
-3 + Sqrt[5] + 2*x])/(400*(3 - Sqrt[5])) - (189*E^10*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(160*Sqrt[5
]*(3 - Sqrt[5])) + (189*(9 - Sqrt[5])*E^10*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(800*(3 - Sqrt[5])) -
(9*E^15*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(20*Sqrt[5]) - (81*E^5*(19 - 2*E^5)*Log[(3 - Sqrt[5])/2
]*Log[-3 + Sqrt[5] + 2*x])/(160*Sqrt[5]) - (243*E^10*(6 - E^5)*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(
800*Sqrt[5]) + (27*E^5*(7 - E^5)*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/160 - (81*E^5*(1 + E^5)*Log[(3
- Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(80*(3 - Sqrt[5])) + (27*E^10*(7 + 3*E^5)*Log[(3 - Sqrt[5])/2]*Log[-3 +
Sqrt[5] + 2*x])/(400*Sqrt[5]) + (9*E^5*(71 + 13*E^5 - E^10)*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/(16
0*Sqrt[5]) - (9*E^5*(15 - Sqrt[5]*(49 - E^5))*Log[(3 - Sqrt[5])/2]*Log[-3 + Sqrt[5] + 2*x])/320 - (63*E^15*Log
[2*(9 - 4*Sqrt[5]) - (7 - 3*Sqrt[5])*x])/(400*Sqrt[5]*(7 - 3*Sqrt[5])) - (81*(5 - 6*Sqrt[5])*E^15*Log[2*(9 - 4
*Sqrt[5]) - (7 - 3*Sqrt[5])*x])/(4000*(7 - 3*Sqrt[5])) - (27*(5 - 3*Sqrt[5])*E^10*(6 - E^5)*Log[2*(9 - 4*Sqrt[
5]) - (7 - 3*Sqrt[5])*x])/(1600*(7 - 3*Sqrt[5])) - (9*E^10*(7 + 3*E^5)*Log[2*(9 - 4*Sqrt[5]) - (7 - 3*Sqrt[5])
*x])/(160*Sqrt[5]*(7 - 3*Sqrt[5])) - (243*E^5*Log[x]^2*Log[1 - (2*x)/(3 - Sqrt[5])])/320 - (81*E^5*Log[x]^2*Lo
g[1 - (2*x)/(3 - Sqrt[5])])/(32*Sqrt[5]) + (81*E^5*Log[x]^2*Log[1 - (2*x)/(3 - Sqrt[5])])/(80*(3 - Sqrt[5])) +
(243*E^10*Log[x]^2*Log[1 - (2*x)/(3 - Sqrt[5])])/(320*Sqrt[5]) + (81*E^5*(7 - E^5)*Log[x]^2*Log[1 - (2*x)/(3
- Sqrt[5])])/(320*Sqrt[5]) - (81*E^5*(1 + E^5)*Log[x]^2*Log[1 - (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) - (243*E^5
*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5])])/320 + (81*E^5*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5])])/(32*Sqrt[5]) + (8
1*E^5*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5])])/(80*(3 + Sqrt[5])) - (243*E^10*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5
])])/(320*Sqrt[5]) - (81*E^5*(7 - E^5)*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5])])/(320*Sqrt[5]) + (81*E^5*(1 + E^5
)*Log[x]^2*Log[1 - (2*x)/(3 + Sqrt[5])])/(160*Sqrt[5]) - (243*E^5*Log[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])])/160
- (81*E^5*Log[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])])/(16*Sqrt[5]) + (81*E^5*Log[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])
])/(40*(3 - Sqrt[5])) + (243*E^10*Log[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) + (81*E^5*(7 - E^5)*Lo
g[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) - (81*E^5*(1 + E^5)*Log[x]*PolyLog[2, (2*x)/(3 - Sqrt[5])]
)/(80*Sqrt[5]) - (243*E^5*Log[x]*PolyLog[2, (2*x)/(3 + Sqrt[5])])/160 + (81*E^5*Log[x]*PolyLog[2, (2*x)/(3 + S
qrt[5])])/(16*Sqrt[5]) + (81*E^5*Log[x]*PolyLog[2, (2*x)/(3 + Sqrt[5])])/(40*(3 + Sqrt[5])) - (243*E^10*Log[x]
*PolyLog[2, (2*x)/(3 + Sqrt[5])])/(160*Sqrt[5]) - (81*E^5*(7 - E^5)*Log[x]*PolyLog[2, (2*x)/(3 + Sqrt[5])])/(1
60*Sqrt[5]) + (81*E^5*(1 + E^5)*Log[x]*PolyLog[2, (2*x)/(3 + Sqrt[5])])/(80*Sqrt[5]) - (81*E^10*PolyLog[2, 1 -
(2*x)/(3 - Sqrt[5])])/(80*Sqrt[5]*(3 - Sqrt[5])^2) + (243*E^10*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(400*(3 -
Sqrt[5])) + (189*E^10*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]*(3 - Sqrt[5])) - (189*(9 - Sqrt[5])*E
^10*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(800*(3 - Sqrt[5])) + (9*E^15*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(2
0*Sqrt[5]) + (81*E^5*(19 - 2*E^5)*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) + (243*E^10*(6 - E^5)*Pol
yLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(800*Sqrt[5]) - (27*E^5*(7 - E^5)*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/160 +
(81*E^5*(1 + E^5)*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(80*(3 - Sqrt[5])) - (27*E^10*(7 + 3*E^5)*PolyLog[2, 1
- (2*x)/(3 - Sqrt[5])])/(400*Sqrt[5]) - (9*E^5*(71 + 13*E^5 - E^10)*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/(160
*Sqrt[5]) + (9*E^5*(15 - Sqrt[5]*(49 - E^5))*PolyLog[2, 1 - (2*x)/(3 - Sqrt[5])])/320 + (81*E^10*PolyLog[2, 1
- (2*x)/(3 + Sqrt[5])])/(80*Sqrt[5]*(3 + Sqrt[5])^2) + (243*E^10*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(400*(3
+ Sqrt[5])) - (189*E^10*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(160*Sqrt[5]*(3 + Sqrt[5])) - (189*(9 + Sqrt[5])*
E^10*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(800*(3 + Sqrt[5])) - (9*E^15*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(
20*Sqrt[5]) - (81*E^5*(19 - 2*E^5)*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(160*Sqrt[5]) - (243*E^10*(6 - E^5)*Po
lyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(800*Sqrt[5]) - (27*E^5*(7 - E^5)*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/160
+ (81*E^5*(1 + E^5)*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(80*(3 + Sqrt[5])) + (27*E^10*(7 + 3*E^5)*PolyLog[2,
1 - (2*x)/(3 + Sqrt[5])])/(400*Sqrt[5]) + (9*E^5*(71 + 13*E^5 - E^10)*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/(16
0*Sqrt[5]) + (9*E^5*(15 + Sqrt[5]*(49 - E^5))*PolyLog[2, 1 - (2*x)/(3 + Sqrt[5])])/320 + (243*E^5*PolyLog[3, (
2*x)/(3 - Sqrt[5])])/160 + (81*E^5*PolyLog[3, (2*x)/(3 - Sqrt[5])])/(16*Sqrt[5]) - (81*E^5*PolyLog[3, (2*x)/(3
- Sqrt[5])])/(40*(3 - Sqrt[5])) - (243*E^10*PolyLog[3, (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) - (81*E^5*(7 - E^5
)*PolyLog[3, (2*x)/(3 - Sqrt[5])])/(160*Sqrt[5]) + (81*E^5*(1 + E^5)*PolyLog[3, (2*x)/(3 - Sqrt[5])])/(80*Sqrt
[5]) + (243*E^5*PolyLog[3, (2*x)/(3 + Sqrt[5])])/160 - (81*E^5*PolyLog[3, (2*x)/(3 + Sqrt[5])])/(16*Sqrt[5]) -
(81*E^5*PolyLog[3, (2*x)/(3 + Sqrt[5])])/(40*(3 + Sqrt[5])) + (243*E^10*PolyLog[3, (2*x)/(3 + Sqrt[5])])/(160
*Sqrt[5]) + (81*E^5*(7 - E^5)*PolyLog[3, (2*x)/(3 + Sqrt[5])])/(160*Sqrt[5]) - (81*E^5*(1 + E^5)*PolyLog[3, (2
*x)/(3 + Sqrt[5])])/(80*Sqrt[5])
Rule 12
Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]
Rule 30
Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]
Rule 31
Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]
Rule 44
Int[((a_) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d*
x)^n, x], x] /; FreeQ[{a, b, c, d}, x] && NeQ[b*c - a*d, 0] && ILtQ[m, 0] && IntegerQ[n] && !(IGtQ[n, 0] && L
tQ[m + n + 2, 0])
Rule 632
Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Dist[
(c*d - e*(b/2 - q/2))/q, Int[1/(b/2 - q/2 + c*x), x], x] - Dist[(c*d - e*(b/2 + q/2))/q, Int[1/(b/2 + q/2 + c*
x), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] && NiceSqrtQ[b^2 - 4*a*
c]
Rule 1657
Int[(Pq_)*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Int[ExpandIntegrand[Pq*(a + b*x + c*x^2)^p, x
], x] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && IGtQ[p, -2]
Rule 1660
Int[(Pq_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> With[{Q = PolynomialQuotient[Pq, a + b*x + c*
x^2, x], f = Coeff[PolynomialRemainder[Pq, a + b*x + c*x^2, x], x, 0], g = Coeff[PolynomialRemainder[Pq, a + b
*x + c*x^2, x], x, 1]}, Simp[((b*f - 2*a*g + (2*c*f - b*g)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c
)), x] + Dist[1/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1)*ExpandToSum[(p + 1)*(b^2 - 4*a*c)*Q - (
2*p + 3)*(2*c*f - b*g), x], x], x]] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1
]
Rule 2295
Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]
Rule 2296
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]
Rule 2301
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]
Rule 2302
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]
Rule 2304
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Log[c*x^
n]))/(d*(m + 1)), x] - Simp[(b*n*(d*x)^(m + 1))/(d*(m + 1)^2), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]
Rule 2305
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[((d*x)^(m + 1)*(a + b*Lo
g[c*x^n])^p)/(d*(m + 1)), x] - Dist[(b*n*p)/(m + 1), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]
Rule 2314
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_) + (e_.)*(x_)^(r_.))^(q_), x_Symbol] :> Simp[(x*(d + e*x^r)^(q
+ 1)*(a + b*Log[c*x^n]))/d, x] - Dist[(b*n)/d, Int[(d + e*x^r)^(q + 1), x], x] /; FreeQ[{a, b, c, d, e, n, q,
r}, x] && EqQ[r*(q + 1) + 1, 0]
Rule 2315
Int[Log[(c_.)*(x_)]/((d_) + (e_.)*(x_)), x_Symbol] :> -Simp[PolyLog[2, 1 - c*x]/e, x] /; FreeQ[{c, d, e}, x] &
& EqQ[e + c*d, 0]
Rule 2316
Int[((a_.) + Log[(c_.)*(x_)]*(b_.))/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[((a + b*Log[-((c*d)/e)])*Log[d + e*
x])/e, x] + Dist[b, Int[Log[-((e*x)/d)]/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e}, x] && GtQ[-((c*d)/e), 0]
Rule 2317
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[(Log[1 + (e*x)/d]*(a +
b*Log[c*x^n])^p)/e, x] - Dist[(b*n*p)/e, Int[(Log[1 + (e*x)/d]*(a + b*Log[c*x^n])^(p - 1))/x, x], x] /; FreeQ[
{a, b, c, d, e, n}, x] && IGtQ[p, 0]
Rule 2318
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_))^2, x_Symbol] :> Simp[(x*(a + b*Log[c*x^n])
^p)/(d*(d + e*x)), x] - Dist[(b*n*p)/d, Int[(a + b*Log[c*x^n])^(p - 1)/(d + e*x), x], x] /; FreeQ[{a, b, c, d,
e, n, p}, x] && GtQ[p, 0]
Rule 2319
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.), x_Symbol] :> Simp[((d + e*x)^(q + 1
)*(a + b*Log[c*x^n])^p)/(e*(q + 1)), x] - Dist[(b*n*p)/(e*(q + 1)), Int[((d + e*x)^(q + 1)*(a + b*Log[c*x^n])^
(p - 1))/x, x], x] /; FreeQ[{a, b, c, d, e, n, p, q}, x] && GtQ[p, 0] && NeQ[q, -1] && (EqQ[p, 1] || (Integers
Q[2*p, 2*q] && !IGtQ[q, 0]) || (EqQ[p, 2] && NeQ[q, 1]))
Rule 2344
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((x_)*((d_) + (e_.)*(x_))), x_Symbol] :> Dist[1/d, Int[(a + b*
Log[c*x^n])^p/x, x], x] - Dist[e/d, Int[(a + b*Log[c*x^n])^p/(d + e*x), x], x] /; FreeQ[{a, b, c, d, e, n}, x]
&& IGtQ[p, 0]
Rule 2347
Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_))/(x_), x_Symbol] :> Dist[1/d, Int[((
d + e*x)^(q + 1)*(a + b*Log[c*x^n])^p)/x, x], x] - Dist[e/d, Int[(d + e*x)^q*(a + b*Log[c*x^n])^p, x], x] /; F
reeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && LtQ[q, -1] && IntegerQ[2*q]
Rule 2357
Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*(RFx_), x_Symbol] :> With[{u = ExpandIntegrand[(a + b*Log[c*x^
n])^p, RFx, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, n}, x] && RationalFunctionQ[RFx, x] && IGtQ[p, 0]
Rule 2374
Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :> -Sim
p[(PolyLog[2, -(d*f*x^m)]*(a + b*Log[c*x^n])^p)/m, x] + Dist[(b*n*p)/m, Int[(PolyLog[2, -(d*f*x^m)]*(a + b*Log
[c*x^n])^(p - 1))/x, x], x] /; FreeQ[{a, b, c, d, e, f, m, n}, x] && IGtQ[p, 0] && EqQ[d*e, 1]
Rule 2383
Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*PolyLog[k_, (e_.)*(x_)^(q_.)])/(x_), x_Symbol] :> Simp[(PolyL
og[k + 1, e*x^q]*(a + b*Log[c*x^n])^p)/q, x] - Dist[(b*n*p)/q, Int[(PolyLog[k + 1, e*x^q]*(a + b*Log[c*x^n])^(
p - 1))/x, x], x] /; FreeQ[{a, b, c, e, k, n, q}, x] && GtQ[p, 0]
Rule 6589
Int[PolyLog[n_, (c_.)*((a_.) + (b_.)*(x_))^(p_.)]/((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[PolyLog[n + 1, c*(a
+ b*x)^p]/(e*p), x] /; FreeQ[{a, b, c, d, e, n, p}, x] && EqQ[b*d, a*e]
Rule 6688
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]
Rule 6742
Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (3+\left (-19+e^5\right ) x+39 x^2-\left (29+e^5\right ) x^3+9 x^4-x^5\right ) \left (-x \left (-e^{15} x^2+3 e^{10} x^2 \left (1-3 x+x^2\right )-3 e^5 \left (32+x^2\right ) \left (1-3 x+x^2\right )^2+\left (96+x^2\right ) \left (1-3 x+x^2\right )^3\right )+9 \left (32-288 x+\left (961-2 e^5+e^{10}\right ) x^2-3 \left (483-4 e^5+e^{10}\right ) x^3+\left (990-22 e^5+e^{10}\right ) x^4+3 \left (-111+4 e^5\right ) x^5-2 \left (-31+e^5\right ) x^6-9 x^7+x^8\right ) \log (x)-27 x \left (1-3 x+x^2\right )^2 \left (1-e^5-3 x+x^2\right ) \log ^2(x)+27 \left (1-3 x+x^2\right )^3 \log ^3(x)\right )}{64 x \left (1-3 x+x^2\right )^5} \, dx\\ &=\frac {1}{64} \int \frac {\left (3+\left (-19+e^5\right ) x+39 x^2-\left (29+e^5\right ) x^3+9 x^4-x^5\right ) \left (-x \left (-e^{15} x^2+3 e^{10} x^2 \left (1-3 x+x^2\right )-3 e^5 \left (32+x^2\right ) \left (1-3 x+x^2\right )^2+\left (96+x^2\right ) \left (1-3 x+x^2\right )^3\right )+9 \left (32-288 x+\left (961-2 e^5+e^{10}\right ) x^2-3 \left (483-4 e^5+e^{10}\right ) x^3+\left (990-22 e^5+e^{10}\right ) x^4+3 \left (-111+4 e^5\right ) x^5-2 \left (-31+e^5\right ) x^6-9 x^7+x^8\right ) \log (x)-27 x \left (1-3 x+x^2\right )^2 \left (1-e^5-3 x+x^2\right ) \log ^2(x)+27 \left (1-3 x+x^2\right )^3 \log ^3(x)\right )}{x \left (1-3 x+x^2\right )^5} \, dx\\ &=\frac {1}{64} \int \left (\frac {\left (1-e^5-3 x+x^2\right ) \left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \left (-96+576 x-1057 \left (1+\frac {e^5 \left (-2+e^5\right )}{1057}\right ) x^2+582 \left (1-\frac {e^5}{97}\right ) x^3-107 \left (1-\frac {2 e^5}{107}\right ) x^4+6 x^5-x^6\right )}{\left (1-3 x+x^2\right )^5}+\frac {9 \left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \left (32-192 x+353 \left (1+\frac {1}{353} e^5 \left (-2+e^5\right )\right ) x^2-198 \left (1-\frac {e^5}{33}\right ) x^3+43 \left (1-\frac {2 e^5}{43}\right ) x^4-6 x^5+x^6\right ) \log (x)}{x \left (1-3 x+x^2\right )^4}+\frac {27 \left (1-e^5-3 x+x^2\right ) \left (-3+19 \left (1-\frac {e^5}{19}\right ) x-39 x^2+29 \left (1+\frac {e^5}{29}\right ) x^3-9 x^4+x^5\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^3}+\frac {27 \left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \log ^3(x)}{x \left (1-3 x+x^2\right )^2}\right ) \, dx\\ &=\frac {1}{64} \int \frac {\left (1-e^5-3 x+x^2\right ) \left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \left (-96+576 x-1057 \left (1+\frac {e^5 \left (-2+e^5\right )}{1057}\right ) x^2+582 \left (1-\frac {e^5}{97}\right ) x^3-107 \left (1-\frac {2 e^5}{107}\right ) x^4+6 x^5-x^6\right )}{\left (1-3 x+x^2\right )^5} \, dx+\frac {9}{64} \int \frac {\left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \left (32-192 x+353 \left (1+\frac {1}{353} e^5 \left (-2+e^5\right )\right ) x^2-198 \left (1-\frac {e^5}{33}\right ) x^3+43 \left (1-\frac {2 e^5}{43}\right ) x^4-6 x^5+x^6\right ) \log (x)}{x \left (1-3 x+x^2\right )^4} \, dx+\frac {27}{64} \int \frac {\left (1-e^5-3 x+x^2\right ) \left (-3+19 \left (1-\frac {e^5}{19}\right ) x-39 x^2+29 \left (1+\frac {e^5}{29}\right ) x^3-9 x^4+x^5\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^3} \, dx+\frac {27}{64} \int \frac {\left (3-19 \left (1-\frac {e^5}{19}\right ) x+39 x^2-29 \left (1+\frac {e^5}{29}\right ) x^3+9 x^4-x^5\right ) \log ^3(x)}{x \left (1-3 x+x^2\right )^2} \, dx\\ &=-\frac {e^{20} (8-21 x)}{256 \left (1-3 x+x^2\right )^4}-\frac {\int \frac {15 \left (384-384 e^5-25 e^{20}\right )-20 \left (3552-2784 e^5+96 e^{10}-7 e^{20}\right ) x+60 \left (5953-3363 e^5+99 e^{10}-e^{15}+e^{20}\right ) x^2-20 \left (47077-16885 e^5+60 e^{10}-13 e^{15}-e^{20}\right ) x^3+60 \left (23390-4421 e^5-54 e^{10}-2 e^{15}\right ) x^4-20 \left (60682-5017 e^5-9 e^{10}+2 e^{15}\right ) x^5+180 \left (3473-109 e^5+2 e^{10}\right ) x^6-20 \left (9651-161 e^5\right ) x^7+120 \left (293-5 e^5\right ) x^8-40 \left (95-e^5\right ) x^9+300 x^{10}-20 x^{11}}{\left (1-3 x+x^2\right )^4} \, dx}{1280}+\frac {9}{64} \int \left (-32 \left (1-\frac {e^5}{32}\right ) \log (x)+\frac {96 \log (x)}{x}+3 x \log (x)-x^2 \log (x)-\frac {e^{15} (-7+18 x) \log (x)}{\left (1-3 x+x^2\right )^4}+\frac {2 e^{10} \left (-7-3 e^5+3 \left (6-e^5\right ) x\right ) \log (x)}{\left (1-3 x+x^2\right )^3}+\frac {e^5 \left (71+13 e^5-e^{10}-6 \left (19-2 e^5\right ) x\right ) \log (x)}{\left (1-3 x+x^2\right )^2}+\frac {e^5 \left (-40+e^5-6 x\right ) \log (x)}{1-3 x+x^2}\right ) \, dx+\frac {27}{64} \int \left (-3 \log ^2(x)+x \log ^2(x)-\frac {e^{10} (-3+7 x) \log ^2(x)}{\left (1-3 x+x^2\right )^3}+\frac {e^5 \left (-3 \left (1+e^5\right )+\left (7-e^5\right ) x\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^2}+\frac {6 e^5 \log ^2(x)}{1-3 x+x^2}\right ) \, dx+\frac {27}{64} \int \left (-\log ^3(x)+\frac {3 \log ^3(x)}{x}-\frac {e^5 (-2+3 x) \log ^3(x)}{\left (1-3 x+x^2\right )^2}-\frac {e^5 \log ^3(x)}{1-3 x+x^2}\right ) \, dx\\ &=-\frac {e^{20} (8-21 x)}{256 \left (1-3 x+x^2\right )^4}+\frac {e^{15} \left (32+7 e^5-6 \left (14-e^5\right ) x\right )}{256 \left (1-3 x+x^2\right )^3}+\frac {\int \frac {-450 \left (192-192 e^5+34 e^{15}-e^{20}\right )+300 \left (2688-1920 e^5+96 e^{10}+21 e^{15}-e^{20}\right ) x-900 \left (3169-1347 e^5+3 e^{10}-4 e^{15}\right ) x^2+300 \left (15868-2842 e^5-63 e^{10}+2 e^{15}\right ) x^3-900 \left (4353-232 e^5+6 e^{10}\right ) x^4+900 \left (1879-29 e^5\right ) x^5-900 \left (429-8 e^5\right ) x^6+300 \left (153-2 e^5\right ) x^7-3600 x^8+300 x^9}{\left (1-3 x+x^2\right )^3} \, dx}{19200}-\frac {9}{64} \int x^2 \log (x) \, dx+\frac {27}{64} \int x \log (x) \, dx+\frac {27}{64} \int x \log ^2(x) \, dx-\frac {27}{64} \int \log ^3(x) \, dx-\frac {81}{64} \int \log ^2(x) \, dx+\frac {81}{64} \int \frac {\log ^3(x)}{x} \, dx+\frac {27}{2} \int \frac {\log (x)}{x} \, dx+\frac {1}{64} \left (9 e^5\right ) \int \frac {\left (71+13 e^5-e^{10}-6 \left (19-2 e^5\right ) x\right ) \log (x)}{\left (1-3 x+x^2\right )^2} \, dx+\frac {1}{64} \left (9 e^5\right ) \int \frac {\left (-40+e^5-6 x\right ) \log (x)}{1-3 x+x^2} \, dx+\frac {1}{64} \left (27 e^5\right ) \int \frac {\left (-3 \left (1+e^5\right )+\left (7-e^5\right ) x\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^2} \, dx-\frac {1}{64} \left (27 e^5\right ) \int \frac {(-2+3 x) \log ^3(x)}{\left (1-3 x+x^2\right )^2} \, dx-\frac {1}{64} \left (27 e^5\right ) \int \frac {\log ^3(x)}{1-3 x+x^2} \, dx+\frac {1}{32} \left (81 e^5\right ) \int \frac {\log ^2(x)}{1-3 x+x^2} \, dx+\frac {1}{32} \left (9 e^{10}\right ) \int \frac {\left (-7-3 e^5+3 \left (6-e^5\right ) x\right ) \log (x)}{\left (1-3 x+x^2\right )^3} \, dx-\frac {1}{64} \left (27 e^{10}\right ) \int \frac {(-3+7 x) \log ^2(x)}{\left (1-3 x+x^2\right )^3} \, dx-\frac {1}{64} \left (9 e^{15}\right ) \int \frac {(-7+18 x) \log (x)}{\left (1-3 x+x^2\right )^4} \, dx-\frac {1}{64} \left (9 \left (32-e^5\right )\right ) \int \log (x) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.35, size = 329, normalized size = 10.97 \begin {gather*} \frac {1}{256} \left (-12 e^5 x-4 \left (-48+e^5\right ) x^2+x^4+\frac {e^{20} (-8+21 x)}{\left (1-3 x+x^2\right )^4}+\frac {2 e^5 \left (208-2 e^{10}-618 x+9 e^5 (13+2 x)\right )}{1-3 x+x^2}+\frac {e^{10} \left (-240+e^{10}+702 x-4 e^5 (7+6 x)\right )}{\left (1-3 x+x^2\right )^2}+\frac {e^{15} \left (32-84 x+e^5 (7+6 x)\right )}{\left (1-3 x+x^2\right )^3}+108 e^5 \log (x)+\frac {12 \left (e^{15} x^3-3 e^{10} x^3 \left (1-3 x+x^2\right )-x \left (96+x^2\right ) \left (1-3 x+x^2\right )^3+3 e^5 \left (1-3 x+x^2\right )^2 \left (-3+41 x-3 x^2+x^3\right )\right ) \log (x)}{\left (1-3 x+x^2\right )^3}+\frac {54 \left (32-192 x+\left (353-2 e^5+e^{10}\right ) x^2+6 \left (-33+e^5\right ) x^3+\left (43-2 e^5\right ) x^4-6 x^5+x^6\right ) \log ^2(x)}{\left (1-3 x+x^2\right )^2}-\frac {108 x \left (1-e^5-3 x+x^2\right ) \log ^3(x)}{1-3 x+x^2}+81 \log ^4(x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-288*x + 4416*x^2 - 28803*x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283473*x^7 + 164104*x^8 - 61
968*x^9 + 15115*x^10 - 2343*x^11 + 236*x^12 - 18*x^13 + x^14 + E^20*(x^4 - x^6) + E^15*(3*x^3 - 22*x^4 + 48*x^
5 - 29*x^6 + 2*x^8) + E^10*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171*x^7 + 45*x^8 - 18*x^9) + E^5
*(288*x - 3648*x^2 + 18729*x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^1
0 + 36*x^11 - 2*x^12) + (864 - 13248*x + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961317*x^5 + 864729*x^6 - 51213
6*x^7 + 203472*x^8 - 55395*x^9 + 10719*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + E^15*(9*x^3 - 27*x^4 + 27*x^6 -
9*x^7) + E^10*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^9) + E^5*(288*x - 2646*x^2 + 9
027*x^3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x^9 - 189*x^10 + 9*x^11))*Log[x] + (-81
*x + 1242*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 -
486*x^11 + 27*x^12 + E^10*(27*x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 162*x^7 - 27*x^8) + E^5*(81*x - 1026*x^2 +
5265*x^3 - 14013*x^4 + 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9))*Log[x]^2 + (81 - 1242*x + 8100*
x^2 - 29295*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 +
E^5*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9))*Log[x]^3)/(64*x - 960*x^2 + 6
080*x^3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^10 + 64*x^11),x]
[Out]
(-12*E^5*x - 4*(-48 + E^5)*x^2 + x^4 + (E^20*(-8 + 21*x))/(1 - 3*x + x^2)^4 + (2*E^5*(208 - 2*E^10 - 618*x + 9
*E^5*(13 + 2*x)))/(1 - 3*x + x^2) + (E^10*(-240 + E^10 + 702*x - 4*E^5*(7 + 6*x)))/(1 - 3*x + x^2)^2 + (E^15*(
32 - 84*x + E^5*(7 + 6*x)))/(1 - 3*x + x^2)^3 + 108*E^5*Log[x] + (12*(E^15*x^3 - 3*E^10*x^3*(1 - 3*x + x^2) -
x*(96 + x^2)*(1 - 3*x + x^2)^3 + 3*E^5*(1 - 3*x + x^2)^2*(-3 + 41*x - 3*x^2 + x^3))*Log[x])/(1 - 3*x + x^2)^3
+ (54*(32 - 192*x + (353 - 2*E^5 + E^10)*x^2 + 6*(-33 + E^5)*x^3 + (43 - 2*E^5)*x^4 - 6*x^5 + x^6)*Log[x]^2)/(
1 - 3*x + x^2)^2 - (108*x*(1 - E^5 - 3*x + x^2)*Log[x]^3)/(1 - 3*x + x^2) + 81*Log[x]^4)/256
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fricas [B] time = 0.68, size = 592, normalized size = 19.73 \begin {gather*} \frac {x^{12} - 12 \, x^{11} + 250 \, x^{10} - 2448 \, x^{9} + 11331 \, x^{8} - 27792 \, x^{7} + 37498 \, x^{6} - 27660 \, x^{5} + x^{4} e^{20} + 81 \, {\left (x^{8} - 12 \, x^{7} + 58 \, x^{6} - 144 \, x^{5} + 195 \, x^{4} - 144 \, x^{3} + 58 \, x^{2} - 12 \, x + 1\right )} \log \relax (x)^{4} + 11137 \, x^{4} - 108 \, {\left (x^{9} - 12 \, x^{8} + 58 \, x^{7} - 144 \, x^{6} + 195 \, x^{5} - 144 \, x^{4} + 58 \, x^{3} - 12 \, x^{2} - {\left (x^{7} - 9 \, x^{6} + 30 \, x^{5} - 45 \, x^{4} + 30 \, x^{3} - 9 \, x^{2} + x\right )} e^{5} + x\right )} \log \relax (x)^{3} - 2304 \, x^{3} + 54 \, {\left (x^{10} - 12 \, x^{9} + 90 \, x^{8} - 528 \, x^{7} + 2051 \, x^{6} - 4752 \, x^{5} + 6298 \, x^{4} - 4620 \, x^{3} + 1857 \, x^{2} + {\left (x^{6} - 6 \, x^{5} + 11 \, x^{4} - 6 \, x^{3} + x^{2}\right )} e^{10} - 2 \, {\left (x^{8} - 9 \, x^{7} + 30 \, x^{6} - 45 \, x^{5} + 30 \, x^{4} - 9 \, x^{3} + x^{2}\right )} e^{5} - 384 \, x + 32\right )} \log \relax (x)^{2} + 192 \, x^{2} - 4 \, {\left (x^{6} - 3 \, x^{5} + x^{4}\right )} e^{15} + 6 \, {\left (6 \, x^{7} - 15 \, x^{6} - 54 \, x^{5} + 158 \, x^{4} - 48 \, x^{3} - 26 \, x^{2} + 12 \, x - 1\right )} e^{10} - 4 \, {\left (x^{10} - 9 \, x^{9} + 22 \, x^{8} + 339 \, x^{7} - 3122 \, x^{6} + 10647 \, x^{5} - 17399 \, x^{4} + 14112 \, x^{3} - 5936 \, x^{2} + 1248 \, x - 104\right )} e^{5} - 12 \, {\left (x^{11} - 12 \, x^{10} + 154 \, x^{9} - 1296 \, x^{8} + 5763 \, x^{7} - 13968 \, x^{6} + 18778 \, x^{5} - 13836 \, x^{4} + 5569 \, x^{3} - 1152 \, x^{2} - {\left (x^{5} - 3 \, x^{4} + x^{3}\right )} e^{15} + 3 \, {\left (x^{7} - 6 \, x^{6} + 11 \, x^{5} - 6 \, x^{4} + x^{3}\right )} e^{10} - 3 \, {\left (x^{9} - 9 \, x^{8} + 62 \, x^{7} - 333 \, x^{6} + 990 \, x^{5} - 1449 \, x^{4} + 961 \, x^{3} - 288 \, x^{2} + 32 \, x\right )} e^{5} + 96 \, x\right )} \log \relax (x)}{256 \, {\left (x^{8} - 12 \, x^{7} + 58 \, x^{6} - 144 \, x^{5} + 195 \, x^{4} - 144 \, x^{3} + 58 \, x^{2} - 12 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x)*exp(5)-27*x^11+486*x^10-3780*x^9+16
605*x^8-45225*x^7+79056*x^6-89208*x^5+64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x
^6+270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+20655*x^5-14013*x^4+5265*x^3-1026*x^2
+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10-16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+
1242*x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+1215*x^6-1665*x^5+999*x^4-270*x^
3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+2
88*x)*exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^7+864729*x^6-961317*x^5+689580
*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x)+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+
(-18*x^9+45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12+36*x^11-253*x^10+1494*x^9-8
121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^
11+15115*x^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803*x^3+4416*x^2-288*x)/(64*x
^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872*x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm="f
ricas")
[Out]
1/256*(x^12 - 12*x^11 + 250*x^10 - 2448*x^9 + 11331*x^8 - 27792*x^7 + 37498*x^6 - 27660*x^5 + x^4*e^20 + 81*(x
^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1)*log(x)^4 + 11137*x^4 - 108*(x^9 - 12*x
^8 + 58*x^7 - 144*x^6 + 195*x^5 - 144*x^4 + 58*x^3 - 12*x^2 - (x^7 - 9*x^6 + 30*x^5 - 45*x^4 + 30*x^3 - 9*x^2
+ x)*e^5 + x)*log(x)^3 - 2304*x^3 + 54*(x^10 - 12*x^9 + 90*x^8 - 528*x^7 + 2051*x^6 - 4752*x^5 + 6298*x^4 - 46
20*x^3 + 1857*x^2 + (x^6 - 6*x^5 + 11*x^4 - 6*x^3 + x^2)*e^10 - 2*(x^8 - 9*x^7 + 30*x^6 - 45*x^5 + 30*x^4 - 9*
x^3 + x^2)*e^5 - 384*x + 32)*log(x)^2 + 192*x^2 - 4*(x^6 - 3*x^5 + x^4)*e^15 + 6*(6*x^7 - 15*x^6 - 54*x^5 + 15
8*x^4 - 48*x^3 - 26*x^2 + 12*x - 1)*e^10 - 4*(x^10 - 9*x^9 + 22*x^8 + 339*x^7 - 3122*x^6 + 10647*x^5 - 17399*x
^4 + 14112*x^3 - 5936*x^2 + 1248*x - 104)*e^5 - 12*(x^11 - 12*x^10 + 154*x^9 - 1296*x^8 + 5763*x^7 - 13968*x^6
+ 18778*x^5 - 13836*x^4 + 5569*x^3 - 1152*x^2 - (x^5 - 3*x^4 + x^3)*e^15 + 3*(x^7 - 6*x^6 + 11*x^5 - 6*x^4 +
x^3)*e^10 - 3*(x^9 - 9*x^8 + 62*x^7 - 333*x^6 + 990*x^5 - 1449*x^4 + 961*x^3 - 288*x^2 + 32*x)*e^5 + 96*x)*log
(x))/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1)
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{14} - 18 \, x^{13} + 236 \, x^{12} - 2343 \, x^{11} + 15115 \, x^{10} - 61968 \, x^{9} + 164104 \, x^{8} - 283473 \, x^{7} + 318269 \, x^{6} - 229260 \, x^{5} + 104206 \, x^{4} - 27 \, {\left (x^{11} - 18 \, x^{10} + 140 \, x^{9} - 615 \, x^{8} + 1675 \, x^{7} - 2928 \, x^{6} + 3304 \, x^{5} - 2385 \, x^{4} + 1085 \, x^{3} - 300 \, x^{2} + {\left (x^{9} - 9 \, x^{8} + 29 \, x^{7} - 36 \, x^{6} + 36 \, x^{4} - 29 \, x^{3} + 9 \, x^{2} - x\right )} e^{5} + 46 \, x - 3\right )} \log \relax (x)^{3} - 28803 \, x^{3} + 27 \, {\left (x^{12} - 18 \, x^{11} + 140 \, x^{10} - 615 \, x^{9} + 1675 \, x^{8} - 2928 \, x^{7} + 3304 \, x^{6} - 2385 \, x^{5} + 1085 \, x^{4} - 300 \, x^{3} + 46 \, x^{2} - {\left (x^{8} - 6 \, x^{7} + 10 \, x^{6} - 10 \, x^{4} + 6 \, x^{3} - x^{2}\right )} e^{10} + {\left (6 \, x^{9} - 65 \, x^{8} + 282 \, x^{7} - 627 \, x^{6} + 765 \, x^{5} - 519 \, x^{4} + 195 \, x^{3} - 38 \, x^{2} + 3 \, x\right )} e^{5} - 3 \, x\right )} \log \relax (x)^{2} + 4416 \, x^{2} - {\left (x^{6} - x^{4}\right )} e^{20} + {\left (2 \, x^{8} - 29 \, x^{6} + 48 \, x^{5} - 22 \, x^{4} + 3 \, x^{3}\right )} e^{15} - 3 \, {\left (6 \, x^{9} - 15 \, x^{8} - 57 \, x^{7} + 145 \, x^{6} + 105 \, x^{5} - 349 \, x^{4} + 195 \, x^{3} - 32 \, x^{2}\right )} e^{10} - {\left (2 \, x^{12} - 36 \, x^{11} + 253 \, x^{10} - 1494 \, x^{9} + 8121 \, x^{8} - 29295 \, x^{7} + 61691 \, x^{6} - 74007 \, x^{5} + 49936 \, x^{4} - 18729 \, x^{3} + 3648 \, x^{2} - 288 \, x\right )} e^{5} - 9 \, {\left (x^{13} - 18 \, x^{12} + 172 \, x^{11} - 1191 \, x^{10} + 6155 \, x^{9} - 22608 \, x^{8} + 56904 \, x^{7} - 96081 \, x^{6} + 106813 \, x^{5} - 76620 \, x^{4} + 34766 \, x^{3} - 9603 \, x^{2} + {\left (x^{7} - 3 \, x^{6} + 3 \, x^{4} - x^{3}\right )} e^{15} - {\left (x^{9} - 37 \, x^{7} + 135 \, x^{6} - 185 \, x^{5} + 111 \, x^{4} - 30 \, x^{3} + 3 \, x^{2}\right )} e^{10} - {\left (x^{11} - 21 \, x^{10} + 127 \, x^{9} - 312 \, x^{8} + 326 \, x^{7} - 342 \, x^{6} + 1009 \, x^{5} - 1533 \, x^{4} + 1003 \, x^{3} - 294 \, x^{2} + 32 \, x\right )} e^{5} + 1472 \, x - 96\right )} \log \relax (x) - 288 \, x}{64 \, {\left (x^{11} - 15 \, x^{10} + 95 \, x^{9} - 330 \, x^{8} + 685 \, x^{7} - 873 \, x^{6} + 685 \, x^{5} - 330 \, x^{4} + 95 \, x^{3} - 15 \, x^{2} + x\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x)*exp(5)-27*x^11+486*x^10-3780*x^9+16
605*x^8-45225*x^7+79056*x^6-89208*x^5+64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x
^6+270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+20655*x^5-14013*x^4+5265*x^3-1026*x^2
+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10-16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+
1242*x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+1215*x^6-1665*x^5+999*x^4-270*x^
3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+2
88*x)*exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^7+864729*x^6-961317*x^5+689580
*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x)+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+
(-18*x^9+45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12+36*x^11-253*x^10+1494*x^9-8
121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^
11+15115*x^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803*x^3+4416*x^2-288*x)/(64*x
^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872*x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm="g
iac")
[Out]
integrate(1/64*(x^14 - 18*x^13 + 236*x^12 - 2343*x^11 + 15115*x^10 - 61968*x^9 + 164104*x^8 - 283473*x^7 + 318
269*x^6 - 229260*x^5 + 104206*x^4 - 27*(x^11 - 18*x^10 + 140*x^9 - 615*x^8 + 1675*x^7 - 2928*x^6 + 3304*x^5 -
2385*x^4 + 1085*x^3 - 300*x^2 + (x^9 - 9*x^8 + 29*x^7 - 36*x^6 + 36*x^4 - 29*x^3 + 9*x^2 - x)*e^5 + 46*x - 3)*
log(x)^3 - 28803*x^3 + 27*(x^12 - 18*x^11 + 140*x^10 - 615*x^9 + 1675*x^8 - 2928*x^7 + 3304*x^6 - 2385*x^5 + 1
085*x^4 - 300*x^3 + 46*x^2 - (x^8 - 6*x^7 + 10*x^6 - 10*x^4 + 6*x^3 - x^2)*e^10 + (6*x^9 - 65*x^8 + 282*x^7 -
627*x^6 + 765*x^5 - 519*x^4 + 195*x^3 - 38*x^2 + 3*x)*e^5 - 3*x)*log(x)^2 + 4416*x^2 - (x^6 - x^4)*e^20 + (2*x
^8 - 29*x^6 + 48*x^5 - 22*x^4 + 3*x^3)*e^15 - 3*(6*x^9 - 15*x^8 - 57*x^7 + 145*x^6 + 105*x^5 - 349*x^4 + 195*x
^3 - 32*x^2)*e^10 - (2*x^12 - 36*x^11 + 253*x^10 - 1494*x^9 + 8121*x^8 - 29295*x^7 + 61691*x^6 - 74007*x^5 + 4
9936*x^4 - 18729*x^3 + 3648*x^2 - 288*x)*e^5 - 9*(x^13 - 18*x^12 + 172*x^11 - 1191*x^10 + 6155*x^9 - 22608*x^8
+ 56904*x^7 - 96081*x^6 + 106813*x^5 - 76620*x^4 + 34766*x^3 - 9603*x^2 + (x^7 - 3*x^6 + 3*x^4 - x^3)*e^15 -
(x^9 - 37*x^7 + 135*x^6 - 185*x^5 + 111*x^4 - 30*x^3 + 3*x^2)*e^10 - (x^11 - 21*x^10 + 127*x^9 - 312*x^8 + 326
*x^7 - 342*x^6 + 1009*x^5 - 1533*x^4 + 1003*x^3 - 294*x^2 + 32*x)*e^5 + 1472*x - 96)*log(x) - 288*x)/(x^11 - 1
5*x^10 + 95*x^9 - 330*x^8 + 685*x^7 - 873*x^6 + 685*x^5 - 330*x^4 + 95*x^3 - 15*x^2 + x), x)
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maple [B] time = 0.36, size = 594, normalized size = 19.80
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\(\frac {81 \ln \relax (x )^{4}}{256}+\frac {27 x \left (-x^{2}+{\mathrm e}^{5}+3 x -1\right ) \ln \relax (x )^{3}}{64 \left (x^{2}-3 x +1\right )}+\frac {27 \left (x^{6}-2 x^{4} {\mathrm e}^{5}-6 x^{5}+x^{2} {\mathrm e}^{10}+6 x^{3} {\mathrm e}^{5}+43 x^{4}-2 x^{2} {\mathrm e}^{5}-198 x^{3}+353 x^{2}-192 x +32\right ) \ln \relax (x )^{2}}{128 \left (x^{2}-3 x +1\right )^{2}}+\frac {3 \left (-x^{9}+3 x^{7} {\mathrm e}^{5}+9 x^{8}-3 x^{5} {\mathrm e}^{10}-27 x^{6} {\mathrm e}^{5}-126 x^{7}+x^{3} {\mathrm e}^{15}+9 x^{4} {\mathrm e}^{10}+210 x^{5} {\mathrm e}^{5}+909 x^{6}-3 x^{3} {\mathrm e}^{10}-864 x^{4} {\mathrm e}^{5}-2910 x^{5}+1464 x^{3} {\mathrm e}^{5}+4329 x^{4}-846 x^{2} {\mathrm e}^{5}-2881 x^{3}+177 x \,{\mathrm e}^{5}+864 x^{2}-9 \,{\mathrm e}^{5}-96 x \right ) \ln \relax (x )}{64 \left (x^{2}-3 x +1\right ) \left (x^{4}-6 x^{3}+11 x^{2}-6 x +1\right )}+\frac {72 x \,{\mathrm e}^{10}-6 \,{\mathrm e}^{10}-12 x^{11}+x^{12}-4992 x \,{\mathrm e}^{5}-27792 x^{7}+11331 x^{8}+250 x^{10}-2448 x^{9}+416 \,{\mathrm e}^{5}+37498 x^{6}-27660 x^{5}+11137 x^{4}-2304 x^{3}+192 x^{2}-1356 x^{7} {\mathrm e}^{5}+23744 x^{2} {\mathrm e}^{5}-42588 x^{5} {\mathrm e}^{5}-88 x^{8} {\mathrm e}^{5}+69596 x^{4} {\mathrm e}^{5}-56448 x^{3} {\mathrm e}^{5}+108 \ln \left (-x \right ) {\mathrm e}^{5}+12488 x^{6} {\mathrm e}^{5}-288 x^{3} {\mathrm e}^{10}-4 \,{\mathrm e}^{5} x^{10}+36 \,{\mathrm e}^{5} x^{9}-1296 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{7}+6264 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{6}-15552 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{5}+21060 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{4}-15552 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{3}+6264 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{2}-1296 \,{\mathrm e}^{5} \ln \left (-x \right ) x +108 \,{\mathrm e}^{5} \ln \left (-x \right ) x^{8}-90 x^{6} {\mathrm e}^{10}-4 x^{4} {\mathrm e}^{15}+36 \,{\mathrm e}^{10} x^{7}+x^{4} {\mathrm e}^{20}+12 x^{5} {\mathrm e}^{15}-156 x^{2} {\mathrm e}^{10}-324 x^{5} {\mathrm e}^{10}+948 x^{4} {\mathrm e}^{10}-4 x^{6} {\mathrm e}^{15}}{256 \left (x^{4}-6 x^{3}+11 x^{2}-6 x +1\right ) \left (x^{2}-3 x +1\right )^{2}}\) |
\(594\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x)*exp(5)-27*x^11+486*x^10-3780*x^9+16605*x^
8-45225*x^7+79056*x^6-89208*x^5+64395*x^4-29295*x^3+8100*x^2-1242*x+81)*ln(x)^3+((-27*x^8+162*x^7-270*x^6+270*
x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+20655*x^5-14013*x^4+5265*x^3-1026*x^2+81*x)*
exp(5)+27*x^12-486*x^11+3780*x^10-16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+1242*x^
2-81*x)*ln(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+1215*x^6-1665*x^5+999*x^4-270*x^3+27*x^2
)*exp(5)^2+(9*x^11-189*x^10+1143*x^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+288*x)*ex
p(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^7+864729*x^6-961317*x^5+689580*x^4-312
894*x^3+86427*x^2-13248*x+864)*ln(x)+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+(-18*x^9+
45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12+36*x^11-253*x^10+1494*x^9-8121*x^8+2
9295*x^7-61691*x^6+74007*x^5-49936*x^4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^11+15115*
x^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803*x^3+4416*x^2-288*x)/(64*x^11-960*x
^10+6080*x^9-21120*x^8+43840*x^7-55872*x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x,method=_RETURNVERBOSE)
[Out]
81/256*ln(x)^4+27/64*x*(-x^2+exp(5)+3*x-1)/(x^2-3*x+1)*ln(x)^3+27/128*(x^6-2*x^4*exp(5)-6*x^5+x^2*exp(10)+6*x^
3*exp(5)+43*x^4-2*x^2*exp(5)-198*x^3+353*x^2-192*x+32)/(x^2-3*x+1)^2*ln(x)^2+3/64*(-x^9+3*x^7*exp(5)+9*x^8-3*x
^5*exp(10)-27*x^6*exp(5)-126*x^7+x^3*exp(15)+9*x^4*exp(10)+210*x^5*exp(5)+909*x^6-3*x^3*exp(10)-864*x^4*exp(5)
-2910*x^5+1464*x^3*exp(5)+4329*x^4-846*x^2*exp(5)-2881*x^3+177*x*exp(5)+864*x^2-9*exp(5)-96*x)/(x^2-3*x+1)/(x^
4-6*x^3+11*x^2-6*x+1)*ln(x)+1/256*(72*x*exp(10)-6*exp(10)-12*x^11+x^12-4992*x*exp(5)-27792*x^7+11331*x^8+250*x
^10-2448*x^9+416*exp(5)+37498*x^6-27660*x^5+11137*x^4-2304*x^3+192*x^2-1356*x^7*exp(5)+23744*x^2*exp(5)-42588*
x^5*exp(5)-88*x^8*exp(5)+69596*x^4*exp(5)-56448*x^3*exp(5)+108*ln(-x)*exp(5)+12488*x^6*exp(5)-288*x^3*exp(10)-
4*exp(5)*x^10+36*exp(5)*x^9-1296*exp(5)*ln(-x)*x^7+6264*exp(5)*ln(-x)*x^6-15552*exp(5)*ln(-x)*x^5+21060*exp(5)
*ln(-x)*x^4-15552*exp(5)*ln(-x)*x^3+6264*exp(5)*ln(-x)*x^2-1296*exp(5)*ln(-x)*x+108*exp(5)*ln(-x)*x^8-90*x^6*e
xp(10)-4*x^4*exp(15)+36*exp(10)*x^7+x^4*exp(20)+12*x^5*exp(15)-156*x^2*exp(10)-324*x^5*exp(10)+948*x^4*exp(10)
-4*x^6*exp(15))/(x^4-6*x^3+11*x^2-6*x+1)/(x^2-3*x+1)^2
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maxima [B] time = 0.96, size = 4571, normalized size = 152.37 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-27*x^9+243*x^8-783*x^7+972*x^6-972*x^4+783*x^3-243*x^2+27*x)*exp(5)-27*x^11+486*x^10-3780*x^9+16
605*x^8-45225*x^7+79056*x^6-89208*x^5+64395*x^4-29295*x^3+8100*x^2-1242*x+81)*log(x)^3+((-27*x^8+162*x^7-270*x
^6+270*x^4-162*x^3+27*x^2)*exp(5)^2+(162*x^9-1755*x^8+7614*x^7-16929*x^6+20655*x^5-14013*x^4+5265*x^3-1026*x^2
+81*x)*exp(5)+27*x^12-486*x^11+3780*x^10-16605*x^9+45225*x^8-79056*x^7+89208*x^6-64395*x^5+29295*x^4-8100*x^3+
1242*x^2-81*x)*log(x)^2+((-9*x^7+27*x^6-27*x^4+9*x^3)*exp(5)^3+(9*x^9-333*x^7+1215*x^6-1665*x^5+999*x^4-270*x^
3+27*x^2)*exp(5)^2+(9*x^11-189*x^10+1143*x^9-2808*x^8+2934*x^7-3078*x^6+9081*x^5-13797*x^4+9027*x^3-2646*x^2+2
88*x)*exp(5)-9*x^13+162*x^12-1548*x^11+10719*x^10-55395*x^9+203472*x^8-512136*x^7+864729*x^6-961317*x^5+689580
*x^4-312894*x^3+86427*x^2-13248*x+864)*log(x)+(-x^6+x^4)*exp(5)^4+(2*x^8-29*x^6+48*x^5-22*x^4+3*x^3)*exp(5)^3+
(-18*x^9+45*x^8+171*x^7-435*x^6-315*x^5+1047*x^4-585*x^3+96*x^2)*exp(5)^2+(-2*x^12+36*x^11-253*x^10+1494*x^9-8
121*x^8+29295*x^7-61691*x^6+74007*x^5-49936*x^4+18729*x^3-3648*x^2+288*x)*exp(5)+x^14-18*x^13+236*x^12-2343*x^
11+15115*x^10-61968*x^9+164104*x^8-283473*x^7+318269*x^6-229260*x^5+104206*x^4-28803*x^3+4416*x^2-288*x)/(64*x
^11-960*x^10+6080*x^9-21120*x^8+43840*x^7-55872*x^6+43840*x^5-21120*x^4+6080*x^3-960*x^2+64*x),x, algorithm="m
axima")
[Out]
1/256*x^4 - 1/64*x^3 - 3/16000*sqrt(5)*(22*e^15 + 60*e^10 + 5325*e^5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) -
3)) + 3/4*x^2 + 1/480000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 +
18432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144
*x^3 + 58*x^2 - 12*x + 1))*e^20 - 1/480000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*
x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^
5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^20 - 11/240000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(
5) - 3)) + 5*(432*x^7 - 4536*x^6 + 18432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7
+ 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^15 - 29/480000*(432*sqrt(5)*log((2*x - sqrt(5)
- 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280*x^3 - 17098*x^2 + 4044*x -
373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^15 + 1/160000*(348*sqrt(5)*l
og((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14848*x^5 - 29145*x^4 + 28420*x^3 - 1357
2*x^2 + 3216*x - 297)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^15 + 3/1000
0*(156*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(156*x^7 - 1638*x^6 + 6656*x^5 - 13065*x^4 + 1
2640*x^3 - 6134*x^2 + 1452*x - 134)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))
*e^15 + 1/80000*(84*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(84*x^7 - 1132*x^6 + 4084*x^5 - 7
785*x^4 + 7360*x^3 - 3526*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12
*x + 1))*e^15 + 349/160000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 +
18432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 14
4*x^3 + 58*x^2 - 12*x + 1))*e^10 - 29/32000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432
*x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x
^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^10 - 39/32000*(348*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(
5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14848*x^5 - 29145*x^4 + 28420*x^3 - 13572*x^2 + 3216*x - 297)/(x^8 - 12*x^7
+ 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^10 + 57/160000*(348*sqrt(5)*log((2*x - sqrt(5)
- 3)/(2*x + sqrt(5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14348*x^5 - 28770*x^4 + 27920*x^3 - 13572*x^2 + 3216*x -
297)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^10 - 3/80000*(168*sqrt(5)*lo
g((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) - 5*(1332*x^7 - 4986*x^6 + 9832*x^5 - 8805*x^4 + 3280*x^3 - 198*x^2
- 156*x + 27)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^10 - 63/32000*(156
*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(156*x^7 - 1638*x^6 + 6656*x^5 - 13065*x^4 + 12640*x
^3 - 6134*x^2 + 1452*x - 134)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^10
+ 3/5000*(84*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(84*x^7 - 882*x^6 + 3584*x^5 - 7035*x^4
+ 6860*x^3 - 3276*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))
*e^10 + 9/32000*(84*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(84*x^7 - 1132*x^6 + 4084*x^5 - 7
785*x^4 + 7360*x^3 - 3526*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12
*x + 1))*e^10 - 1/240000*(3750*x^2 + 218052*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 112500*x -
5*(771948*x^7 - 6376704*x^6 + 20652948*x^5 - 32587395*x^4 + 26188920*x^3 - 11088472*x^2 + 2368416*x - 201697)/
(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 487500*log(x^2 - 3*x + 1))*e^5 + 9
/40000*(8406*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 2500*x - 5*(45344*x^7 - 356112*x^6 + 11188
44*x^5 - 1732185*x^4 + 1377260*x^3 - 579416*x^2 + 123248*x - 10466)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4
- 144*x^3 + 58*x^2 - 12*x + 1) + 18750*log(x^2 - 3*x + 1))*e^5 - 253/480000*(1782*sqrt(5)*log((2*x - sqrt(5)
- 3)/(2*x + sqrt(5) - 3)) - 5*(18468*x^7 - 129414*x^6 + 382968*x^5 - 571320*x^4 + 444420*x^3 - 184402*x^2 + 38
856*x - 3277)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 3750*log(x^2 - 3*x +
1))*e^5 - 3121/30000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x^7 - 4536*x^6 + 1843
2*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3
+ 58*x^2 - 12*x + 1))*e^5 - 61691/480000*(432*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(432*x
^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5
+ 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^5 + 6243/160000*(348*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(
5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14848*x^5 - 29145*x^4 + 28420*x^3 - 13572*x^2 + 3216*x - 297)/(x^8 - 12*x^7
+ 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^5 + 1953/32000*(348*sqrt(5)*log((2*x - sqrt(5)
- 3)/(2*x + sqrt(5) - 3)) + 5*(348*x^7 - 3654*x^6 + 14348*x^5 - 28770*x^4 + 27920*x^3 - 13572*x^2 + 3216*x -
297)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^5 + 249/80000*(168*sqrt(5)*l
og((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) - 5*(1332*x^7 - 4986*x^6 + 9832*x^5 - 8805*x^4 + 3280*x^3 - 198*x^
2 - 156*x + 27)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^5 + 3/5000*(168*s
qrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(168*x^7 - 1764*x^6 + 7168*x^5 - 14070*x^4 + 13720*x^3
- 6552*x^2 + 1656*x - 27)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1))*e^5 + 74
007/160000*(156*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(156*x^7 - 1638*x^6 + 6656*x^5 - 1306
5*x^4 + 12640*x^3 - 6134*x^2 + 1452*x - 134)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 1
2*x + 1))*e^5 - 57/2500*(84*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(84*x^7 - 882*x^6 + 3584*
x^5 - 7035*x^4 + 6860*x^3 - 3276*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x
^2 - 12*x + 1))*e^5 - 8121/160000*(84*sqrt(5)*log((2*x - sqrt(5) - 3)/(2*x + sqrt(5) - 3)) + 5*(84*x^7 - 1132*
x^6 + 4084*x^5 - 7785*x^4 + 7360*x^3 - 3526*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144
*x^3 + 58*x^2 - 12*x + 1))*e^5 - 27/128*e^5*log(x^2 - 3*x + 1) - 9/2*x - 1/32000*(5481756*x^7 - 47451938*x^6 +
158601256*x^5 - 255478065*x^4 + 207743740*x^3 - 88580984*x^2 + 19006452*x - 1623684)/(x^8 - 12*x^7 + 58*x^6 -
144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 3/16000*(3752352*x^7 - 31893696*x^6 + 105253352*x^5 - 1681
07730*x^4 + 136035080*x^3 - 57835728*x^2 + 12386184*x - 1056753)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 -
144*x^3 + 58*x^2 - 12*x + 1) - 59/24000*(771948*x^7 - 6376704*x^6 + 20652948*x^5 - 32587395*x^4 + 26188920*x^3
- 11088472*x^2 + 2368416*x - 201697)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1
) + 2343/32000*(45344*x^7 - 356112*x^6 + 1118844*x^5 - 1732185*x^4 + 1377260*x^3 - 579416*x^2 + 123248*x - 104
66)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) - 3023/19200*(18468*x^7 - 129414
*x^6 + 382968*x^5 - 571320*x^4 + 444420*x^3 - 184402*x^2 + 38856*x - 3277)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 +
195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 1291/2000*(1332*x^7 - 4986*x^6 + 9832*x^5 - 8805*x^4 + 3280*x^3 - 198
*x^2 - 156*x + 27)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 52103/48000*(43
2*x^7 - 4536*x^6 + 18432*x^5 - 36180*x^4 + 35280*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*
x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 318269/96000*(432*x^7 - 4536*x^6 + 18432*x^5 - 36555*x^4 + 3528
0*x^3 - 17098*x^2 + 4044*x - 373)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) -
9601/32000*(348*x^7 - 3654*x^6 + 14848*x^5 - 29145*x^4 + 28420*x^3 - 13572*x^2 + 3216*x - 297)/(x^8 - 12*x^7 +
58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) - 94491/32000*(348*x^7 - 3654*x^6 + 14348*x^5 - 287
70*x^4 + 27920*x^3 - 13572*x^2 + 3216*x - 297)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 -
12*x + 1) - 3/1000*(168*x^7 - 1764*x^6 + 7168*x^5 - 14070*x^4 + 13720*x^3 - 6552*x^2 + 1656*x - 27)/(x^8 - 12
*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) - 11463/1600*(156*x^7 - 1638*x^6 + 6656*x^5 -
13065*x^4 + 12640*x^3 - 6134*x^2 + 1452*x - 134)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^
2 - 12*x + 1) + 69/500*(84*x^7 - 882*x^6 + 3584*x^5 - 7035*x^4 + 6860*x^3 - 3276*x^2 + 828*x - 76)/(x^8 - 12*x
^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*x + 1) + 20513/4000*(84*x^7 - 1132*x^6 + 4084*x^5 - 77
85*x^4 + 7360*x^3 - 3526*x^2 + 828*x - 76)/(x^8 - 12*x^7 + 58*x^6 - 144*x^5 + 195*x^4 - 144*x^3 + 58*x^2 - 12*
x + 1) + 1/6400*(100*x^9 - 900*x^8 - 300*x^7*(3*e^5 - 106) + 900*x^6*(9*e^5 - 293) - 12*x^5*(11*e^15 + 105*e^1
0 + 2250*e^5 - 72250) + 90*x^4*(11*e^15 + 90*e^10 + 450*e^5 - 14410) + 2025*(x^6 - 9*x^5 + 30*x^4 - 45*x^3 + 3
0*x^2 - 9*x + 1)*log(x)^4 - 10*x^3*(243*e^15 + 1710*e^10 + 2700*e^5 - 86410) - 2700*(x^7 - 9*x^6 - x^5*(e^5 -
30) + 3*x^4*(2*e^5 - 15) - x^3*(11*e^5 - 30) + 3*x^2*(2*e^5 - 3) - x*(e^5 - 1))*log(x)^3 + 450*x^2*(5*e^15 + 3
0*e^10 + 18*e^5 - 576) + 1350*(x^8 - 9*x^7 - 2*x^6*(e^5 - 31) + 3*x^5*(4*e^5 - 111) + x^4*(e^10 - 22*e^5 + 990
) - 3*x^3*(e^10 - 4*e^5 + 483) + x^2*(e^10 - 2*e^5 + 961) - 288*x + 32)*log(x)^2 - 60*x*(14*e^15 + 75*e^10 + 1
5*e^5 - 480) - 300*(x^9 - 9*x^8 - 3*x^7*(e^5 - 42) + 9*x^6*(2*e^5 - 101) + 3*x^5*(e^10 - 43*e^5 + 970) - 9*x^4
*(e^10 - 66*e^5 + 481) - x^3*(e^15 - 3*e^10 + 1059*e^5 - 2881) + 288*x^2*(2*e^5 - 3) - 96*x*(e^5 - 1))*log(x)
+ 108*e^15 + 540*e^10)/(x^6 - 9*x^5 + 30*x^4 - 45*x^3 + 30*x^2 - 9*x + 1)
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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{20}\,\left (x^4-x^6\right )-288\,x+{\mathrm {e}}^{15}\,\left (2\,x^8-29\,x^6+48\,x^5-22\,x^4+3\,x^3\right )+{\ln \relax (x)}^2\,\left ({\mathrm {e}}^{10}\,\left (-27\,x^8+162\,x^7-270\,x^6+270\,x^4-162\,x^3+27\,x^2\right )-81\,x+{\mathrm {e}}^5\,\left (162\,x^9-1755\,x^8+7614\,x^7-16929\,x^6+20655\,x^5-14013\,x^4+5265\,x^3-1026\,x^2+81\,x\right )+1242\,x^2-8100\,x^3+29295\,x^4-64395\,x^5+89208\,x^6-79056\,x^7+45225\,x^8-16605\,x^9+3780\,x^{10}-486\,x^{11}+27\,x^{12}\right )+{\mathrm {e}}^5\,\left (-2\,x^{12}+36\,x^{11}-253\,x^{10}+1494\,x^9-8121\,x^8+29295\,x^7-61691\,x^6+74007\,x^5-49936\,x^4+18729\,x^3-3648\,x^2+288\,x\right )+{\ln \relax (x)}^3\,\left ({\mathrm {e}}^5\,\left (-27\,x^9+243\,x^8-783\,x^7+972\,x^6-972\,x^4+783\,x^3-243\,x^2+27\,x\right )-1242\,x+8100\,x^2-29295\,x^3+64395\,x^4-89208\,x^5+79056\,x^6-45225\,x^7+16605\,x^8-3780\,x^9+486\,x^{10}-27\,x^{11}+81\right )+\ln \relax (x)\,\left ({\mathrm {e}}^5\,\left (9\,x^{11}-189\,x^{10}+1143\,x^9-2808\,x^8+2934\,x^7-3078\,x^6+9081\,x^5-13797\,x^4+9027\,x^3-2646\,x^2+288\,x\right )-13248\,x+{\mathrm {e}}^{10}\,\left (9\,x^9-333\,x^7+1215\,x^6-1665\,x^5+999\,x^4-270\,x^3+27\,x^2\right )+86427\,x^2-312894\,x^3+689580\,x^4-961317\,x^5+864729\,x^6-512136\,x^7+203472\,x^8-55395\,x^9+10719\,x^{10}-1548\,x^{11}+162\,x^{12}-9\,x^{13}+{\mathrm {e}}^{15}\,\left (-9\,x^7+27\,x^6-27\,x^4+9\,x^3\right )+864\right )+4416\,x^2-28803\,x^3+104206\,x^4-229260\,x^5+318269\,x^6-283473\,x^7+164104\,x^8-61968\,x^9+15115\,x^{10}-2343\,x^{11}+236\,x^{12}-18\,x^{13}+x^{14}+{\mathrm {e}}^{10}\,\left (-18\,x^9+45\,x^8+171\,x^7-435\,x^6-315\,x^5+1047\,x^4-585\,x^3+96\,x^2\right )}{64\,x^{11}-960\,x^{10}+6080\,x^9-21120\,x^8+43840\,x^7-55872\,x^6+43840\,x^5-21120\,x^4+6080\,x^3-960\,x^2+64\,x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((exp(20)*(x^4 - x^6) - 288*x + exp(15)*(3*x^3 - 22*x^4 + 48*x^5 - 29*x^6 + 2*x^8) + log(x)^2*(exp(10)*(27*
x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 162*x^7 - 27*x^8) - 81*x + exp(5)*(81*x - 1026*x^2 + 5265*x^3 - 14013*x^4
+ 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9) + 1242*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208
*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12) + exp(5)*(288*x - 3648*x^2 + 18729*
x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^10 + 36*x^11 - 2*x^12) + log
(x)^3*(exp(5)*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9) - 1242*x + 8100*x^2
- 29295*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 + 81)
+ log(x)*(exp(5)*(288*x - 2646*x^2 + 9027*x^3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x
^9 - 189*x^10 + 9*x^11) - 13248*x + exp(10)*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^
9) + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961317*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 107
19*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + exp(15)*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + 864) + 4416*x^2 - 28803*
x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 23
6*x^12 - 18*x^13 + x^14 + exp(10)*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171*x^7 + 45*x^8 - 18*x^9
))/(64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^1
0 + 64*x^11),x)
[Out]
int((exp(20)*(x^4 - x^6) - 288*x + exp(15)*(3*x^3 - 22*x^4 + 48*x^5 - 29*x^6 + 2*x^8) + log(x)^2*(exp(10)*(27*
x^2 - 162*x^3 + 270*x^4 - 270*x^6 + 162*x^7 - 27*x^8) - 81*x + exp(5)*(81*x - 1026*x^2 + 5265*x^3 - 14013*x^4
+ 20655*x^5 - 16929*x^6 + 7614*x^7 - 1755*x^8 + 162*x^9) + 1242*x^2 - 8100*x^3 + 29295*x^4 - 64395*x^5 + 89208
*x^6 - 79056*x^7 + 45225*x^8 - 16605*x^9 + 3780*x^10 - 486*x^11 + 27*x^12) + exp(5)*(288*x - 3648*x^2 + 18729*
x^3 - 49936*x^4 + 74007*x^5 - 61691*x^6 + 29295*x^7 - 8121*x^8 + 1494*x^9 - 253*x^10 + 36*x^11 - 2*x^12) + log
(x)^3*(exp(5)*(27*x - 243*x^2 + 783*x^3 - 972*x^4 + 972*x^6 - 783*x^7 + 243*x^8 - 27*x^9) - 1242*x + 8100*x^2
- 29295*x^3 + 64395*x^4 - 89208*x^5 + 79056*x^6 - 45225*x^7 + 16605*x^8 - 3780*x^9 + 486*x^10 - 27*x^11 + 81)
+ log(x)*(exp(5)*(288*x - 2646*x^2 + 9027*x^3 - 13797*x^4 + 9081*x^5 - 3078*x^6 + 2934*x^7 - 2808*x^8 + 1143*x
^9 - 189*x^10 + 9*x^11) - 13248*x + exp(10)*(27*x^2 - 270*x^3 + 999*x^4 - 1665*x^5 + 1215*x^6 - 333*x^7 + 9*x^
9) + 86427*x^2 - 312894*x^3 + 689580*x^4 - 961317*x^5 + 864729*x^6 - 512136*x^7 + 203472*x^8 - 55395*x^9 + 107
19*x^10 - 1548*x^11 + 162*x^12 - 9*x^13 + exp(15)*(9*x^3 - 27*x^4 + 27*x^6 - 9*x^7) + 864) + 4416*x^2 - 28803*
x^3 + 104206*x^4 - 229260*x^5 + 318269*x^6 - 283473*x^7 + 164104*x^8 - 61968*x^9 + 15115*x^10 - 2343*x^11 + 23
6*x^12 - 18*x^13 + x^14 + exp(10)*(96*x^2 - 585*x^3 + 1047*x^4 - 315*x^5 - 435*x^6 + 171*x^7 + 45*x^8 - 18*x^9
))/(64*x - 960*x^2 + 6080*x^3 - 21120*x^4 + 43840*x^5 - 55872*x^6 + 43840*x^7 - 21120*x^8 + 6080*x^9 - 960*x^1
0 + 64*x^11), x)
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sympy [B] time = 19.17, size = 508, normalized size = 16.93 \begin {gather*} \frac {x^{4}}{256} + x^{2} \left (\frac {3}{4} - \frac {e^{5}}{64}\right ) - \frac {3 x e^{5}}{64} + \frac {81 \log {\relax (x )}^{4}}{256} + \frac {27 e^{5} \log {\relax (x )}}{64} + \frac {x^{7} \left (- 1236 e^{5} + 36 e^{10}\right ) + x^{6} \left (- 4 e^{15} - 90 e^{10} + 11540 e^{5}\right ) + x^{5} \left (- 324 e^{10} - 40824 e^{5} + 12 e^{15}\right ) + x^{4} \left (- 4 e^{15} + 68100 e^{5} + 948 e^{10} + e^{20}\right ) + x^{3} \left (- 55800 e^{5} - 288 e^{10}\right ) + x^{2} \left (- 156 e^{10} + 23604 e^{5}\right ) + x \left (- 4980 e^{5} + 72 e^{10}\right ) - 6 e^{10} + 416 e^{5}}{256 x^{8} - 3072 x^{7} + 14848 x^{6} - 36864 x^{5} + 49920 x^{4} - 36864 x^{3} + 14848 x^{2} - 3072 x + 256} + \frac {\left (- 3 x^{9} + 27 x^{8} - 378 x^{7} + 9 x^{7} e^{5} - 81 x^{6} e^{5} + 2727 x^{6} - 9 x^{5} e^{10} - 8730 x^{5} + 630 x^{5} e^{5} - 2592 x^{4} e^{5} + 12987 x^{4} + 27 x^{4} e^{10} - 9 x^{3} e^{10} - 8643 x^{3} + 4392 x^{3} e^{5} + 3 x^{3} e^{15} - 2538 x^{2} e^{5} + 2592 x^{2} - 288 x + 531 x e^{5} - 27 e^{5}\right ) \log {\relax (x )}}{64 x^{6} - 576 x^{5} + 1920 x^{4} - 2880 x^{3} + 1920 x^{2} - 576 x + 64} + \frac {\left (27 x^{6} - 162 x^{5} - 54 x^{4} e^{5} + 1161 x^{4} - 5346 x^{3} + 162 x^{3} e^{5} - 54 x^{2} e^{5} + 9531 x^{2} + 27 x^{2} e^{10} - 5184 x + 864\right ) \log {\relax (x )}^{2}}{128 x^{4} - 768 x^{3} + 1408 x^{2} - 768 x + 128} + \frac {\left (- 27 x^{3} + 81 x^{2} - 27 x + 27 x e^{5}\right ) \log {\relax (x )}^{3}}{64 x^{2} - 192 x + 64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((-27*x**9+243*x**8-783*x**7+972*x**6-972*x**4+783*x**3-243*x**2+27*x)*exp(5)-27*x**11+486*x**10-37
80*x**9+16605*x**8-45225*x**7+79056*x**6-89208*x**5+64395*x**4-29295*x**3+8100*x**2-1242*x+81)*ln(x)**3+((-27*
x**8+162*x**7-270*x**6+270*x**4-162*x**3+27*x**2)*exp(5)**2+(162*x**9-1755*x**8+7614*x**7-16929*x**6+20655*x**
5-14013*x**4+5265*x**3-1026*x**2+81*x)*exp(5)+27*x**12-486*x**11+3780*x**10-16605*x**9+45225*x**8-79056*x**7+8
9208*x**6-64395*x**5+29295*x**4-8100*x**3+1242*x**2-81*x)*ln(x)**2+((-9*x**7+27*x**6-27*x**4+9*x**3)*exp(5)**3
+(9*x**9-333*x**7+1215*x**6-1665*x**5+999*x**4-270*x**3+27*x**2)*exp(5)**2+(9*x**11-189*x**10+1143*x**9-2808*x
**8+2934*x**7-3078*x**6+9081*x**5-13797*x**4+9027*x**3-2646*x**2+288*x)*exp(5)-9*x**13+162*x**12-1548*x**11+10
719*x**10-55395*x**9+203472*x**8-512136*x**7+864729*x**6-961317*x**5+689580*x**4-312894*x**3+86427*x**2-13248*
x+864)*ln(x)+(-x**6+x**4)*exp(5)**4+(2*x**8-29*x**6+48*x**5-22*x**4+3*x**3)*exp(5)**3+(-18*x**9+45*x**8+171*x*
*7-435*x**6-315*x**5+1047*x**4-585*x**3+96*x**2)*exp(5)**2+(-2*x**12+36*x**11-253*x**10+1494*x**9-8121*x**8+29
295*x**7-61691*x**6+74007*x**5-49936*x**4+18729*x**3-3648*x**2+288*x)*exp(5)+x**14-18*x**13+236*x**12-2343*x**
11+15115*x**10-61968*x**9+164104*x**8-283473*x**7+318269*x**6-229260*x**5+104206*x**4-28803*x**3+4416*x**2-288
*x)/(64*x**11-960*x**10+6080*x**9-21120*x**8+43840*x**7-55872*x**6+43840*x**5-21120*x**4+6080*x**3-960*x**2+64
*x),x)
[Out]
x**4/256 + x**2*(3/4 - exp(5)/64) - 3*x*exp(5)/64 + 81*log(x)**4/256 + 27*exp(5)*log(x)/64 + (x**7*(-1236*exp(
5) + 36*exp(10)) + x**6*(-4*exp(15) - 90*exp(10) + 11540*exp(5)) + x**5*(-324*exp(10) - 40824*exp(5) + 12*exp(
15)) + x**4*(-4*exp(15) + 68100*exp(5) + 948*exp(10) + exp(20)) + x**3*(-55800*exp(5) - 288*exp(10)) + x**2*(-
156*exp(10) + 23604*exp(5)) + x*(-4980*exp(5) + 72*exp(10)) - 6*exp(10) + 416*exp(5))/(256*x**8 - 3072*x**7 +
14848*x**6 - 36864*x**5 + 49920*x**4 - 36864*x**3 + 14848*x**2 - 3072*x + 256) + (-3*x**9 + 27*x**8 - 378*x**7
+ 9*x**7*exp(5) - 81*x**6*exp(5) + 2727*x**6 - 9*x**5*exp(10) - 8730*x**5 + 630*x**5*exp(5) - 2592*x**4*exp(5
) + 12987*x**4 + 27*x**4*exp(10) - 9*x**3*exp(10) - 8643*x**3 + 4392*x**3*exp(5) + 3*x**3*exp(15) - 2538*x**2*
exp(5) + 2592*x**2 - 288*x + 531*x*exp(5) - 27*exp(5))*log(x)/(64*x**6 - 576*x**5 + 1920*x**4 - 2880*x**3 + 19
20*x**2 - 576*x + 64) + (27*x**6 - 162*x**5 - 54*x**4*exp(5) + 1161*x**4 - 5346*x**3 + 162*x**3*exp(5) - 54*x*
*2*exp(5) + 9531*x**2 + 27*x**2*exp(10) - 5184*x + 864)*log(x)**2/(128*x**4 - 768*x**3 + 1408*x**2 - 768*x + 1
28) + (-27*x**3 + 81*x**2 - 27*x + 27*x*exp(5))*log(x)**3/(64*x**2 - 192*x + 64)
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