3.32.4 \(\int \frac {-900000000-4800000000 x-9450000000 x^2-6900000000 x^3+1968750000 x^4+5400000000 x^5+1575000000 x^6-900000000 x^7-337500000 x^8-75000000 x^{10}[phone] x^{12}+e^{2 x} (200000000+2900000000 x+12050000000 x^2+21475000000 x^3+14375000000 x^4-5250000000 x^5-10800000000 x^6-150000000 x^7+4650000000 x^8+500000000 x^9-1450000000 x^{10}-325000000 x^{11}[phone] x^{12}[phone] x^{13})+e^{8 x} (-25000000 x^3-231250000 x^4-850000000 x^5-1525000000 x^6-1050000000 x^7+962500000 x^8+2800000000 x^9+2775000000 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13})+e^{4 x} (-300000000 x-3150000000 x^2-11775000000 x^3-19987500000 x^4-12150000000 x^5+8550000000 x^6+15750000000 x^7+3375000000 x^8-6300000000 x^9-3900000000 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13})+e^{6 x} (150000000 x^2+1425000000 x^3+5175000000 x^4+8850000000 x^5+5400000000 x^6-5250000000 x^7-11550000000 x^8-7200000000 x^9-150000000 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13})+(e^{6 x} (-300000000 x-3300000000 x^2-13050000000 x^3-23850000000 x^4-16200000000 x^5+12600000000 x^6+31500000000 x^7+20700000000 x^8+900000000 x^9-5700000000 x^{10}-2850000000 x^{11}-450000000 x^{12})+e^{4 x} (300000000+4500000000 x+19575000000 x^2+37050000000 x^3+27000000000 x^4-10800000000 x^5-28350000000 x^6-8100000000 x^7+10800000000 x^8+7500000000 x^9-225000000 x^{10}-1350000000 x^{11}-300000000 x^{12})+e^{8 x} (75000000 x^2+750000000 x^3+2900000000 x^4+5400000000 x^5+3850000000 x^6-3500000000 x^7-10500000000 x^8-10600000000 x^9-5725000000 x^{10}-1650000000 x^{11}-200000000 x^{12})+e^{2 x} (-1800000000-10000000000 x-20850000000 x^2-17150000000 x^3+1950000000 x^4+10800000000 x^5+2100000000 x^6-3900000000 x^7-900000000 x^8+1200000000 x^9+350000000 x^{10}-150000000 x^{11}-50000000 x^{12})) \log (x)+(e^{4 x} (-1350000000-7800000000 x-17062500000 x^2-14850000000 x^3+2250000000 x^4+12600000000 x^5+4725000000 x^6-4500000000 x^7-3600000000 x^8+637500000 x^{10}[phone] x^{11})+e^{8 x} (-75000000 x-862500000 x^2-3600000000 x^3-7050000000 x^4-5250000000 x^5+4725000000 x^6+14700000000 x^7+15150000000 x^8+8325000000 x^9+2437500000 x^{10}[phone] x^{11})+e^{6 x} (150000000+2325000000 x+10575000000 x^2+21150000000 x^3+16200000000 x^4-9450000000 x^5-28350000000 x^6-19800000000 x^7-1350000000 x^8+5325000000 x^9+2775000000 x^{10}[phone] x^{11})) \log ^2(x)+(e^{8 x} (25000000+400000000 x+1900000000 x^2+4000000000 x^3+3150000000 x^4-2800000000 x^5-9100000000 x^6-9600000000 x^7-5375000000 x^8-1600000000 x^9-200000000 x^{10})+e^{6 x} (-450000000-2700000000 x-6150000000 x^2-5400000000 x^3+2100000000 x^4+8400000000 x^5+6300000000 x^6+600000000 x^7-1650000000 x^8-900000000 x^9-150000000 x^{10})) \log ^3(x)+e^{8 x} (-56250000-350000000 x-825000000 x^2-700000000 x^3+612500000 x^4+2100000000 x^5+2275000000 x^6+1300000000 x^7+393750000 x^8+50000000 x^9) \log ^4(x)}{x^{10}} \, dx\)

Optimal. Leaf size=32 \[ \frac {16 \left (5+\frac {5}{x}\right )^8 \left (-2+x-e^{2 x} (-x+\log (x))\right )^4}{x} \]

________________________________________________________________________________________

Rubi [F]  time = 150.98, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}

result too large to display

Verification is not applicable to the result.

[In]

Int[(-900000000 - 4800000000*x - 9450000000*x^2 - 6900000000*x^3 + 1968750000*x^4 + 5400000000*x^5 + 157500000
0*x^6 - 900000000*x^7 - 337500000*x^8 - 75000000*x^10 + 18750000*x^12 + E^(2*x)*(200000000 + 2900000000*x + 12
050000000*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 10800000000*x^6 - 150000000*x^7 + 4650000
000*x^8 + 500000000*x^9 - 1450000000*x^10 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13) + E^(8*x)*(-25000
000*x^3 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^7 + 962500000*x^8 + 2800000000*x^9 + 2
775000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + E^(4*x)*(-300000000*x - 3150000000*x^2 -
11775000000*x^3 - 19987500000*x^4 - 12150000000*x^5 + 8550000000*x^6 + 15750000000*x^7 + 3375000000*x^8 - 6300
000000*x^9 - 3900000000*x^10 + 225000000*x^11 + 712500000*x^12 + 150000000*x^13) + E^(6*x)*(150000000*x^2 + 14
25000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000*x^7 - 11550000000*x^8 - 720000000
0*x^9 - 150000000*x^10 + 2025000000*x^11 + 975000000*x^12 + 150000000*x^13) + (E^(6*x)*(-300000000*x - 3300000
000*x^2 - 13050000000*x^3 - 23850000000*x^4 - 16200000000*x^5 + 12600000000*x^6 + 31500000000*x^7 + 2070000000
0*x^8 + 900000000*x^9 - 5700000000*x^10 - 2850000000*x^11 - 450000000*x^12) + E^(4*x)*(300000000 + 4500000000*
x + 19575000000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 10800000000*x^5 - 28350000000*x^6 - 8100000000*x^7 +
10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*x^11 - 300000000*x^12) + E^(8*x)*(75000000*x^2
+ 750000000*x^3 + 2900000000*x^4 + 5400000000*x^5 + 3850000000*x^6 - 3500000000*x^7 - 10500000000*x^8 - 10600
000000*x^9 - 5725000000*x^10 - 1650000000*x^11 - 200000000*x^12) + E^(2*x)*(-1800000000 - 10000000000*x - 2085
0000000*x^2 - 17150000000*x^3 + 1950000000*x^4 + 10800000000*x^5 + 2100000000*x^6 - 3900000000*x^7 - 900000000
*x^8 + 1200000000*x^9 + 350000000*x^10 - 150000000*x^11 - 50000000*x^12))*Log[x] + (E^(4*x)*(-1350000000 - 780
0000000*x - 17062500000*x^2 - 14850000000*x^3 + 2250000000*x^4 + 12600000000*x^5 + 4725000000*x^6 - 4500000000
*x^7 - 3600000000*x^8 + 637500000*x^10 + 150000000*x^11) + E^(8*x)*(-75000000*x - 862500000*x^2 - 3600000000*x
^3 - 7050000000*x^4 - 5250000000*x^5 + 4725000000*x^6 + 14700000000*x^7 + 15150000000*x^8 + 8325000000*x^9 + 2
437500000*x^10 + 300000000*x^11) + E^(6*x)*(150000000 + 2325000000*x + 10575000000*x^2 + 21150000000*x^3 + 162
00000000*x^4 - 9450000000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000*x^9 + 27750000
00*x^10 + 450000000*x^11))*Log[x]^2 + (E^(8*x)*(25000000 + 400000000*x + 1900000000*x^2 + 4000000000*x^3 + 315
0000000*x^4 - 2800000000*x^5 - 9100000000*x^6 - 9600000000*x^7 - 5375000000*x^8 - 1600000000*x^9 - 200000000*x
^10) + E^(6*x)*(-450000000 - 2700000000*x - 6150000000*x^2 - 5400000000*x^3 + 2100000000*x^4 + 8400000000*x^5
+ 6300000000*x^6 + 600000000*x^7 - 1650000000*x^8 - 900000000*x^9 - 150000000*x^10))*Log[x]^3 + E^(8*x)*(-5625
0000 - 350000000*x - 825000000*x^2 - 700000000*x^3 + 612500000*x^4 + 2100000000*x^5 + 2275000000*x^6 + 1300000
000*x^7 + 393750000*x^8 + 50000000*x^9)*Log[x]^4)/x^10,x]

[Out]

-600000000*E^(2*x) - 900000000*E^(4*x) + 350000000*E^(8*x) + 100000000/x^9 - (100000000*E^(4*x))/(27*x^9) + 60
0000000/x^8 - (200000000*E^(2*x))/x^8 - (992187500*E^(4*x))/(27*x^8) + (4687500*E^(6*x))/x^8 + 1350000000/x^7
- (1300000000*E^(2*x))/x^7 - (23506250000*E^(4*x))/(1323*x^7) + (2671875000*E^(6*x))/(49*x^7) - (75000000*E^(8
*x))/(49*x^7) + 1150000000/x^6 - (3350000000*E^(2*x))/x^6 + (2278212500000*E^(4*x))/(3969*x^6) + (12909375000*
E^(6*x))/(49*x^6) - (3100000000*E^(8*x))/(147*x^6) - 393750000/x^5 - (3975000000*E^(2*x))/x^5 + (8156747500000
*E^(4*x))/(3969*x^5) + (43022250000*E^(6*x))/(49*x^5) - (21765250000*E^(8*x))/(147*x^5) - 1350000000/x^4 - (12
00000000*E^(2*x))/x^4 + (10976785000000*E^(4*x))/(3969*x^4) + (152444625000*E^(6*x))/(49*x^4) - (120915500000*
E^(8*x))/(147*x^4) - 525000000/x^3 + (2100000000*E^(2*x))/x^3 - (1778360000000*E^(4*x))/(11907*x^3) + (6716192
50000*E^(6*x))/(49*x^3) - (232271000000*E^(8*x))/(49*x^3) + 450000000/x^2 + (2100000000*E^(2*x))/x^2 - (108464
320000000*E^(4*x))/(11907*x^2) + (3804792750000*E^(6*x))/(49*x^2) - (5276032000000*E^(8*x))/(147*x^2) + 337500
000/x + (150000000*E^(2*x))/x - (691758805000000*E^(4*x))/(11907*x) + (42316126500000*E^(6*x))/(49*x) - (27287
174500000*E^(8*x))/(49*x) - 75000000*x - 200000000*E^(2*x)*x + 300000000*E^(6*x)*x + 175000000*E^(8*x)*x + 500
00000*E^(2*x)*x^2 + 150000000*E^(4*x)*x^2 + 150000000*E^(6*x)*x^2 + 50000000*E^(8*x)*x^2 + 6250000*x^3 + 25000
000*E^(2*x)*x^3 + 37500000*E^(4*x)*x^3 + 25000000*E^(6*x)*x^3 + 6250000*E^(8*x)*x^3 + (2691797863750000*ExpInt
egralEi[4*x])/11907 - (254206684000000*ExpIntegralEi[6*x])/49 + (218468436625000*ExpIntegralEi[8*x])/49 - (609
62800000000*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, 4*x])/189 + (97272360000000*x*HypergeometricPFQ[{1, 1, 1
}, {2, 2, 2}, 6*x])/7 - (359469760000000*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, 8*x])/21 - (22466860000000*
Log[-8*x]^2)/21 + (8106030000000*Log[-6*x]^2)/7 - (7620350000000*Log[-4*x]^2)/189 + 200000000*E^(2*x)*Log[x] +
18750000*E^(4*x)*Log[x] - 875000000*E^(6*x)*Log[x] - 690625000*E^(8*x)*Log[x] + (18081440000000*EulerGamma*Lo
g[x])/189 + (200000000*E^(2*x)*Log[x])/x^9 - (100000000*E^(4*x)*Log[x])/(3*x^9) + (1300000000*E^(2*x)*Log[x])/
x^8 - (1737500000*E^(4*x)*Log[x])/(3*x^8) + (37500000*E^(6*x)*Log[x])/x^8 + (3350000000*E^(2*x)*Log[x])/x^7 -
(65675000000*E^(4*x)*Log[x])/(21*x^7) + (3525000000*E^(6*x)*Log[x])/(7*x^7) - (75000000*E^(8*x)*Log[x])/(7*x^7
) + (3975000000*E^(2*x)*Log[x])/x^6 - (520375000000*E^(4*x)*Log[x])/(63*x^6) + (18750000000*E^(6*x)*Log[x])/(7
*x^6) - (975000000*E^(8*x)*Log[x])/(7*x^6) + (1200000000*E^(2*x)*Log[x])/x^5 - (756500000000*E^(4*x)*Log[x])/(
63*x^5) + (55890000000*E^(6*x)*Log[x])/(7*x^5) - (5620000000*E^(8*x)*Log[x])/(7*x^5) - (2100000000*E^(2*x)*Log
[x])/x^4 - (586400000000*E^(4*x)*Log[x])/(63*x^4) + (112185000000*E^(6*x)*Log[x])/(7*x^4) - (20690000000*E^(8*
x)*Log[x])/(7*x^4) - (2100000000*E^(2*x)*Log[x])/x^3 - (559550000000*E^(4*x)*Log[x])/(189*x^3) + (194970000000
*E^(6*x)*Log[x])/(7*x^3) - (192470000000*E^(8*x)*Log[x])/(21*x^3) - (150000000*E^(2*x)*Log[x])/x^2 - (35365000
0000*E^(4*x)*Log[x])/(189*x^2) + (474660000000*E^(6*x)*Log[x])/(7*x^2) - (733130000000*E^(8*x)*Log[x])/(21*x^2
) + (600000000*E^(2*x)*Log[x])/x - (3455800000000*E^(4*x)*Log[x])/(189*x) + (2703060000000*E^(6*x)*Log[x])/(7*
x) - (5644540000000*E^(8*x)*Log[x])/(21*x) - 50000000*E^(2*x)*x*Log[x] - 300000000*E^(4*x)*x*Log[x] - 45000000
0*E^(6*x)*x*Log[x] - 200000000*E^(8*x)*x*Log[x] - 25000000*E^(2*x)*x^2*Log[x] - 75000000*E^(4*x)*x^2*Log[x] -
75000000*E^(6*x)*x^2*Log[x] - 25000000*E^(8*x)*x^2*Log[x] + (15240700000000*ExpIntegralEi[4*x]*Log[x])/189 - (
15240700000000*(ExpIntegralE[1, -4*x] + ExpIntegralEi[4*x])*Log[x])/189 - (16212060000000*ExpIntegralEi[6*x]*L
og[x])/7 + (16212060000000*(ExpIntegralE[1, -6*x] + ExpIntegralEi[6*x])*Log[x])/7 + (44933720000000*ExpIntegra
lEi[8*x]*Log[x])/21 - (44933720000000*(ExpIntegralE[1, -8*x] + ExpIntegralEi[8*x])*Log[x])/21 + 637500000*Defe
r[Int][E^(4*x)*Log[x]^2, x] + 2775000000*Defer[Int][E^(6*x)*Log[x]^2, x] + 2437500000*Defer[Int][E^(8*x)*Log[x
]^2, x] - 1350000000*Defer[Int][(E^(4*x)*Log[x]^2)/x^10, x] + 150000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^10, x]
- 7800000000*Defer[Int][(E^(4*x)*Log[x]^2)/x^9, x] + 2325000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^9, x] - 75000
000*Defer[Int][(E^(8*x)*Log[x]^2)/x^9, x] - 17062500000*Defer[Int][(E^(4*x)*Log[x]^2)/x^8, x] + 10575000000*De
fer[Int][(E^(6*x)*Log[x]^2)/x^8, x] - 862500000*Defer[Int][(E^(8*x)*Log[x]^2)/x^8, x] - 14850000000*Defer[Int]
[(E^(4*x)*Log[x]^2)/x^7, x] + 21150000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^7, x] - 3600000000*Defer[Int][(E^(8*
x)*Log[x]^2)/x^7, x] + 2250000000*Defer[Int][(E^(4*x)*Log[x]^2)/x^6, x] + 16200000000*Defer[Int][(E^(6*x)*Log[
x]^2)/x^6, x] - 7050000000*Defer[Int][(E^(8*x)*Log[x]^2)/x^6, x] + 12600000000*Defer[Int][(E^(4*x)*Log[x]^2)/x
^5, x] - 9450000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^5, x] - 5250000000*Defer[Int][(E^(8*x)*Log[x]^2)/x^5, x] +
4725000000*Defer[Int][(E^(4*x)*Log[x]^2)/x^4, x] - 28350000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^4, x] + 472500
0000*Defer[Int][(E^(8*x)*Log[x]^2)/x^4, x] - 4500000000*Defer[Int][(E^(4*x)*Log[x]^2)/x^3, x] - 19800000000*De
fer[Int][(E^(6*x)*Log[x]^2)/x^3, x] + 14700000000*Defer[Int][(E^(8*x)*Log[x]^2)/x^3, x] - 3600000000*Defer[Int
][(E^(4*x)*Log[x]^2)/x^2, x] - 1350000000*Defer[Int][(E^(6*x)*Log[x]^2)/x^2, x] + 15150000000*Defer[Int][(E^(8
*x)*Log[x]^2)/x^2, x] + 5325000000*Defer[Int][(E^(6*x)*Log[x]^2)/x, x] + 8325000000*Defer[Int][(E^(8*x)*Log[x]
^2)/x, x] + 150000000*Defer[Int][E^(4*x)*x*Log[x]^2, x] + 450000000*Defer[Int][E^(6*x)*x*Log[x]^2, x] + 300000
000*Defer[Int][E^(8*x)*x*Log[x]^2, x] - 150000000*Defer[Int][E^(6*x)*Log[x]^3, x] - 200000000*Defer[Int][E^(8*
x)*Log[x]^3, x] - 450000000*Defer[Int][(E^(6*x)*Log[x]^3)/x^10, x] + 25000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^
10, x] - 2700000000*Defer[Int][(E^(6*x)*Log[x]^3)/x^9, x] + 400000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^9, x] -
6150000000*Defer[Int][(E^(6*x)*Log[x]^3)/x^8, x] + 1900000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^8, x] - 54000000
00*Defer[Int][(E^(6*x)*Log[x]^3)/x^7, x] + 4000000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^7, x] + 2100000000*Defer
[Int][(E^(6*x)*Log[x]^3)/x^6, x] + 3150000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^6, x] + 8400000000*Defer[Int][(E
^(6*x)*Log[x]^3)/x^5, x] - 2800000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^5, x] + 6300000000*Defer[Int][(E^(6*x)*L
og[x]^3)/x^4, x] - 9100000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^4, x] + 600000000*Defer[Int][(E^(6*x)*Log[x]^3)/
x^3, x] - 9600000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^3, x] - 1650000000*Defer[Int][(E^(6*x)*Log[x]^3)/x^2, x]
- 5375000000*Defer[Int][(E^(8*x)*Log[x]^3)/x^2, x] - 900000000*Defer[Int][(E^(6*x)*Log[x]^3)/x, x] - 160000000
0*Defer[Int][(E^(8*x)*Log[x]^3)/x, x] - 56250000*Defer[Int][(E^(8*x)*Log[x]^4)/x^10, x] - 350000000*Defer[Int]
[(E^(8*x)*Log[x]^4)/x^9, x] - 825000000*Defer[Int][(E^(8*x)*Log[x]^4)/x^8, x] - 700000000*Defer[Int][(E^(8*x)*
Log[x]^4)/x^7, x] + 612500000*Defer[Int][(E^(8*x)*Log[x]^4)/x^6, x] + 2100000000*Defer[Int][(E^(8*x)*Log[x]^4)
/x^5, x] + 2275000000*Defer[Int][(E^(8*x)*Log[x]^4)/x^4, x] + 1300000000*Defer[Int][(E^(8*x)*Log[x]^4)/x^3, x]
+ 393750000*Defer[Int][(E^(8*x)*Log[x]^4)/x^2, x] + 50000000*Defer[Int][(E^(8*x)*Log[x]^4)/x, x]

Rubi steps

Aborted

________________________________________________________________________________________

Mathematica [B]  time = 0.48, size = 218, normalized size = 6.81 \begin {gather*} \frac {6250000 \left (16+96 x+216 x^2+184 x^3-63 x^4-216 x^5-84 x^6+72 x^7+54 x^8-12 x^{10}+x^{12}+4 e^{2 x} (-2+x)^3 x (1+x)^8+6 e^{4 x} (-2+x)^2 x^2 (1+x)^8+4 e^{6 x} (-2+x) x^3 (1+x)^8+e^{8 x} x^4 (1+x)^8-4 e^{2 x} (1+x)^8 \left (-2+x+e^{2 x} x\right )^3 \log (x)+6 e^{4 x} (1+x)^8 \left (-2+x+e^{2 x} x\right )^2 \log ^2(x)-4 e^{6 x} (1+x)^8 \left (-2+x+e^{2 x} x\right ) \log ^3(x)+e^{8 x} (1+x)^8 \log ^4(x)\right )}{x^9} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-900000000 - 4800000000*x - 9450000000*x^2 - 6900000000*x^3 + 1968750000*x^4 + 5400000000*x^5 + 157
5000000*x^6 - 900000000*x^7 - 337500000*x^8 - 75000000*x^10 + 18750000*x^12 + E^(2*x)*(200000000 + 2900000000*
x + 12050000000*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 10800000000*x^6 - 150000000*x^7 + 4
650000000*x^8 + 500000000*x^9 - 1450000000*x^10 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13) + E^(8*x)*(
-25000000*x^3 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^7 + 962500000*x^8 + 2800000000*x
^9 + 2775000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + E^(4*x)*(-300000000*x - 3150000000*
x^2 - 11775000000*x^3 - 19987500000*x^4 - 12150000000*x^5 + 8550000000*x^6 + 15750000000*x^7 + 3375000000*x^8
- 6300000000*x^9 - 3900000000*x^10 + 225000000*x^11 + 712500000*x^12 + 150000000*x^13) + E^(6*x)*(150000000*x^
2 + 1425000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000*x^7 - 11550000000*x^8 - 720
0000000*x^9 - 150000000*x^10 + 2025000000*x^11 + 975000000*x^12 + 150000000*x^13) + (E^(6*x)*(-300000000*x - 3
300000000*x^2 - 13050000000*x^3 - 23850000000*x^4 - 16200000000*x^5 + 12600000000*x^6 + 31500000000*x^7 + 2070
0000000*x^8 + 900000000*x^9 - 5700000000*x^10 - 2850000000*x^11 - 450000000*x^12) + E^(4*x)*(300000000 + 45000
00000*x + 19575000000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 10800000000*x^5 - 28350000000*x^6 - 8100000000
*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*x^11 - 300000000*x^12) + E^(8*x)*(750000
00*x^2 + 750000000*x^3 + 2900000000*x^4 + 5400000000*x^5 + 3850000000*x^6 - 3500000000*x^7 - 10500000000*x^8 -
10600000000*x^9 - 5725000000*x^10 - 1650000000*x^11 - 200000000*x^12) + E^(2*x)*(-1800000000 - 10000000000*x
- 20850000000*x^2 - 17150000000*x^3 + 1950000000*x^4 + 10800000000*x^5 + 2100000000*x^6 - 3900000000*x^7 - 900
000000*x^8 + 1200000000*x^9 + 350000000*x^10 - 150000000*x^11 - 50000000*x^12))*Log[x] + (E^(4*x)*(-1350000000
- 7800000000*x - 17062500000*x^2 - 14850000000*x^3 + 2250000000*x^4 + 12600000000*x^5 + 4725000000*x^6 - 4500
000000*x^7 - 3600000000*x^8 + 637500000*x^10 + 150000000*x^11) + E^(8*x)*(-75000000*x - 862500000*x^2 - 360000
0000*x^3 - 7050000000*x^4 - 5250000000*x^5 + 4725000000*x^6 + 14700000000*x^7 + 15150000000*x^8 + 8325000000*x
^9 + 2437500000*x^10 + 300000000*x^11) + E^(6*x)*(150000000 + 2325000000*x + 10575000000*x^2 + 21150000000*x^3
+ 16200000000*x^4 - 9450000000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000*x^9 + 27
75000000*x^10 + 450000000*x^11))*Log[x]^2 + (E^(8*x)*(25000000 + 400000000*x + 1900000000*x^2 + 4000000000*x^3
+ 3150000000*x^4 - 2800000000*x^5 - 9100000000*x^6 - 9600000000*x^7 - 5375000000*x^8 - 1600000000*x^9 - 20000
0000*x^10) + E^(6*x)*(-450000000 - 2700000000*x - 6150000000*x^2 - 5400000000*x^3 + 2100000000*x^4 + 840000000
0*x^5 + 6300000000*x^6 + 600000000*x^7 - 1650000000*x^8 - 900000000*x^9 - 150000000*x^10))*Log[x]^3 + E^(8*x)*
(-56250000 - 350000000*x - 825000000*x^2 - 700000000*x^3 + 612500000*x^4 + 2100000000*x^5 + 2275000000*x^6 + 1
300000000*x^7 + 393750000*x^8 + 50000000*x^9)*Log[x]^4)/x^10,x]

[Out]

(6250000*(16 + 96*x + 216*x^2 + 184*x^3 - 63*x^4 - 216*x^5 - 84*x^6 + 72*x^7 + 54*x^8 - 12*x^10 + x^12 + 4*E^(
2*x)*(-2 + x)^3*x*(1 + x)^8 + 6*E^(4*x)*(-2 + x)^2*x^2*(1 + x)^8 + 4*E^(6*x)*(-2 + x)*x^3*(1 + x)^8 + E^(8*x)*
x^4*(1 + x)^8 - 4*E^(2*x)*(1 + x)^8*(-2 + x + E^(2*x)*x)^3*Log[x] + 6*E^(4*x)*(1 + x)^8*(-2 + x + E^(2*x)*x)^2
*Log[x]^2 - 4*E^(6*x)*(1 + x)^8*(-2 + x + E^(2*x)*x)*Log[x]^3 + E^(8*x)*(1 + x)^8*Log[x]^4))/x^9

________________________________________________________________________________________

fricas [B]  time = 0.90, size = 758, normalized size = 23.69 \begin {gather*} \frac {6250000 \, {\left (x^{12} - 12 \, x^{10} + 54 \, x^{8} + 72 \, x^{7} - 84 \, x^{6} + {\left (x^{8} + 8 \, x^{7} + 28 \, x^{6} + 56 \, x^{5} + 70 \, x^{4} + 56 \, x^{3} + 28 \, x^{2} + 8 \, x + 1\right )} e^{\left (8 \, x\right )} \log \relax (x)^{4} - 216 \, x^{5} - 63 \, x^{4} - 4 \, {\left ({\left (x^{9} + 8 \, x^{8} + 28 \, x^{7} + 56 \, x^{6} + 70 \, x^{5} + 56 \, x^{4} + 28 \, x^{3} + 8 \, x^{2} + x\right )} e^{\left (8 \, x\right )} + {\left (x^{9} + 6 \, x^{8} + 12 \, x^{7} - 42 \, x^{5} - 84 \, x^{4} - 84 \, x^{3} - 48 \, x^{2} - 15 \, x - 2\right )} e^{\left (6 \, x\right )}\right )} \log \relax (x)^{3} + 184 \, x^{3} + 6 \, {\left ({\left (x^{10} + 8 \, x^{9} + 28 \, x^{8} + 56 \, x^{7} + 70 \, x^{6} + 56 \, x^{5} + 28 \, x^{4} + 8 \, x^{3} + x^{2}\right )} e^{\left (8 \, x\right )} + 2 \, {\left (x^{10} + 6 \, x^{9} + 12 \, x^{8} - 42 \, x^{6} - 84 \, x^{5} - 84 \, x^{4} - 48 \, x^{3} - 15 \, x^{2} - 2 \, x\right )} e^{\left (6 \, x\right )} + {\left (x^{10} + 4 \, x^{9} - 24 \, x^{7} - 42 \, x^{6} + 84 \, x^{4} + 120 \, x^{3} + 81 \, x^{2} + 28 \, x + 4\right )} e^{\left (4 \, x\right )}\right )} \log \relax (x)^{2} + 216 \, x^{2} + {\left (x^{12} + 8 \, x^{11} + 28 \, x^{10} + 56 \, x^{9} + 70 \, x^{8} + 56 \, x^{7} + 28 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{\left (8 \, x\right )} + 4 \, {\left (x^{12} + 6 \, x^{11} + 12 \, x^{10} - 42 \, x^{8} - 84 \, x^{7} - 84 \, x^{6} - 48 \, x^{5} - 15 \, x^{4} - 2 \, x^{3}\right )} e^{\left (6 \, x\right )} + 6 \, {\left (x^{12} + 4 \, x^{11} - 24 \, x^{9} - 42 \, x^{8} + 84 \, x^{6} + 120 \, x^{5} + 81 \, x^{4} + 28 \, x^{3} + 4 \, x^{2}\right )} e^{\left (4 \, x\right )} + 4 \, {\left (x^{12} + 2 \, x^{11} - 8 \, x^{10} - 24 \, x^{9} + 6 \, x^{8} + 84 \, x^{7} + 84 \, x^{6} - 48 \, x^{5} - 159 \, x^{4} - 134 \, x^{3} - 52 \, x^{2} - 8 \, x\right )} e^{\left (2 \, x\right )} - 4 \, {\left ({\left (x^{11} + 8 \, x^{10} + 28 \, x^{9} + 56 \, x^{8} + 70 \, x^{7} + 56 \, x^{6} + 28 \, x^{5} + 8 \, x^{4} + x^{3}\right )} e^{\left (8 \, x\right )} + 3 \, {\left (x^{11} + 6 \, x^{10} + 12 \, x^{9} - 42 \, x^{7} - 84 \, x^{6} - 84 \, x^{5} - 48 \, x^{4} - 15 \, x^{3} - 2 \, x^{2}\right )} e^{\left (6 \, x\right )} + 3 \, {\left (x^{11} + 4 \, x^{10} - 24 \, x^{8} - 42 \, x^{7} + 84 \, x^{5} + 120 \, x^{4} + 81 \, x^{3} + 28 \, x^{2} + 4 \, x\right )} e^{\left (4 \, x\right )} + {\left (x^{11} + 2 \, x^{10} - 8 \, x^{9} - 24 \, x^{8} + 6 \, x^{7} + 84 \, x^{6} + 84 \, x^{5} - 48 \, x^{4} - 159 \, x^{3} - 134 \, x^{2} - 52 \, x - 8\right )} e^{\left (2 \, x\right )}\right )} \log \relax (x) + 96 \, x + 16\right )}}{x^{9}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+2100000000*x^5+612500000*x^4-700000000*x^
3-825000000*x^2-350000000*x-56250000)*exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-960000
0000*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000000*x^2+400000000*x+25000000)*exp(
x)^8+(-150000000*x^10-900000000*x^9-1650000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-
5400000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300000000*x^11+2437500000*x^10+8325
000000*x^9+15150000000*x^8+14700000000*x^7+4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-8625000
00*x^2-75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-1350000000*x^8-19800000000*x^7-2835
0000000*x^6-9450000000*x^5+16200000000*x^4+21150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(1
50000000*x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000000*x^5+2250000000*x^4-14850
000000*x^3-17062500000*x^2-7800000000*x-1350000000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-57250
00000*x^10-10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000*x^5+2900000000*x^4+7500000
00*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+3
1500000000*x^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000000*x^2-300000000*x)*exp
(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-2835000000
0*x^6-10800000000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+300000000)*exp(x)^4+(-50000
000*x^12-150000000*x^11+350000000*x^10+1200000000*x^9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*
x^5+1950000000*x^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log(x)+(50000000*x^13+4
18750000*x^12+1475000000*x^11+2775000000*x^10+2800000000*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-85000
0000*x^5-231250000*x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11-150000000*x^10-72
00000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000
000*x^2)*exp(x)^6+(150000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9+3375000000*x^8+
15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000*x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp
(x)^4+(50000000*x^13+175000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8-150000000*x^7-
10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^
2+18750000*x^12-75000000*x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000*x^4-6900000
000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorithm="fricas")

[Out]

6250000*(x^12 - 12*x^10 + 54*x^8 + 72*x^7 - 84*x^6 + (x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2
+ 8*x + 1)*e^(8*x)*log(x)^4 - 216*x^5 - 63*x^4 - 4*((x^9 + 8*x^8 + 28*x^7 + 56*x^6 + 70*x^5 + 56*x^4 + 28*x^3
+ 8*x^2 + x)*e^(8*x) + (x^9 + 6*x^8 + 12*x^7 - 42*x^5 - 84*x^4 - 84*x^3 - 48*x^2 - 15*x - 2)*e^(6*x))*log(x)^
3 + 184*x^3 + 6*((x^10 + 8*x^9 + 28*x^8 + 56*x^7 + 70*x^6 + 56*x^5 + 28*x^4 + 8*x^3 + x^2)*e^(8*x) + 2*(x^10 +
6*x^9 + 12*x^8 - 42*x^6 - 84*x^5 - 84*x^4 - 48*x^3 - 15*x^2 - 2*x)*e^(6*x) + (x^10 + 4*x^9 - 24*x^7 - 42*x^6
+ 84*x^4 + 120*x^3 + 81*x^2 + 28*x + 4)*e^(4*x))*log(x)^2 + 216*x^2 + (x^12 + 8*x^11 + 28*x^10 + 56*x^9 + 70*x
^8 + 56*x^7 + 28*x^6 + 8*x^5 + x^4)*e^(8*x) + 4*(x^12 + 6*x^11 + 12*x^10 - 42*x^8 - 84*x^7 - 84*x^6 - 48*x^5 -
15*x^4 - 2*x^3)*e^(6*x) + 6*(x^12 + 4*x^11 - 24*x^9 - 42*x^8 + 84*x^6 + 120*x^5 + 81*x^4 + 28*x^3 + 4*x^2)*e^
(4*x) + 4*(x^12 + 2*x^11 - 8*x^10 - 24*x^9 + 6*x^8 + 84*x^7 + 84*x^6 - 48*x^5 - 159*x^4 - 134*x^3 - 52*x^2 - 8
*x)*e^(2*x) - 4*((x^11 + 8*x^10 + 28*x^9 + 56*x^8 + 70*x^7 + 56*x^6 + 28*x^5 + 8*x^4 + x^3)*e^(8*x) + 3*(x^11
+ 6*x^10 + 12*x^9 - 42*x^7 - 84*x^6 - 84*x^5 - 48*x^4 - 15*x^3 - 2*x^2)*e^(6*x) + 3*(x^11 + 4*x^10 - 24*x^8 -
42*x^7 + 84*x^5 + 120*x^4 + 81*x^3 + 28*x^2 + 4*x)*e^(4*x) + (x^11 + 2*x^10 - 8*x^9 - 24*x^8 + 6*x^7 + 84*x^6
+ 84*x^5 - 48*x^4 - 159*x^3 - 134*x^2 - 52*x - 8)*e^(2*x))*log(x) + 96*x + 16)/x^9

________________________________________________________________________________________

giac [B]  time = 0.45, size = 1503, normalized size = 46.97 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+2100000000*x^5+612500000*x^4-700000000*x^
3-825000000*x^2-350000000*x-56250000)*exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-960000
0000*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000000*x^2+400000000*x+25000000)*exp(
x)^8+(-150000000*x^10-900000000*x^9-1650000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-
5400000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300000000*x^11+2437500000*x^10+8325
000000*x^9+15150000000*x^8+14700000000*x^7+4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-8625000
00*x^2-75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-1350000000*x^8-19800000000*x^7-2835
0000000*x^6-9450000000*x^5+16200000000*x^4+21150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(1
50000000*x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000000*x^5+2250000000*x^4-14850
000000*x^3-17062500000*x^2-7800000000*x-1350000000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-57250
00000*x^10-10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000*x^5+2900000000*x^4+7500000
00*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+3
1500000000*x^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000000*x^2-300000000*x)*exp
(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-2835000000
0*x^6-10800000000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+300000000)*exp(x)^4+(-50000
000*x^12-150000000*x^11+350000000*x^10+1200000000*x^9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*
x^5+1950000000*x^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log(x)+(50000000*x^13+4
18750000*x^12+1475000000*x^11+2775000000*x^10+2800000000*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-85000
0000*x^5-231250000*x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11-150000000*x^10-72
00000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000
000*x^2)*exp(x)^6+(150000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9+3375000000*x^8+
15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000*x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp
(x)^4+(50000000*x^13+175000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8-150000000*x^7-
10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^
2+18750000*x^12-75000000*x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000*x^4-6900000
000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorithm="giac")

[Out]

6250000*(x^12*e^(8*x) + 4*x^12*e^(6*x) + 6*x^12*e^(4*x) + 4*x^12*e^(2*x) - 4*x^11*e^(8*x)*log(x) - 12*x^11*e^(
6*x)*log(x) - 12*x^11*e^(4*x)*log(x) - 4*x^11*e^(2*x)*log(x) + 6*x^10*e^(8*x)*log(x)^2 + 12*x^10*e^(6*x)*log(x
)^2 + 6*x^10*e^(4*x)*log(x)^2 - 4*x^9*e^(8*x)*log(x)^3 - 4*x^9*e^(6*x)*log(x)^3 + x^8*e^(8*x)*log(x)^4 + x^12
+ 8*x^11*e^(8*x) + 24*x^11*e^(6*x) + 24*x^11*e^(4*x) + 8*x^11*e^(2*x) - 32*x^10*e^(8*x)*log(x) - 72*x^10*e^(6*
x)*log(x) - 48*x^10*e^(4*x)*log(x) - 8*x^10*e^(2*x)*log(x) + 48*x^9*e^(8*x)*log(x)^2 + 72*x^9*e^(6*x)*log(x)^2
+ 24*x^9*e^(4*x)*log(x)^2 - 32*x^8*e^(8*x)*log(x)^3 - 24*x^8*e^(6*x)*log(x)^3 + 8*x^7*e^(8*x)*log(x)^4 + 28*x
^10*e^(8*x) + 48*x^10*e^(6*x) - 32*x^10*e^(2*x) - 112*x^9*e^(8*x)*log(x) - 144*x^9*e^(6*x)*log(x) + 32*x^9*e^(
2*x)*log(x) + 168*x^8*e^(8*x)*log(x)^2 + 144*x^8*e^(6*x)*log(x)^2 - 112*x^7*e^(8*x)*log(x)^3 - 48*x^7*e^(6*x)*
log(x)^3 + 28*x^6*e^(8*x)*log(x)^4 - 12*x^10 + 56*x^9*e^(8*x) - 144*x^9*e^(4*x) - 96*x^9*e^(2*x) - 224*x^8*e^(
8*x)*log(x) + 288*x^8*e^(4*x)*log(x) + 96*x^8*e^(2*x)*log(x) + 336*x^7*e^(8*x)*log(x)^2 - 144*x^7*e^(4*x)*log(
x)^2 - 224*x^6*e^(8*x)*log(x)^3 + 56*x^5*e^(8*x)*log(x)^4 + 70*x^8*e^(8*x) - 168*x^8*e^(6*x) - 252*x^8*e^(4*x)
+ 24*x^8*e^(2*x) - 280*x^7*e^(8*x)*log(x) + 504*x^7*e^(6*x)*log(x) + 504*x^7*e^(4*x)*log(x) - 24*x^7*e^(2*x)*
log(x) + 420*x^6*e^(8*x)*log(x)^2 - 504*x^6*e^(6*x)*log(x)^2 - 252*x^6*e^(4*x)*log(x)^2 - 280*x^5*e^(8*x)*log(
x)^3 + 168*x^5*e^(6*x)*log(x)^3 + 70*x^4*e^(8*x)*log(x)^4 + 54*x^8 + 56*x^7*e^(8*x) - 336*x^7*e^(6*x) + 336*x^
7*e^(2*x) - 224*x^6*e^(8*x)*log(x) + 1008*x^6*e^(6*x)*log(x) - 336*x^6*e^(2*x)*log(x) + 336*x^5*e^(8*x)*log(x)
^2 - 1008*x^5*e^(6*x)*log(x)^2 - 224*x^4*e^(8*x)*log(x)^3 + 336*x^4*e^(6*x)*log(x)^3 + 56*x^3*e^(8*x)*log(x)^4
+ 72*x^7 + 28*x^6*e^(8*x) - 336*x^6*e^(6*x) + 504*x^6*e^(4*x) + 336*x^6*e^(2*x) - 112*x^5*e^(8*x)*log(x) + 10
08*x^5*e^(6*x)*log(x) - 1008*x^5*e^(4*x)*log(x) - 336*x^5*e^(2*x)*log(x) + 168*x^4*e^(8*x)*log(x)^2 - 1008*x^4
*e^(6*x)*log(x)^2 + 504*x^4*e^(4*x)*log(x)^2 - 112*x^3*e^(8*x)*log(x)^3 + 336*x^3*e^(6*x)*log(x)^3 + 28*x^2*e^
(8*x)*log(x)^4 - 84*x^6 + 8*x^5*e^(8*x) - 192*x^5*e^(6*x) + 720*x^5*e^(4*x) - 192*x^5*e^(2*x) - 32*x^4*e^(8*x)
*log(x) + 576*x^4*e^(6*x)*log(x) - 1440*x^4*e^(4*x)*log(x) + 192*x^4*e^(2*x)*log(x) + 48*x^3*e^(8*x)*log(x)^2
- 576*x^3*e^(6*x)*log(x)^2 + 720*x^3*e^(4*x)*log(x)^2 - 32*x^2*e^(8*x)*log(x)^3 + 192*x^2*e^(6*x)*log(x)^3 + 8
*x*e^(8*x)*log(x)^4 - 216*x^5 + x^4*e^(8*x) - 60*x^4*e^(6*x) + 486*x^4*e^(4*x) - 636*x^4*e^(2*x) - 4*x^3*e^(8*
x)*log(x) + 180*x^3*e^(6*x)*log(x) - 972*x^3*e^(4*x)*log(x) + 636*x^3*e^(2*x)*log(x) + 6*x^2*e^(8*x)*log(x)^2
- 180*x^2*e^(6*x)*log(x)^2 + 486*x^2*e^(4*x)*log(x)^2 - 4*x*e^(8*x)*log(x)^3 + 60*x*e^(6*x)*log(x)^3 + e^(8*x)
*log(x)^4 - 63*x^4 - 8*x^3*e^(6*x) + 168*x^3*e^(4*x) - 536*x^3*e^(2*x) + 24*x^2*e^(6*x)*log(x) - 336*x^2*e^(4*
x)*log(x) + 536*x^2*e^(2*x)*log(x) - 24*x*e^(6*x)*log(x)^2 + 168*x*e^(4*x)*log(x)^2 + 8*e^(6*x)*log(x)^3 + 184
*x^3 + 24*x^2*e^(4*x) - 208*x^2*e^(2*x) - 48*x*e^(4*x)*log(x) + 208*x*e^(2*x)*log(x) + 24*e^(4*x)*log(x)^2 + 2
16*x^2 - 32*x*e^(2*x) + 32*e^(2*x)*log(x) + 96*x + 16)/x^9

________________________________________________________________________________________

maple [B]  time = 0.42, size = 1093, normalized size = 34.16

method	result	size
risch	\(\frac {6250000 \left (x^{8}+8 x^{7}+28 x^{6}+56 x^{5}+70 x^{4}+56 x^{3}+28 x^{2}+8 x +1\right ) {\mathrm e}^{8 x} \ln \relax (x )^{4}}{x^{9}}-\frac {25000000 \,{\mathrm e}^{6 x} \left ({\mathrm e}^{2 x} x^{9}+8 \,{\mathrm e}^{2 x} x^{8}+x^{9}+28 \,{\mathrm e}^{2 x} x^{7}+6 x^{8}+56 x^{6} {\mathrm e}^{2 x}+12 x^{7}+70 x^{5} {\mathrm e}^{2 x}+56 \,{\mathrm e}^{2 x} x^{4}-42 x^{5}+28 \,{\mathrm e}^{2 x} x^{3}-84 x^{4}+8 \,{\mathrm e}^{2 x} x^{2}-84 x^{3}+x \,{\mathrm e}^{2 x}-48 x^{2}-15 x -2\right ) \ln \relax (x )^{3}}{x^{9}}+\frac {37500000 \,{\mathrm e}^{4 x} \left (4+28 x +56 \,{\mathrm e}^{4 x} x^{5}-168 \,{\mathrm e}^{2 x} x^{4}-24 x^{7}+x^{10}+4 x^{9}-42 x^{6}+84 x^{4}+120 x^{3}+81 x^{2}-96 \,{\mathrm e}^{2 x} x^{3}+8 x^{3} {\mathrm e}^{4 x}-168 x^{5} {\mathrm e}^{2 x}-30 \,{\mathrm e}^{2 x} x^{2}-4 x \,{\mathrm e}^{2 x}+28 x^{4} {\mathrm e}^{4 x}+x^{2} {\mathrm e}^{4 x}+{\mathrm e}^{4 x} x^{10}+2 \,{\mathrm e}^{2 x} x^{10}+8 \,{\mathrm e}^{4 x} x^{9}+12 \,{\mathrm e}^{2 x} x^{9}+28 \,{\mathrm e}^{4 x} x^{8}+24 \,{\mathrm e}^{2 x} x^{8}+56 \,{\mathrm e}^{4 x} x^{7}+70 \,{\mathrm e}^{4 x} x^{6}-84 x^{6} {\mathrm e}^{2 x}\right ) \ln \relax (x )^{2}}{x^{9}}-\frac {25000000 \,{\mathrm e}^{2 x} \left (-8-52 x +28 \,{\mathrm e}^{6 x} x^{5}-252 \,{\mathrm e}^{4 x} x^{5}+8 \,{\mathrm e}^{6 x} x^{4}+360 \,{\mathrm e}^{2 x} x^{4}+{\mathrm e}^{6 x} x^{3}+x^{11}+6 x^{7}-24 x^{8}+2 x^{10}-8 x^{9}+84 x^{6}+84 x^{5}-48 x^{4}-159 x^{3}-134 x^{2}+243 \,{\mathrm e}^{2 x} x^{3}-45 x^{3} {\mathrm e}^{4 x}+252 x^{5} {\mathrm e}^{2 x}+84 \,{\mathrm e}^{2 x} x^{2}+12 x \,{\mathrm e}^{2 x}-144 x^{4} {\mathrm e}^{4 x}-6 x^{2} {\mathrm e}^{4 x}+{\mathrm e}^{6 x} x^{11}+3 \,{\mathrm e}^{4 x} x^{11}+3 \,{\mathrm e}^{2 x} x^{11}+8 \,{\mathrm e}^{6 x} x^{10}+18 \,{\mathrm e}^{4 x} x^{10}+12 \,{\mathrm e}^{2 x} x^{10}+28 \,{\mathrm e}^{6 x} x^{9}+36 \,{\mathrm e}^{4 x} x^{9}+56 \,{\mathrm e}^{6 x} x^{8}-72 \,{\mathrm e}^{2 x} x^{8}+70 \,{\mathrm e}^{6 x} x^{7}-126 \,{\mathrm e}^{4 x} x^{7}-126 \,{\mathrm e}^{2 x} x^{7}+56 \,{\mathrm e}^{6 x} x^{6}-252 \,{\mathrm e}^{4 x} x^{6}\right ) \ln \relax (x )}{x^{9}}+\frac {100000000+600000000 x [phone] \,{\mathrm e}^{8 x} x^{5}-1200000000 \,{\mathrm e}^{6 x} x^{5}[phone] \,{\mathrm e}^{4 x} x^{5}+6250000 \,{\mathrm e}^{8 x} x^{4}-375000000 \,{\mathrm e}^{6 x} x^{4}-3975000000 \,{\mathrm e}^{2 x} x^{4}-50000000 \,{\mathrm e}^{6 x} x^{3}+6250000 x^{12}[phone] x^{7}[phone] x^{8}-75000000 x^{10}-525000000 x^{6}-1350000000 x^{5}-393750000 x^{4}[phone] x^{3}[phone] x^{2}-3350000000 \,{\mathrm e}^{2 x} x^{3}[phone] x^{3} {\mathrm e}^{4 x}-1200000000 x^{5} {\mathrm e}^{2 x}-1300000000 \,{\mathrm e}^{2 x} x^{2}-200000000 x \,{\mathrm e}^{2 x}[phone] x^{4} {\mathrm e}^{4 x}[phone] x^{2} {\mathrm e}^{4 x}+6250000 \,{\mathrm e}^{8 x} x^{12}[phone] \,{\mathrm e}^{6 x} x^{12}[phone] \,{\mathrm e}^{4 x} x^{12}[phone] \,{\mathrm e}^{2 x} x^{12}[phone] \,{\mathrm e}^{8 x} x^{11}[phone] \,{\mathrm e}^{6 x} x^{11}[phone] \,{\mathrm e}^{4 x} x^{11}[phone] \,{\mathrm e}^{2 x} x^{11}[phone] \,{\mathrm e}^{8 x} x^{10}[phone] \,{\mathrm e}^{6 x} x^{10}-200000000 \,{\mathrm e}^{2 x} x^{10}[phone] \,{\mathrm e}^{8 x} x^{9}-900000000 \,{\mathrm e}^{4 x} x^{9}-600000000 \,{\mathrm e}^{2 x} x^{9}[phone] \,{\mathrm e}^{8 x} x^{8}-1050000000 \,{\mathrm e}^{6 x} x^{8}-1575000000 \,{\mathrm e}^{4 x} x^{8}[phone] \,{\mathrm e}^{2 x} x^{8}[phone] \,{\mathrm e}^{8 x} x^{7}-2100000000 \,{\mathrm e}^{6 x} x^{7}[phone] \,{\mathrm e}^{2 x} x^{7}[phone] \,{\mathrm e}^{8 x} x^{6}-2100000000 \,{\mathrm e}^{6 x} x^{6}[phone] \,{\mathrm e}^{4 x} x^{6}[phone] x^{6} {\mathrm e}^{2 x}}{x^{9}}\)	\(1093\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+2100000000*x^5+612500000*x^4-700000000*x^3-8250
00000*x^2-350000000*x-56250000)*exp(x)^8*ln(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-9600000000*x^
7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000000*x^2+400000000*x+25000000)*exp(x)^8+(-
150000000*x^10-900000000*x^9-1650000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-5400000
000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*ln(x)^3+((300000000*x^11+2437500000*x^10+8325000000*x
^9+15150000000*x^8+14700000000*x^7+4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-862500000*x^2-7
5000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-1350000000*x^8-19800000000*x^7-28350000000*
x^6-9450000000*x^5+16200000000*x^4+21150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(150000000
*x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000000*x^5+2250000000*x^4-14850000000*x
^3-17062500000*x^2-7800000000*x-1350000000)*exp(x)^4)*ln(x)^2+((-200000000*x^12-1650000000*x^11-5725000000*x^1
0-10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000*x^5+2900000000*x^4+750000000*x^3+75
000000*x^2)*exp(x)^8+(-450000000*x^12-2850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+3150000000
0*x^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000000*x^2-300000000*x)*exp(x)^6+(-3
00000000*x^12-1350000000*x^11-225000000*x^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-28350000000*x^6-108
00000000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+300000000)*exp(x)^4+(-50000000*x^12-
150000000*x^11+350000000*x^10+1200000000*x^9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*x^5+19500
00000*x^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*ln(x)+(50000000*x^13+418750000*x
^12+1475000000*x^11+2775000000*x^10+2800000000*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-850000000*x^5-2
31250000*x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11-150000000*x^10-7200000000*x
^9-11550000000*x^8-5250000000*x^7+5400000000*x^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000000*x^2)*e
xp(x)^6+(150000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9+3375000000*x^8+1575000000
0*x^7+8550000000*x^6-12150000000*x^5-19987500000*x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp(x)^4+(500
00000*x^13+175000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8-150000000*x^7-1080000000
0*x^6-5250000000*x^5+14375000000*x^4+21475000000*x^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^2+18750000
*x^12-75000000*x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000*x^4-6900000000*x^3-94
50000000*x^2-4800000000*x-900000000)/x^10,x,method=_RETURNVERBOSE)

[Out]

6250000*(x^8+8*x^7+28*x^6+56*x^5+70*x^4+56*x^3+28*x^2+8*x+1)/x^9*exp(8*x)*ln(x)^4-25000000*exp(6*x)*(exp(2*x)*
x^9+8*exp(2*x)*x^8+x^9+28*exp(2*x)*x^7+6*x^8+56*x^6*exp(2*x)+12*x^7+70*x^5*exp(2*x)+56*exp(2*x)*x^4-42*x^5+28*
exp(2*x)*x^3-84*x^4+8*exp(2*x)*x^2-84*x^3+x*exp(2*x)-48*x^2-15*x-2)/x^9*ln(x)^3+37500000*exp(4*x)*(4+28*x+56*e
xp(4*x)*x^5-168*exp(2*x)*x^4-24*x^7+x^10+4*x^9-42*x^6+84*x^4+120*x^3+81*x^2-96*exp(2*x)*x^3+8*x^3*exp(4*x)-168
*x^5*exp(2*x)-30*exp(2*x)*x^2-4*x*exp(2*x)+28*x^4*exp(4*x)+x^2*exp(4*x)+exp(4*x)*x^10+2*exp(2*x)*x^10+8*exp(4*
x)*x^9+12*exp(2*x)*x^9+28*exp(4*x)*x^8+24*exp(2*x)*x^8+56*exp(4*x)*x^7+70*exp(4*x)*x^6-84*x^6*exp(2*x))/x^9*ln
(x)^2-25000000*exp(2*x)*(-8-52*x+28*exp(6*x)*x^5-252*exp(4*x)*x^5+8*exp(6*x)*x^4+360*exp(2*x)*x^4+exp(6*x)*x^3
+x^11+6*x^7-24*x^8+2*x^10-8*x^9+84*x^6+84*x^5-48*x^4-159*x^3-134*x^2+243*exp(2*x)*x^3-45*x^3*exp(4*x)+252*x^5*
exp(2*x)+84*exp(2*x)*x^2+12*x*exp(2*x)-144*x^4*exp(4*x)-6*x^2*exp(4*x)+exp(6*x)*x^11+3*exp(4*x)*x^11+3*exp(2*x
)*x^11+8*exp(6*x)*x^10+18*exp(4*x)*x^10+12*exp(2*x)*x^10+28*exp(6*x)*x^9+36*exp(4*x)*x^9+56*exp(6*x)*x^8-72*ex
p(2*x)*x^8+70*exp(6*x)*x^7-126*exp(4*x)*x^7-126*exp(2*x)*x^7+56*exp(6*x)*x^6-252*exp(4*x)*x^6)/x^9*ln(x)+62500
00*(16+96*x+8*exp(8*x)*x^5-192*exp(6*x)*x^5+720*exp(4*x)*x^5+exp(8*x)*x^4-60*exp(6*x)*x^4-636*exp(2*x)*x^4-8*e
xp(6*x)*x^3+x^12+72*x^7+54*x^8-12*x^10-84*x^6-216*x^5-63*x^4+184*x^3+216*x^2-536*exp(2*x)*x^3+168*x^3*exp(4*x)
-192*x^5*exp(2*x)-208*exp(2*x)*x^2-32*x*exp(2*x)+486*x^4*exp(4*x)+24*x^2*exp(4*x)+exp(8*x)*x^12+4*exp(6*x)*x^1
2+6*exp(4*x)*x^12+4*exp(2*x)*x^12+8*exp(8*x)*x^11+24*exp(6*x)*x^11+24*exp(4*x)*x^11+8*exp(2*x)*x^11+28*exp(8*x
)*x^10+48*exp(6*x)*x^10-32*exp(2*x)*x^10+56*exp(8*x)*x^9-144*exp(4*x)*x^9-96*exp(2*x)*x^9+70*exp(8*x)*x^8-168*
exp(6*x)*x^8-252*exp(4*x)*x^8+24*exp(2*x)*x^8+56*exp(8*x)*x^7-336*exp(6*x)*x^7+336*exp(2*x)*x^7+28*exp(8*x)*x^
6-336*exp(6*x)*x^6+504*exp(4*x)*x^6+336*x^6*exp(2*x))/x^9

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+2100000000*x^5+612500000*x^4-700000000*x^
3-825000000*x^2-350000000*x-56250000)*exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-960000
0000*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000000*x^2+400000000*x+25000000)*exp(
x)^8+(-150000000*x^10-900000000*x^9-1650000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-
5400000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300000000*x^11+2437500000*x^10+8325
000000*x^9+15150000000*x^8+14700000000*x^7+4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-8625000
00*x^2-75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-1350000000*x^8-19800000000*x^7-2835
0000000*x^6-9450000000*x^5+16200000000*x^4+21150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(1
50000000*x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000000*x^5+2250000000*x^4-14850
000000*x^3-17062500000*x^2-7800000000*x-1350000000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-57250
00000*x^10-10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000*x^5+2900000000*x^4+7500000
00*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+3
1500000000*x^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000000*x^2-300000000*x)*exp
(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-2835000000
0*x^6-10800000000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+300000000)*exp(x)^4+(-50000
000*x^12-150000000*x^11+350000000*x^10+1200000000*x^9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*
x^5+1950000000*x^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log(x)+(50000000*x^13+4
18750000*x^12+1475000000*x^11+2775000000*x^10+2800000000*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-85000
0000*x^5-231250000*x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11-150000000*x^10-72
00000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000
000*x^2)*exp(x)^6+(150000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9+3375000000*x^8+
15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000*x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp
(x)^4+(50000000*x^13+175000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8-150000000*x^7-
10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^
2+18750000*x^12-75000000*x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000*x^4-6900000
000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorithm="maxima")

[Out]

6250000*x^3 + 390625/16*(256*x^3 - 96*x^2 + 24*x - 3)*e^(8*x) + 26171875/16*(32*x^2 - 8*x + 1)*e^(8*x) + 23046
875*(8*x - 1)*e^(8*x) + 6250000/9*(36*x^3 - 18*x^2 + 6*x - 1)*e^(6*x) + 81250000/9*(18*x^2 - 6*x + 1)*e^(6*x)
+ 56250000*(6*x - 1)*e^(6*x) + 1171875*(32*x^3 - 24*x^2 + 12*x - 3)*e^(4*x) + 22265625*(8*x^2 - 4*x + 1)*e^(4*
x) + 14062500*(4*x - 1)*e^(4*x) + 6250000*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x) + 43750000*(2*x^2 - 2*x + 1)*e^(2*
x) - 81250000*(2*x - 1)*e^(2*x) + 175000000*e^(2*x)*log(x) - 75000000*x + 337500000/x + 450000000/x^2 - 525000
000/x^3 - 1350000000/x^4 - 393750000/x^5 + 1150000000/x^6 + 1350000000/x^7 - 6250000*(4*(x^11 + 2*x^10 - x^9 -
24*x^8 + 6*x^7 + 84*x^6 + 84*x^5 - 48*x^4 - 159*x^3 - 134*x^2 - 52*x - 8)*e^(2*x)*log(x) - ((x^8 + 8*x^7 + 28
*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1)*log(x)^4 - 4*(x^9 + 8*x^8 + 28*x^7 + 56*x^6 + 70*x^5 + 56*
x^4 + 28*x^3 + 8*x^2 + x)*log(x)^3 + 6*(x^10 + 8*x^9 + 28*x^8 + 56*x^7 + 70*x^6 + 56*x^5 + 28*x^4 + 8*x^3 + x^
2)*log(x)^2 - 4*(x^11 + 8*x^10 + 28*x^9 + 56*x^8 + 70*x^7 + 56*x^6 + 28*x^5 + 8*x^4 + x^3)*log(x))*e^(8*x) + 4
*((x^9 + 6*x^8 + 12*x^7 - 42*x^5 - 84*x^4 - 84*x^3 - 48*x^2 - 15*x - 2)*log(x)^3 - 3*(x^10 + 6*x^9 + 12*x^8 -
42*x^6 - 84*x^5 - 84*x^4 - 48*x^3 - 15*x^2 - 2*x)*log(x)^2 + 3*(x^11 + 6*x^10 + 12*x^9 - 42*x^7 - 84*x^6 - 84*
x^5 - 48*x^4 - 15*x^3 - 2*x^2)*log(x))*e^(6*x) - 6*((x^10 + 4*x^9 - 24*x^7 - 42*x^6 + 84*x^4 + 120*x^3 + 81*x^
2 + 28*x + 4)*log(x)^2 - 2*(x^11 + 4*x^10 - 24*x^8 - 42*x^7 + 84*x^5 + 120*x^4 + 81*x^3 + 28*x^2 + 4*x)*log(x)
)*e^(4*x))/x^9 + 600000000/x^8 + 100000000/x^9 + 2800000000*Ei(8*x) - 7200000000*Ei(6*x) - 6300000000*Ei(4*x)
+ 325000000*Ei(2*x) + 346875000*e^(8*x) - 25000000*e^(6*x) - 975000000*e^(4*x) - 725000000*e^(2*x) + 930000000
0*gamma(-1, -2*x) + 13500000000*gamma(-1, -4*x) - 69300000000*gamma(-1, -6*x) + 7700000000*gamma(-1, -8*x) + 6
00000000*gamma(-2, -2*x) - 252000000000*gamma(-2, -4*x) + 189000000000*gamma(-2, -6*x) + 67200000000*gamma(-2,
-8*x) - 86400000000*gamma(-3, -2*x) + 547200000000*gamma(-3, -4*x) + 1166400000000*gamma(-3, -6*x) - 78080000
0000*gamma(-3, -8*x) + 84000000000*gamma(-4, -2*x) + 3110400000000*gamma(-4, -4*x) - 11469600000000*gamma(-4,
-6*x) + 3481600000000*gamma(-4, -8*x) + 460000000000*gamma(-5, -2*x) - 20467200000000*gamma(-5, -4*x) + 402408
00000000*gamma(-5, -6*x) - 7577600000000*gamma(-5, -8*x) - 1374400000000*gamma(-6, -2*x) + 48230400000000*gamm
a(-6, -4*x) - 66484800000000*gamma(-6, -6*x) + 6553600000000*gamma(-6, -8*x) + 1542400000000*gamma(-7, -2*x) -
51609600000000*gamma(-7, -4*x) + 41990400000000*gamma(-7, -6*x) - 742400000000*gamma(-8, -2*x) + 196608000000
00*gamma(-8, -4*x) + 102400000000*gamma(-9, -2*x) + 6250000*integrate(4*(x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^
4 + 56*x^3 + 28*x^2 + 8*x + 1)*e^(8*x)/x^7, x) + 6250000*integrate(12*(x^9 + 6*x^8 + 12*x^7 - 42*x^5 - 84*x^4
- 84*x^3 - 48*x^2 - 15*x - 2)*e^(6*x)/x^8, x) + 6250000*integrate(12*(x^10 + 4*x^9 - 24*x^7 - 42*x^6 + 84*x^4
+ 120*x^3 + 81*x^2 + 28*x + 4)*e^(4*x)/x^9, x) + 6250000*integrate(4*(x^11 + 2*x^10 - x^9 - 24*x^8 + 6*x^7 + 8
4*x^6 + 84*x^5 - 48*x^4 - 159*x^3 - 134*x^2 - 52*x - 8)*e^(2*x)/x^10, x)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.03 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4800000000*x - exp(8*x)*(962500000*x^8 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^7
- 25000000*x^3 + 2800000000*x^9 + 2775000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + exp(4
*x)*(300000000*x + 3150000000*x^2 + 11775000000*x^3 + 19987500000*x^4 + 12150000000*x^5 - 8550000000*x^6 - 157
50000000*x^7 - 3375000000*x^8 + 6300000000*x^9 + 3900000000*x^10 - 225000000*x^11 - 712500000*x^12 - 150000000
*x^13) + log(x)*(exp(2*x)*(10000000000*x + 20850000000*x^2 + 17150000000*x^3 - 1950000000*x^4 - 10800000000*x^
5 - 2100000000*x^6 + 3900000000*x^7 + 900000000*x^8 - 1200000000*x^9 - 350000000*x^10 + 150000000*x^11 + 50000
000*x^12 + 1800000000) - exp(4*x)*(4500000000*x + 19575000000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 108000
00000*x^5 - 28350000000*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*
x^11 - 300000000*x^12 + 300000000) + exp(6*x)*(300000000*x + 3300000000*x^2 + 13050000000*x^3 + 23850000000*x^
4 + 16200000000*x^5 - 12600000000*x^6 - 31500000000*x^7 - 20700000000*x^8 - 900000000*x^9 + 5700000000*x^10 +
2850000000*x^11 + 450000000*x^12) + exp(8*x)*(3500000000*x^7 - 750000000*x^3 - 2900000000*x^4 - 5400000000*x^5
- 3850000000*x^6 - 75000000*x^2 + 10500000000*x^8 + 10600000000*x^9 + 5725000000*x^10 + 1650000000*x^11 + 200
000000*x^12)) + log(x)^3*(exp(8*x)*(2800000000*x^5 - 1900000000*x^2 - 4000000000*x^3 - 3150000000*x^4 - 400000
000*x + 9100000000*x^6 + 9600000000*x^7 + 5375000000*x^8 + 1600000000*x^9 + 200000000*x^10 - 25000000) + exp(6
*x)*(2700000000*x + 6150000000*x^2 + 5400000000*x^3 - 2100000000*x^4 - 8400000000*x^5 - 6300000000*x^6 - 60000
0000*x^7 + 1650000000*x^8 + 900000000*x^9 + 150000000*x^10 + 450000000)) - exp(2*x)*(2900000000*x + 1205000000
0*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 10800000000*x^6 - 150000000*x^7 + 4650000000*x^8
+ 500000000*x^9 - 1450000000*x^10 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13 + 200000000) - exp(6*x)*(1
50000000*x^2 + 1425000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000*x^7 - 1155000000
0*x^8 - 7200000000*x^9 - 150000000*x^10 + 2025000000*x^11 + 975000000*x^12 + 150000000*x^13) + 9450000000*x^2
+ 6900000000*x^3 - 1968750000*x^4 - 5400000000*x^5 - 1575000000*x^6 + 900000000*x^7 + 337500000*x^8 + 75000000
*x^10 - 18750000*x^12 - log(x)^2*(exp(6*x)*(2325000000*x + 10575000000*x^2 + 21150000000*x^3 + 16200000000*x^4
- 9450000000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000*x^9 + 2775000000*x^10 + 45
0000000*x^11 + 150000000) + exp(8*x)*(4725000000*x^6 - 862500000*x^2 - 3600000000*x^3 - 7050000000*x^4 - 52500
00000*x^5 - 75000000*x + 14700000000*x^7 + 15150000000*x^8 + 8325000000*x^9 + 2437500000*x^10 + 300000000*x^11
) - exp(4*x)*(7800000000*x + 17062500000*x^2 + 14850000000*x^3 - 2250000000*x^4 - 12600000000*x^5 - 4725000000
*x^6 + 4500000000*x^7 + 3600000000*x^8 - 637500000*x^10 - 150000000*x^11 + 1350000000)) - exp(8*x)*log(x)^4*(6
12500000*x^4 - 825000000*x^2 - 700000000*x^3 - 350000000*x + 2100000000*x^5 + 2275000000*x^6 + 1300000000*x^7
+ 393750000*x^8 + 50000000*x^9 - 56250000) + 900000000)/x^10,x)

[Out]

int(-(4800000000*x - exp(8*x)*(962500000*x^8 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^7
- 25000000*x^3 + 2800000000*x^9 + 2775000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + exp(4
*x)*(300000000*x + 3150000000*x^2 + 11775000000*x^3 + 19987500000*x^4 + 12150000000*x^5 - 8550000000*x^6 - 157
50000000*x^7 - 3375000000*x^8 + 6300000000*x^9 + 3900000000*x^10 - 225000000*x^11 - 712500000*x^12 - 150000000
*x^13) + log(x)*(exp(2*x)*(10000000000*x + 20850000000*x^2 + 17150000000*x^3 - 1950000000*x^4 - 10800000000*x^
5 - 2100000000*x^6 + 3900000000*x^7 + 900000000*x^8 - 1200000000*x^9 - 350000000*x^10 + 150000000*x^11 + 50000
000*x^12 + 1800000000) - exp(4*x)*(4500000000*x + 19575000000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 108000
00000*x^5 - 28350000000*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*
x^11 - 300000000*x^12 + 300000000) + exp(6*x)*(300000000*x + 3300000000*x^2 + 13050000000*x^3 + 23850000000*x^
4 + 16200000000*x^5 - 12600000000*x^6 - 31500000000*x^7 - 20700000000*x^8 - 900000000*x^9 + 5700000000*x^10 +
2850000000*x^11 + 450000000*x^12) + exp(8*x)*(3500000000*x^7 - 750000000*x^3 - 2900000000*x^4 - 5400000000*x^5
- 3850000000*x^6 - 75000000*x^2 + 10500000000*x^8 + 10600000000*x^9 + 5725000000*x^10 + 1650000000*x^11 + 200
000000*x^12)) + log(x)^3*(exp(8*x)*(2800000000*x^5 - 1900000000*x^2 - 4000000000*x^3 - 3150000000*x^4 - 400000
000*x + 9100000000*x^6 + 9600000000*x^7 + 5375000000*x^8 + 1600000000*x^9 + 200000000*x^10 - 25000000) + exp(6
*x)*(2700000000*x + 6150000000*x^2 + 5400000000*x^3 - 2100000000*x^4 - 8400000000*x^5 - 6300000000*x^6 - 60000
0000*x^7 + 1650000000*x^8 + 900000000*x^9 + 150000000*x^10 + 450000000)) - exp(2*x)*(2900000000*x + 1205000000
0*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 10800000000*x^6 - 150000000*x^7 + 4650000000*x^8
+ 500000000*x^9 - 1450000000*x^10 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13 + 200000000) - exp(6*x)*(1
50000000*x^2 + 1425000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000*x^7 - 1155000000
0*x^8 - 7200000000*x^9 - 150000000*x^10 + 2025000000*x^11 + 975000000*x^12 + 150000000*x^13) + 9450000000*x^2
+ 6900000000*x^3 - 1968750000*x^4 - 5400000000*x^5 - 1575000000*x^6 + 900000000*x^7 + 337500000*x^8 + 75000000
*x^10 - 18750000*x^12 - log(x)^2*(exp(6*x)*(2325000000*x + 10575000000*x^2 + 21150000000*x^3 + 16200000000*x^4
- 9450000000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000*x^9 + 2775000000*x^10 + 45
0000000*x^11 + 150000000) + exp(8*x)*(4725000000*x^6 - 862500000*x^2 - 3600000000*x^3 - 7050000000*x^4 - 52500
00000*x^5 - 75000000*x + 14700000000*x^7 + 15150000000*x^8 + 8325000000*x^9 + 2437500000*x^10 + 300000000*x^11
) - exp(4*x)*(7800000000*x + 17062500000*x^2 + 14850000000*x^3 - 2250000000*x^4 - 12600000000*x^5 - 4725000000
*x^6 + 4500000000*x^7 + 3600000000*x^8 - 637500000*x^10 - 150000000*x^11 + 1350000000)) - exp(8*x)*log(x)^4*(6
12500000*x^4 - 825000000*x^2 - 700000000*x^3 - 350000000*x + 2100000000*x^5 + 2275000000*x^6 + 1300000000*x^7
+ 393750000*x^8 + 50000000*x^9 - 56250000) + 900000000)/x^10, x)

________________________________________________________________________________________

sympy [B]  time = 2.58, size = 1156, normalized size = 36.12 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((50000000*x**9+393750000*x**8+1300000000*x**7+2275000000*x**6+2100000000*x**5+612500000*x**4-700000
000*x**3-825000000*x**2-350000000*x-56250000)*exp(x)**8*ln(x)**4+((-200000000*x**10-1600000000*x**9-5375000000
*x**8-9600000000*x**7-9100000000*x**6-2800000000*x**5+3150000000*x**4+4000000000*x**3+1900000000*x**2+40000000
0*x+25000000)*exp(x)**8+(-150000000*x**10-900000000*x**9-1650000000*x**8+600000000*x**7+6300000000*x**6+840000
0000*x**5+2100000000*x**4-5400000000*x**3-6150000000*x**2-2700000000*x-450000000)*exp(x)**6)*ln(x)**3+((300000
000*x**11+2437500000*x**10+8325000000*x**9+15150000000*x**8+14700000000*x**7+4725000000*x**6-5250000000*x**5-7
050000000*x**4-3600000000*x**3-862500000*x**2-75000000*x)*exp(x)**8+(450000000*x**11+2775000000*x**10+53250000
00*x**9-1350000000*x**8-19800000000*x**7-28350000000*x**6-9450000000*x**5+16200000000*x**4+21150000000*x**3+10
575000000*x**2+2325000000*x+150000000)*exp(x)**6+(150000000*x**11+637500000*x**10-3600000000*x**8-4500000000*x
**7+4725000000*x**6+12600000000*x**5+2250000000*x**4-14850000000*x**3-17062500000*x**2-7800000000*x-1350000000
)*exp(x)**4)*ln(x)**2+((-200000000*x**12-1650000000*x**11-5725000000*x**10-10600000000*x**9-10500000000*x**8-3
500000000*x**7+3850000000*x**6+5400000000*x**5+2900000000*x**4+750000000*x**3+75000000*x**2)*exp(x)**8+(-45000
0000*x**12-2850000000*x**11-5700000000*x**10+900000000*x**9+20700000000*x**8+31500000000*x**7+12600000000*x**6
-16200000000*x**5-23850000000*x**4-13050000000*x**3-3300000000*x**2-300000000*x)*exp(x)**6+(-300000000*x**12-1
350000000*x**11-225000000*x**10+7500000000*x**9+10800000000*x**8-8100000000*x**7-28350000000*x**6-10800000000*
x**5+27000000000*x**4+37050000000*x**3+19575000000*x**2+4500000000*x+300000000)*exp(x)**4+(-50000000*x**12-150
000000*x**11+350000000*x**10+1200000000*x**9-900000000*x**8-3900000000*x**7+2100000000*x**6+10800000000*x**5+1
950000000*x**4-17150000000*x**3-20850000000*x**2-10000000000*x-1800000000)*exp(x)**2)*ln(x)+(50000000*x**13+41
8750000*x**12+1475000000*x**11+2775000000*x**10+2800000000*x**9+962500000*x**8-1050000000*x**7-1525000000*x**6
-850000000*x**5-231250000*x**4-25000000*x**3)*exp(x)**8+(150000000*x**13+975000000*x**12+2025000000*x**11-1500
00000*x**10-7200000000*x**9-11550000000*x**8-5250000000*x**7+5400000000*x**6+8850000000*x**5+5175000000*x**4+1
425000000*x**3+150000000*x**2)*exp(x)**6+(150000000*x**13+712500000*x**12+225000000*x**11-3900000000*x**10-630
0000000*x**9+3375000000*x**8+15750000000*x**7+8550000000*x**6-12150000000*x**5-19987500000*x**4-11775000000*x*
*3-3150000000*x**2-300000000*x)*exp(x)**4+(50000000*x**13+175000000*x**12-325000000*x**11-1450000000*x**10+500
000000*x**9+4650000000*x**8-150000000*x**7-10800000000*x**6-5250000000*x**5+14375000000*x**4+21475000000*x**3+
12050000000*x**2+2900000000*x+200000000)*exp(x)**2+18750000*x**12-75000000*x**10-337500000*x**8-900000000*x**7
[phone]*x**6+5400000000*x**5+1968750000*x**4-6900000000*x**3-9450000000*x**2-4800000000*x-900000000)/x**10
,x)

[Out]

6250000*x**3 - 75000000*x + (337500000*x**8 + 450000000*x**7 - 525000000*x**6 - 1350000000*x**5 - 393750000*x*
*4 + 1150000000*x**3 + 1350000000*x**2 + 600000000*x + 100000000)/x**9 + ((25000000*x**39 - 25000000*x**38*log
(x) + 50000000*x**38 - 50000000*x**37*log(x) - 200000000*x**37 + 200000000*x**36*log(x) - 600000000*x**36 + 60
0000000*x**35*log(x) + 150000000*x**35 - 150000000*x**34*log(x) + 2100000000*x**34 - 2100000000*x**33*log(x) +
2100000000*x**33 - 2100000000*x**32*log(x) - 1200000000*x**32 + 1200000000*x**31*log(x) - 3975000000*x**31 +
3975000000*x**30*log(x) - 3350000000*x**30 + 3350000000*x**29*log(x) - 1300000000*x**29 + 1300000000*x**28*log
(x) - 200000000*x**28 + 200000000*x**27*log(x))*exp(2*x) + (37500000*x**39 - 75000000*x**38*log(x) + 150000000
*x**38 + 37500000*x**37*log(x)**2 - 300000000*x**37*log(x) + 150000000*x**36*log(x)**2 - 900000000*x**36 + 180
0000000*x**35*log(x) - 1575000000*x**35 - 900000000*x**34*log(x)**2 + 3150000000*x**34*log(x) - 1575000000*x**
33*log(x)**2 + 3150000000*x**33 - 6300000000*x**32*log(x) + 4500000000*x**32 + 3150000000*x**31*log(x)**2 - 90
00000000*x**31*log(x) + 3037500000*x**31 + 4500000000*x**30*log(x)**2 - 6075000000*x**30*log(x) + 1050000000*x
**30 + 3037500000*x**29*log(x)**2 - 2100000000*x**29*log(x) + 150000000*x**29 + 1050000000*x**28*log(x)**2 - 3
00000000*x**28*log(x) + 150000000*x**27*log(x)**2)*exp(4*x) + (25000000*x**39 - 75000000*x**38*log(x) + 150000
000*x**38 + 75000000*x**37*log(x)**2 - 450000000*x**37*log(x) + 300000000*x**37 - 25000000*x**36*log(x)**3 + 4
50000000*x**36*log(x)**2 - 900000000*x**36*log(x) - 150000000*x**35*log(x)**3 + 900000000*x**35*log(x)**2 - 10
50000000*x**35 - 300000000*x**34*log(x)**3 + 3150000000*x**34*log(x) - 2100000000*x**34 - 3150000000*x**33*log
(x)**2 + 6300000000*x**33*log(x) - 2100000000*x**33 + 1050000000*x**32*log(x)**3 - 6300000000*x**32*log(x)**2
+ 6300000000*x**32*log(x) - 1200000000*x**32 + 2100000000*x**31*log(x)**3 - 6300000000*x**31*log(x)**2 + 36000
00000*x**31*log(x) - 375000000*x**31 + 2100000000*x**30*log(x)**3 - 3600000000*x**30*log(x)**2 + 1125000000*x*
*30*log(x) - 50000000*x**30 + 1200000000*x**29*log(x)**3 - 1125000000*x**29*log(x)**2 + 150000000*x**29*log(x)
+ 375000000*x**28*log(x)**3 - 150000000*x**28*log(x)**2 + 50000000*x**27*log(x)**3)*exp(6*x) + (6250000*x**39
- 25000000*x**38*log(x) + 50000000*x**38 + 37500000*x**37*log(x)**2 - 200000000*x**37*log(x) + 175000000*x**3
7 - 25000000*x**36*log(x)**3 + 300000000*x**36*log(x)**2 - 700000000*x**36*log(x) + 350000000*x**36 + 6250000*
x**35*log(x)**4 - 200000000*x**35*log(x)**3 + 1050000000*x**35*log(x)**2 - 1400000000*x**35*log(x) + 437500000
*x**35 + 50000000*x**34*log(x)**4 - 700000000*x**34*log(x)**3 + 2100000000*x**34*log(x)**2 - 1750000000*x**34*
log(x) + 350000000*x**34 + 175000000*x**33*log(x)**4 - 1400000000*x**33*log(x)**3 + 2625000000*x**33*log(x)**2
- 1400000000*x**33*log(x) + 175000000*x**33 + 350000000*x**32*log(x)**4 - 1750000000*x**32*log(x)**3 + 210000
0000*x**32*log(x)**2 - 700000000*x**32*log(x) + 50000000*x**32 + 437500000*x**31*log(x)**4 - 1400000000*x**31*
log(x)**3 + 1050000000*x**31*log(x)**2 - 200000000*x**31*log(x) + 6250000*x**31 + 350000000*x**30*log(x)**4 -
700000000*x**30*log(x)**3 + 300000000*x**30*log(x)**2 - 25000000*x**30*log(x) + 175000000*x**29*log(x)**4 - 20
0000000*x**29*log(x)**3 + 37500000*x**29*log(x)**2 + 50000000*x**28*log(x)**4 - 25000000*x**28*log(x)**3 + 625
0000*x**27*log(x)**4)*exp(8*x))/x**36

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