3.13.46 \(\int \frac {(2400000000 x^{15}-800000000 x^{16}) \log ^8(-3+x)+(800000000 x^{16} \log ^7(-3+x)+(-4800000000 x^{15}+10000000000 x^{16}-2800000000 x^{17}) \log ^8(-3+x)) \log (x)+(3200000000 x^{17} \log ^7(-3+x)+(-20400000000 x^{16}+19400000000 x^{17}-4200000000 x^{18}) \log ^8(-3+x)) \log ^2(x)+(5600000000 x^{18} \log ^7(-3+x)+(-37800000000 x^{17}+23100000000 x^{18}-3500000000 x^{19}) \log ^8(-3+x)) \log ^3(x)+(5600000000 x^{19} \log ^7(-3+x)+(-39900000000 x^{18}+18550000000 x^{19}-1750000000 x^{20}) \log ^8(-3+x)) \log ^4(x)+(3500000000 x^{20} \log ^7(-3+x)+(-26250000000 x^{19}+10325000000 x^{20}-525000000 x^{21}) \log ^8(-3+x)) \log ^5(x)+(1400000000 x^{21} \log ^7(-3+x)+(-11025000000 x^{20}+3937500000 x^{21}-87500000 x^{22}) \log ^8(-3+x)) \log ^6(x)+(350000000 x^{22} \log ^7(-3+x)+(-2887500000 x^{21}+981250000 x^{22}-6250000 x^{23}) \log ^8(-3+x)) \log ^7(x)+(50000000 x^{23} \log ^7(-3+x)+(-431250000 x^{22}+143750000 x^{23}) \log ^8(-3+x)) \log ^8(x)+(3125000 x^{24} \log ^7(-3+x)+(-28125000 x^{23}+9375000 x^{24}) \log ^8(-3+x)) \log ^9(x)}{(-3+x) \log ^9(x)} \, dx\)
Optimal. Leaf size=21 \[ 390625 x^{16} \log ^8(-3+x) \left (x+\frac {2}{\log (x)}\right )^8 \]
________________________________________________________________________________________
Rubi [F] time = 122.69, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \int \frac {\left (2400000000 x^{15}-800000000 x^{16}\right ) \log ^8(-3+x)+\left (800000000 x^{16} \log ^7(-3+x)+\left (-4800000000 x^{15}+10000000000 x^{16}-2800000000 x^{17}\right ) \log ^8(-3+x)\right ) \log (x)+\left (3200000000 x^{17} \log ^7(-3+x)+\left (-20400000000 x^{16}+19400000000 x^{17}-4200000000 x^{18}\right ) \log ^8(-3+x)\right ) \log ^2(x)+\left (5600000000 x^{18} \log ^7(-3+x)+\left (-37800000000 x^{17}+23100000000 x^{18}-3500000000 x^{19}\right ) \log ^8(-3+x)\right ) \log ^3(x)+\left (5600000000 x^{19} \log ^7(-3+x)+\left (-39900000000 x^{18}+18550000000 x^{19}-1750000000 x^{20}\right ) \log ^8(-3+x)\right ) \log ^4(x)+\left (3500000000 x^{20} \log ^7(-3+x)+\left (-26250000000 x^{19}+10325000000 x^{20}-525000000 x^{21}\right ) \log ^8(-3+x)\right ) \log ^5(x)+\left (1400000000 x^{21} \log ^7(-3+x)+\left (-11025000000 x^{20}+3937500000 x^{21}-87500000 x^{22}\right ) \log ^8(-3+x)\right ) \log ^6(x)+\left (350000000 x^{22} \log ^7(-3+x)+\left (-2887500000 x^{21}+981250000 x^{22}-6250000 x^{23}\right ) \log ^8(-3+x)\right ) \log ^7(x)+\left (50000000 x^{23} \log ^7(-3+x)+\left (-431250000 x^{22}+143750000 x^{23}\right ) \log ^8(-3+x)\right ) \log ^8(x)+\left (3125000 x^{24} \log ^7(-3+x)+\left (-28125000 x^{23}+9375000 x^{24}\right ) \log ^8(-3+x)\right ) \log ^9(x)}{(-3+x) \log ^9(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[((2400000000*x^15 - 800000000*x^16)*Log[-3 + x]^8 + (800000000*x^16*Log[-3 + x]^7 + (-4800000000*x^15 + 10
000000000*x^16 - 2800000000*x^17)*Log[-3 + x]^8)*Log[x] + (3200000000*x^17*Log[-3 + x]^7 + (-20400000000*x^16
+ 19400000000*x^17 - 4200000000*x^18)*Log[-3 + x]^8)*Log[x]^2 + (5600000000*x^18*Log[-3 + x]^7 + (-37800000000
*x^17 + 23100000000*x^18 - 3500000000*x^19)*Log[-3 + x]^8)*Log[x]^3 + (5600000000*x^19*Log[-3 + x]^7 + (-39900
000000*x^18 + 18550000000*x^19 - 1750000000*x^20)*Log[-3 + x]^8)*Log[x]^4 + (3500000000*x^20*Log[-3 + x]^7 + (
-26250000000*x^19 + 10325000000*x^20 - 525000000*x^21)*Log[-3 + x]^8)*Log[x]^5 + (1400000000*x^21*Log[-3 + x]^
7 + (-11025000000*x^20 + 3937500000*x^21 - 87500000*x^22)*Log[-3 + x]^8)*Log[x]^6 + (350000000*x^22*Log[-3 + x
]^7 + (-2887500000*x^21 + 981250000*x^22 - 6250000*x^23)*Log[-3 + x]^8)*Log[x]^7 + (50000000*x^23*Log[-3 + x]^
7 + (-431250000*x^22 + 143750000*x^23)*Log[-3 + x]^8)*Log[x]^8 + (3125000*x^24*Log[-3 + x]^7 + (-28125000*x^23
+ 9375000*x^24)*Log[-3 + x]^8)*Log[x]^9)/((-3 + x)*Log[x]^9),x]
[Out]
110324037687890625*Log[-3 + x]^8 - 882592301503125000*(3 - x)*Log[-3 + x]^8 + 3383270489095312500*(3 - x)^2*Lo
g[-3 + x]^8 - 8270216751121875000*(3 - x)^3*Log[-3 + x]^8 + 14472879314463281250*(3 - x)^4*Log[-3 + x]^8 - 192
97172419284375000*(3 - x)^5*Log[-3 + x]^8 + 20369237553689062500*(3 - x)^6*Log[-3 + x]^8 - 1745934647459062500
0*(3 - x)^7*Log[-3 + x]^8 + 12367037086168359375*(3 - x)^8*Log[-3 + x]^8 - 7328614569581250000*(3 - x)^9*Log[-
3 + x]^8 + 3664307284790625000*(3 - x)^10*Log[-3 + x]^8 - 1554554605668750000*(3 - x)^11*Log[-3 + x]^8 + 56136
6940935937500*(3 - x)^12*Log[-3 + x]^8 - 172728289518750000*(3 - x)^13*Log[-3 + x]^8 + 45238361540625000*(3 -
x)^14*Log[-3 + x]^8 - 10052969231250000*(3 - x)^15*Log[-3 + x]^8 + 1884931730859375*(3 - x)^16*Log[-3 + x]^8 -
295675565625000*(3 - x)^17*Log[-3 + x]^8 + 38328314062500*(3 - x)^18*Log[-3 + x]^8 - 4034559375000*(3 - x)^19
*Log[-3 + x]^8 + 336213281250*(3 - x)^20*Log[-3 + x]^8 - 21346875000*(3 - x)^21*Log[-3 + x]^8 + 970312500*(3 -
x)^22*Log[-3 + x]^8 - 28125000*(3 - x)^23*Log[-3 + x]^8 + 390625*(3 - x)^24*Log[-3 + x]^8 - 800000000*Defer[I
nt][(x^15*Log[-3 + x]^8)/Log[x]^9, x] + 11479125600000000*Defer[Int][Log[-3 + x]^7/Log[x]^8, x] + 344373768000
00000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^8), x] + 3826375200000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^
8, x] + 1275458400000000*Defer[Int][(x^2*Log[-3 + x]^7)/Log[x]^8, x] + 425152800000000*Defer[Int][(x^3*Log[-3
+ x]^7)/Log[x]^8, x] + 141717600000000*Defer[Int][(x^4*Log[-3 + x]^7)/Log[x]^8, x] + 47239200000000*Defer[Int]
[(x^5*Log[-3 + x]^7)/Log[x]^8, x] + 15746400000000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x]^8, x] + 5248800000000
*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x]^8, x] + 1749600000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x]^8, x] + 583
200000000*Defer[Int][(x^9*Log[-3 + x]^7)/Log[x]^8, x] + 194400000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^8,
x] + 64800000000*Defer[Int][(x^11*Log[-3 + x]^7)/Log[x]^8, x] + 21600000000*Defer[Int][(x^12*Log[-3 + x]^7)/L
og[x]^8, x] + 7200000000*Defer[Int][(x^13*Log[-3 + x]^7)/Log[x]^8, x] + 2400000000*Defer[Int][(x^14*Log[-3 + x
]^7)/Log[x]^8, x] + 800000000*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x]^8, x] + 1600000000*Defer[Int][(x^15*Log[-
3 + x]^8)/Log[x]^8, x] - 2800000000*Defer[Int][(x^16*Log[-3 + x]^8)/Log[x]^8, x] + 137749507200000000*Defer[In
t][Log[-3 + x]^7/Log[x]^7, x] + 413248521600000000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^7), x] + 45916502
400000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^7, x] + 15305500800000000*Defer[Int][(x^2*Log[-3 + x]^7)/Log[x]^
7, x] + 5101833600000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x]^7, x] + 1700611200000000*Defer[Int][(x^4*Log[-3
+ x]^7)/Log[x]^7, x] + 566870400000000*Defer[Int][(x^5*Log[-3 + x]^7)/Log[x]^7, x] + 188956800000000*Defer[In
t][(x^6*Log[-3 + x]^7)/Log[x]^7, x] + 62985600000000*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x]^7, x] + 20995200000
000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x]^7, x] + 6998400000000*Defer[Int][(x^9*Log[-3 + x]^7)/Log[x]^7, x] +
2332800000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^7, x] + 777600000000*Defer[Int][(x^11*Log[-3 + x]^7)/Log[
x]^7, x] + 259200000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x]^7, x] + 86400000000*Defer[Int][(x^13*Log[-3 + x
]^7)/Log[x]^7, x] + 28800000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x]^7, x] + 9600000000*Defer[Int][(x^15*Log
[-3 + x]^7)/Log[x]^7, x] + 3200000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[x]^7, x] + 6800000000*Defer[Int][(x^
16*Log[-3 + x]^8)/Log[x]^7, x] - 4200000000*Defer[Int][(x^17*Log[-3 + x]^8)/Log[x]^7, x] + 723184912800000000*
Defer[Int][Log[-3 + x]^7/Log[x]^6, x] + 2169554738400000000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^6), x] +
241061637600000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^6, x] + 80353879200000000*Defer[Int][(x^2*Log[-3 + x]^
7)/Log[x]^6, x] + 26784626400000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x]^6, x] + 8928208800000000*Defer[Int][
(x^4*Log[-3 + x]^7)/Log[x]^6, x] + 2976069600000000*Defer[Int][(x^5*Log[-3 + x]^7)/Log[x]^6, x] + 992023200000
000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x]^6, x] + 330674400000000*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x]^6, x]
+ 110224800000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x]^6, x] + 36741600000000*Defer[Int][(x^9*Log[-3 + x]^7)/
Log[x]^6, x] + 12247200000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^6, x] + 4082400000000*Defer[Int][(x^11*Lo
g[-3 + x]^7)/Log[x]^6, x] + 1360800000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x]^6, x] + 453600000000*Defer[In
t][(x^13*Log[-3 + x]^7)/Log[x]^6, x] + 151200000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x]^6, x] + 50400000000
*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x]^6, x] + 16800000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[x]^6, x] + 560
0000000*Defer[Int][(x^17*Log[-3 + x]^7)/Log[x]^6, x] + 12600000000*Defer[Int][(x^17*Log[-3 + x]^8)/Log[x]^6, x
] - 3500000000*Defer[Int][(x^18*Log[-3 + x]^8)/Log[x]^6, x] + 2169554738400000000*Defer[Int][Log[-3 + x]^7/Log
[x]^5, x] + 6508664215200000000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^5), x] + 723184912800000000*Defer[In
t][(x*Log[-3 + x]^7)/Log[x]^5, x] + 241061637600000000*Defer[Int][(x^2*Log[-3 + x]^7)/Log[x]^5, x] + 803538792
00000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x]^5, x] + 26784626400000000*Defer[Int][(x^4*Log[-3 + x]^7)/Log[x]
^5, x] + 8928208800000000*Defer[Int][(x^5*Log[-3 + x]^7)/Log[x]^5, x] + 2976069600000000*Defer[Int][(x^6*Log[-
3 + x]^7)/Log[x]^5, x] + 992023200000000*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x]^5, x] + 330674400000000*Defer[I
nt][(x^8*Log[-3 + x]^7)/Log[x]^5, x] + 110224800000000*Defer[Int][(x^9*Log[-3 + x]^7)/Log[x]^5, x] + 367416000
00000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^5, x] + 12247200000000*Defer[Int][(x^11*Log[-3 + x]^7)/Log[x]^5,
x] + 4082400000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x]^5, x] + 1360800000000*Defer[Int][(x^13*Log[-3 + x]^7
)/Log[x]^5, x] + 453600000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x]^5, x] + 151200000000*Defer[Int][(x^15*Log
[-3 + x]^7)/Log[x]^5, x] + 50400000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[x]^5, x] + 16800000000*Defer[Int][(
x^17*Log[-3 + x]^7)/Log[x]^5, x] + 5600000000*Defer[Int][(x^18*Log[-3 + x]^7)/Log[x]^5, x] + 13300000000*Defer
[Int][(x^18*Log[-3 + x]^8)/Log[x]^5, x] - 1750000000*Defer[Int][(x^19*Log[-3 + x]^8)/Log[x]^5, x] + 4067915134
500000000*Defer[Int][Log[-3 + x]^7/Log[x]^4, x] + 12203745403500000000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[
x]^4), x] + 1355971711500000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^4, x] + 451990570500000000*Defer[Int][(x^2
*Log[-3 + x]^7)/Log[x]^4, x] + 150663523500000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x]^4, x] + 50221174500000
000*Defer[Int][(x^4*Log[-3 + x]^7)/Log[x]^4, x] + 16740391500000000*Defer[Int][(x^5*Log[-3 + x]^7)/Log[x]^4, x
] + 5580130500000000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x]^4, x] + 1860043500000000*Defer[Int][(x^7*Log[-3 + x
]^7)/Log[x]^4, x] + 620014500000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x]^4, x] + 206671500000000*Defer[Int][(
x^9*Log[-3 + x]^7)/Log[x]^4, x] + 68890500000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^4, x] + 22963500000000
*Defer[Int][(x^11*Log[-3 + x]^7)/Log[x]^4, x] + 7654500000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x]^4, x] + 2
551500000000*Defer[Int][(x^13*Log[-3 + x]^7)/Log[x]^4, x] + 850500000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x
]^4, x] + 283500000000*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x]^4, x] + 94500000000*Defer[Int][(x^16*Log[-3 + x]
^7)/Log[x]^4, x] + 31500000000*Defer[Int][(x^17*Log[-3 + x]^7)/Log[x]^4, x] + 10500000000*Defer[Int][(x^18*Log
[-3 + x]^7)/Log[x]^4, x] + 3500000000*Defer[Int][(x^19*Log[-3 + x]^7)/Log[x]^4, x] + 8750000000*Defer[Int][(x^
19*Log[-3 + x]^8)/Log[x]^4, x] - 525000000*Defer[Int][(x^20*Log[-3 + x]^8)/Log[x]^4, x] + 4881498161400000000*
Defer[Int][Log[-3 + x]^7/Log[x]^3, x] + 14644494484200000000*Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^3), x]
+ 1627166053800000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^3, x] + 542388684600000000*Defer[Int][(x^2*Log[-3 +
x]^7)/Log[x]^3, x] + 180796228200000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x]^3, x] + 60265409400000000*Defer[
Int][(x^4*Log[-3 + x]^7)/Log[x]^3, x] + 20088469800000000*Defer[Int][(x^5*Log[-3 + x]^7)/Log[x]^3, x] + 669615
6600000000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x]^3, x] + 2232052200000000*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x
]^3, x] + 744017400000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x]^3, x] + 248005800000000*Defer[Int][(x^9*Log[-3
+ x]^7)/Log[x]^3, x] + 82668600000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x]^3, x] + 27556200000000*Defer[Int
][(x^11*Log[-3 + x]^7)/Log[x]^3, x] + 9185400000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x]^3, x] + 30618000000
00*Defer[Int][(x^13*Log[-3 + x]^7)/Log[x]^3, x] + 1020600000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x]^3, x] +
340200000000*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x]^3, x] + 113400000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[
x]^3, x] + 37800000000*Defer[Int][(x^17*Log[-3 + x]^7)/Log[x]^3, x] + 12600000000*Defer[Int][(x^18*Log[-3 + x]
^7)/Log[x]^3, x] + 4200000000*Defer[Int][(x^19*Log[-3 + x]^7)/Log[x]^3, x] + 1400000000*Defer[Int][(x^20*Log[-
3 + x]^7)/Log[x]^3, x] + 3675000000*Defer[Int][(x^20*Log[-3 + x]^8)/Log[x]^3, x] - 87500000*Defer[Int][(x^21*L
og[-3 + x]^8)/Log[x]^3, x] + 3661123621050000000*Defer[Int][Log[-3 + x]^7/Log[x]^2, x] + 10983370863150000000*
Defer[Int][Log[-3 + x]^7/((-3 + x)*Log[x]^2), x] + 1220374540350000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x]^2,
x] + 406791513450000000*Defer[Int][(x^2*Log[-3 + x]^7)/Log[x]^2, x] + 135597171150000000*Defer[Int][(x^3*Log[-
3 + x]^7)/Log[x]^2, x] + 45199057050000000*Defer[Int][(x^4*Log[-3 + x]^7)/Log[x]^2, x] + 15066352350000000*Def
er[Int][(x^5*Log[-3 + x]^7)/Log[x]^2, x] + 5022117450000000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x]^2, x] + 1674
039150000000*Defer[Int][(x^7*Log[-3 + x]^7)/Log[x]^2, x] + 558013050000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[
x]^2, x] + 186004350000000*Defer[Int][(x^9*Log[-3 + x]^7)/Log[x]^2, x] + 62001450000000*Defer[Int][(x^10*Log[-
3 + x]^7)/Log[x]^2, x] + 20667150000000*Defer[Int][(x^11*Log[-3 + x]^7)/Log[x]^2, x] + 6889050000000*Defer[Int
][(x^12*Log[-3 + x]^7)/Log[x]^2, x] + 2296350000000*Defer[Int][(x^13*Log[-3 + x]^7)/Log[x]^2, x] + 76545000000
0*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x]^2, x] + 255150000000*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x]^2, x] + 8
5050000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[x]^2, x] + 28350000000*Defer[Int][(x^17*Log[-3 + x]^7)/Log[x]^2
, x] + 9450000000*Defer[Int][(x^18*Log[-3 + x]^7)/Log[x]^2, x] + 3150000000*Defer[Int][(x^19*Log[-3 + x]^7)/Lo
g[x]^2, x] + 1050000000*Defer[Int][(x^20*Log[-3 + x]^7)/Log[x]^2, x] + 350000000*Defer[Int][(x^21*Log[-3 + x]^
7)/Log[x]^2, x] + 962500000*Defer[Int][(x^21*Log[-3 + x]^8)/Log[x]^2, x] - 6250000*Defer[Int][(x^22*Log[-3 + x
]^8)/Log[x]^2, x] + 1569052980450000000*Defer[Int][Log[-3 + x]^7/Log[x], x] + 4707158941350000000*Defer[Int][L
og[-3 + x]^7/((-3 + x)*Log[x]), x] + 523017660150000000*Defer[Int][(x*Log[-3 + x]^7)/Log[x], x] + 174339220050
000000*Defer[Int][(x^2*Log[-3 + x]^7)/Log[x], x] + 58113073350000000*Defer[Int][(x^3*Log[-3 + x]^7)/Log[x], x]
+ 19371024450000000*Defer[Int][(x^4*Log[-3 + x]^7)/Log[x], x] + 6457008150000000*Defer[Int][(x^5*Log[-3 + x]^
7)/Log[x], x] + 2152336050000000*Defer[Int][(x^6*Log[-3 + x]^7)/Log[x], x] + 717445350000000*Defer[Int][(x^7*L
og[-3 + x]^7)/Log[x], x] + 239148450000000*Defer[Int][(x^8*Log[-3 + x]^7)/Log[x], x] + 79716150000000*Defer[In
t][(x^9*Log[-3 + x]^7)/Log[x], x] + 26572050000000*Defer[Int][(x^10*Log[-3 + x]^7)/Log[x], x] + 8857350000000*
Defer[Int][(x^11*Log[-3 + x]^7)/Log[x], x] + 2952450000000*Defer[Int][(x^12*Log[-3 + x]^7)/Log[x], x] + 984150
000000*Defer[Int][(x^13*Log[-3 + x]^7)/Log[x], x] + 328050000000*Defer[Int][(x^14*Log[-3 + x]^7)/Log[x], x] +
109350000000*Defer[Int][(x^15*Log[-3 + x]^7)/Log[x], x] + 36450000000*Defer[Int][(x^16*Log[-3 + x]^7)/Log[x],
x] + 12150000000*Defer[Int][(x^17*Log[-3 + x]^7)/Log[x], x] + 4050000000*Defer[Int][(x^18*Log[-3 + x]^7)/Log[x
], x] + 1350000000*Defer[Int][(x^19*Log[-3 + x]^7)/Log[x], x] + 450000000*Defer[Int][(x^20*Log[-3 + x]^7)/Log[
x], x] + 150000000*Defer[Int][(x^21*Log[-3 + x]^7)/Log[x], x] + 50000000*Defer[Int][(x^22*Log[-3 + x]^7)/Log[x
], x] + 143750000*Defer[Int][(x^22*Log[-3 + x]^8)/Log[x], x]
Rubi steps
Aborted
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Mathematica [B] time = 5.17, size = 136, normalized size = 6.48 \begin {gather*} 3125000 \left (\frac {1}{8} x^{24} \log ^8(-3+x)+\frac {32 x^{16} \log ^8(-3+x)}{\log ^8(x)}+\frac {128 x^{17} \log ^8(-3+x)}{\log ^7(x)}+\frac {224 x^{18} \log ^8(-3+x)}{\log ^6(x)}+\frac {224 x^{19} \log ^8(-3+x)}{\log ^5(x)}+\frac {140 x^{20} \log ^8(-3+x)}{\log ^4(x)}+\frac {56 x^{21} \log ^8(-3+x)}{\log ^3(x)}+\frac {14 x^{22} \log ^8(-3+x)}{\log ^2(x)}+\frac {2 x^{23} \log ^8(-3+x)}{\log (x)}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((2400000000*x^15 - 800000000*x^16)*Log[-3 + x]^8 + (800000000*x^16*Log[-3 + x]^7 + (-4800000000*x^1
5 + 10000000000*x^16 - 2800000000*x^17)*Log[-3 + x]^8)*Log[x] + (3200000000*x^17*Log[-3 + x]^7 + (-20400000000
*x^16 + 19400000000*x^17 - 4200000000*x^18)*Log[-3 + x]^8)*Log[x]^2 + (5600000000*x^18*Log[-3 + x]^7 + (-37800
000000*x^17 + 23100000000*x^18 - 3500000000*x^19)*Log[-3 + x]^8)*Log[x]^3 + (5600000000*x^19*Log[-3 + x]^7 + (
-39900000000*x^18 + 18550000000*x^19 - 1750000000*x^20)*Log[-3 + x]^8)*Log[x]^4 + (3500000000*x^20*Log[-3 + x]
^7 + (-26250000000*x^19 + 10325000000*x^20 - 525000000*x^21)*Log[-3 + x]^8)*Log[x]^5 + (1400000000*x^21*Log[-3
+ x]^7 + (-11025000000*x^20 + 3937500000*x^21 - 87500000*x^22)*Log[-3 + x]^8)*Log[x]^6 + (350000000*x^22*Log[
-3 + x]^7 + (-2887500000*x^21 + 981250000*x^22 - 6250000*x^23)*Log[-3 + x]^8)*Log[x]^7 + (50000000*x^23*Log[-3
+ x]^7 + (-431250000*x^22 + 143750000*x^23)*Log[-3 + x]^8)*Log[x]^8 + (3125000*x^24*Log[-3 + x]^7 + (-2812500
0*x^23 + 9375000*x^24)*Log[-3 + x]^8)*Log[x]^9)/((-3 + x)*Log[x]^9),x]
[Out]
3125000*((x^24*Log[-3 + x]^8)/8 + (32*x^16*Log[-3 + x]^8)/Log[x]^8 + (128*x^17*Log[-3 + x]^8)/Log[x]^7 + (224*
x^18*Log[-3 + x]^8)/Log[x]^6 + (224*x^19*Log[-3 + x]^8)/Log[x]^5 + (140*x^20*Log[-3 + x]^8)/Log[x]^4 + (56*x^2
1*Log[-3 + x]^8)/Log[x]^3 + (14*x^22*Log[-3 + x]^8)/Log[x]^2 + (2*x^23*Log[-3 + x]^8)/Log[x])
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fricas [B] time = 0.83, size = 135, normalized size = 6.43 \begin {gather*} \frac {390625 \, {\left (x^{24} \log \left (x - 3\right )^{8} \log \relax (x)^{8} + 16 \, x^{23} \log \left (x - 3\right )^{8} \log \relax (x)^{7} + 112 \, x^{22} \log \left (x - 3\right )^{8} \log \relax (x)^{6} + 448 \, x^{21} \log \left (x - 3\right )^{8} \log \relax (x)^{5} + 1120 \, x^{20} \log \left (x - 3\right )^{8} \log \relax (x)^{4} + 1792 \, x^{19} \log \left (x - 3\right )^{8} \log \relax (x)^{3} + 1792 \, x^{18} \log \left (x - 3\right )^{8} \log \relax (x)^{2} + 1024 \, x^{17} \log \left (x - 3\right )^{8} \log \relax (x) + 256 \, x^{16} \log \left (x - 3\right )^{8}\right )}}{\log \relax (x)^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((9375000*x^24-28125000*x^23)*log(x-3)^8+3125000*x^24*log(x-3)^7)*log(x)^9+((143750000*x^23-4312500
00*x^22)*log(x-3)^8+50000000*x^23*log(x-3)^7)*log(x)^8+((-6250000*x^23+981250000*x^22-2887500000*x^21)*log(x-3
)^8+350000000*x^22*log(x-3)^7)*log(x)^7+((-87500000*x^22+3937500000*x^21-11025000000*x^20)*log(x-3)^8+14000000
00*x^21*log(x-3)^7)*log(x)^6+((-525000000*x^21+10325000000*x^20-26250000000*x^19)*log(x-3)^8+3500000000*x^20*l
og(x-3)^7)*log(x)^5+((-1750000000*x^20+18550000000*x^19-39900000000*x^18)*log(x-3)^8+5600000000*x^19*log(x-3)^
7)*log(x)^4+((-3500000000*x^19+23100000000*x^18-37800000000*x^17)*log(x-3)^8+5600000000*x^18*log(x-3)^7)*log(x
)^3+((-4200000000*x^18+19400000000*x^17-20400000000*x^16)*log(x-3)^8+3200000000*x^17*log(x-3)^7)*log(x)^2+((-2
800000000*x^17+10000000000*x^16-4800000000*x^15)*log(x-3)^8+800000000*x^16*log(x-3)^7)*log(x)+(-800000000*x^16
+2400000000*x^15)*log(x-3)^8)/(x-3)/log(x)^9,x, algorithm="fricas")
[Out]
390625*(x^24*log(x - 3)^8*log(x)^8 + 16*x^23*log(x - 3)^8*log(x)^7 + 112*x^22*log(x - 3)^8*log(x)^6 + 448*x^21
*log(x - 3)^8*log(x)^5 + 1120*x^20*log(x - 3)^8*log(x)^4 + 1792*x^19*log(x - 3)^8*log(x)^3 + 1792*x^18*log(x -
3)^8*log(x)^2 + 1024*x^17*log(x - 3)^8*log(x) + 256*x^16*log(x - 3)^8)/log(x)^8
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giac [B] time = 1.56, size = 84, normalized size = 4.00 \begin {gather*} 390625 \, {\left (x^{24} + \frac {16 \, {\left (x^{23} \log \relax (x)^{7} + 7 \, x^{22} \log \relax (x)^{6} + 28 \, x^{21} \log \relax (x)^{5} + 70 \, x^{20} \log \relax (x)^{4} + 112 \, x^{19} \log \relax (x)^{3} + 112 \, x^{18} \log \relax (x)^{2} + 64 \, x^{17} \log \relax (x) + 16 \, x^{16}\right )}}{\log \relax (x)^{8}}\right )} \log \left (x - 3\right )^{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((9375000*x^24-28125000*x^23)*log(x-3)^8+3125000*x^24*log(x-3)^7)*log(x)^9+((143750000*x^23-4312500
00*x^22)*log(x-3)^8+50000000*x^23*log(x-3)^7)*log(x)^8+((-6250000*x^23+981250000*x^22-2887500000*x^21)*log(x-3
)^8+350000000*x^22*log(x-3)^7)*log(x)^7+((-87500000*x^22+3937500000*x^21-11025000000*x^20)*log(x-3)^8+14000000
00*x^21*log(x-3)^7)*log(x)^6+((-525000000*x^21+10325000000*x^20-26250000000*x^19)*log(x-3)^8+3500000000*x^20*l
og(x-3)^7)*log(x)^5+((-1750000000*x^20+18550000000*x^19-39900000000*x^18)*log(x-3)^8+5600000000*x^19*log(x-3)^
7)*log(x)^4+((-3500000000*x^19+23100000000*x^18-37800000000*x^17)*log(x-3)^8+5600000000*x^18*log(x-3)^7)*log(x
)^3+((-4200000000*x^18+19400000000*x^17-20400000000*x^16)*log(x-3)^8+3200000000*x^17*log(x-3)^7)*log(x)^2+((-2
800000000*x^17+10000000000*x^16-4800000000*x^15)*log(x-3)^8+800000000*x^16*log(x-3)^7)*log(x)+(-800000000*x^16
+2400000000*x^15)*log(x-3)^8)/(x-3)/log(x)^9,x, algorithm="giac")
[Out]
390625*(x^24 + 16*(x^23*log(x)^7 + 7*x^22*log(x)^6 + 28*x^21*log(x)^5 + 70*x^20*log(x)^4 + 112*x^19*log(x)^3 +
112*x^18*log(x)^2 + 64*x^17*log(x) + 16*x^16)/log(x)^8)*log(x - 3)^8
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maple [B] time = 0.23, size = 85, normalized size = 4.05
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\(\frac {390625 x^{16} \left (x^{8} \ln \relax (x )^{8}+16 x^{7} \ln \relax (x )^{7}+112 x^{6} \ln \relax (x )^{6}+448 x^{5} \ln \relax (x )^{5}+1120 x^{4} \ln \relax (x )^{4}+1792 x^{3} \ln \relax (x )^{3}+1792 x^{2} \ln \relax (x )^{2}+1024 x \ln \relax (x )+256\right ) \ln \left (x -3\right )^{8}}{\ln \relax (x )^{8}}\) |
\(85\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((((9375000*x^24-28125000*x^23)*ln(x-3)^8+3125000*x^24*ln(x-3)^7)*ln(x)^9+((143750000*x^23-431250000*x^22)*
ln(x-3)^8+50000000*x^23*ln(x-3)^7)*ln(x)^8+((-6250000*x^23+981250000*x^22-2887500000*x^21)*ln(x-3)^8+350000000
*x^22*ln(x-3)^7)*ln(x)^7+((-87500000*x^22+3937500000*x^21-11025000000*x^20)*ln(x-3)^8+1400000000*x^21*ln(x-3)^
7)*ln(x)^6+((-525000000*x^21+10325000000*x^20-26250000000*x^19)*ln(x-3)^8+3500000000*x^20*ln(x-3)^7)*ln(x)^5+(
(-1750000000*x^20+18550000000*x^19-39900000000*x^18)*ln(x-3)^8+5600000000*x^19*ln(x-3)^7)*ln(x)^4+((-350000000
0*x^19+23100000000*x^18-37800000000*x^17)*ln(x-3)^8+5600000000*x^18*ln(x-3)^7)*ln(x)^3+((-4200000000*x^18+1940
0000000*x^17-20400000000*x^16)*ln(x-3)^8+3200000000*x^17*ln(x-3)^7)*ln(x)^2+((-2800000000*x^17+10000000000*x^1
6-4800000000*x^15)*ln(x-3)^8+800000000*x^16*ln(x-3)^7)*ln(x)+(-800000000*x^16+2400000000*x^15)*ln(x-3)^8)/(x-3
)/ln(x)^9,x,method=_RETURNVERBOSE)
[Out]
390625*x^16*(x^8*ln(x)^8+16*x^7*ln(x)^7+112*x^6*ln(x)^6+448*x^5*ln(x)^5+1120*x^4*ln(x)^4+1792*x^3*ln(x)^3+1792
*x^2*ln(x)^2+1024*x*ln(x)+256)/ln(x)^8*ln(x-3)^8
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maxima [B] time = 0.43, size = 87, normalized size = 4.14 \begin {gather*} \frac {390625 \, {\left (x^{24} \log \relax (x)^{8} + 16 \, x^{23} \log \relax (x)^{7} + 112 \, x^{22} \log \relax (x)^{6} + 448 \, x^{21} \log \relax (x)^{5} + 1120 \, x^{20} \log \relax (x)^{4} + 1792 \, x^{19} \log \relax (x)^{3} + 1792 \, x^{18} \log \relax (x)^{2} + 1024 \, x^{17} \log \relax (x) + 256 \, x^{16}\right )} \log \left (x - 3\right )^{8}}{\log \relax (x)^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((9375000*x^24-28125000*x^23)*log(x-3)^8+3125000*x^24*log(x-3)^7)*log(x)^9+((143750000*x^23-4312500
00*x^22)*log(x-3)^8+50000000*x^23*log(x-3)^7)*log(x)^8+((-6250000*x^23+981250000*x^22-2887500000*x^21)*log(x-3
)^8+350000000*x^22*log(x-3)^7)*log(x)^7+((-87500000*x^22+3937500000*x^21-11025000000*x^20)*log(x-3)^8+14000000
00*x^21*log(x-3)^7)*log(x)^6+((-525000000*x^21+10325000000*x^20-26250000000*x^19)*log(x-3)^8+3500000000*x^20*l
og(x-3)^7)*log(x)^5+((-1750000000*x^20+18550000000*x^19-39900000000*x^18)*log(x-3)^8+5600000000*x^19*log(x-3)^
7)*log(x)^4+((-3500000000*x^19+23100000000*x^18-37800000000*x^17)*log(x-3)^8+5600000000*x^18*log(x-3)^7)*log(x
)^3+((-4200000000*x^18+19400000000*x^17-20400000000*x^16)*log(x-3)^8+3200000000*x^17*log(x-3)^7)*log(x)^2+((-2
800000000*x^17+10000000000*x^16-4800000000*x^15)*log(x-3)^8+800000000*x^16*log(x-3)^7)*log(x)+(-800000000*x^16
+2400000000*x^15)*log(x-3)^8)/(x-3)/log(x)^9,x, algorithm="maxima")
[Out]
390625*(x^24*log(x)^8 + 16*x^23*log(x)^7 + 112*x^22*log(x)^6 + 448*x^21*log(x)^5 + 1120*x^20*log(x)^4 + 1792*x
^19*log(x)^3 + 1792*x^18*log(x)^2 + 1024*x^17*log(x) + 256*x^16)*log(x - 3)^8/log(x)^8
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mupad [B] time = 1.30, size = 132, normalized size = 6.29 \begin {gather*} 390625\,x^{24}\,{\ln \left (x-3\right )}^8+\frac {100000000\,x^{16}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^8}+\frac {400000000\,x^{17}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^7}+\frac {700000000\,x^{18}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^6}+\frac {700000000\,x^{19}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^5}+\frac {437500000\,x^{20}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^4}+\frac {175000000\,x^{21}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^3}+\frac {43750000\,x^{22}\,{\ln \left (x-3\right )}^8}{{\ln \relax (x)}^2}+\frac {6250000\,x^{23}\,{\ln \left (x-3\right )}^8}{\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(log(x)^3*(log(x - 3)^8*(37800000000*x^17 - 23100000000*x^18 + 3500000000*x^19) - 5600000000*x^18*log(x -
3)^7) + log(x)^4*(log(x - 3)^8*(39900000000*x^18 - 18550000000*x^19 + 1750000000*x^20) - 5600000000*x^19*log(
x - 3)^7) + log(x)^5*(log(x - 3)^8*(26250000000*x^19 - 10325000000*x^20 + 525000000*x^21) - 3500000000*x^20*lo
g(x - 3)^7) - log(x - 3)^8*(2400000000*x^15 - 800000000*x^16) + log(x)^9*(log(x - 3)^8*(28125000*x^23 - 937500
0*x^24) - 3125000*x^24*log(x - 3)^7) + log(x)^6*(log(x - 3)^8*(11025000000*x^20 - 3937500000*x^21 + 87500000*x
^22) - 1400000000*x^21*log(x - 3)^7) + log(x)*(log(x - 3)^8*(4800000000*x^15 - 10000000000*x^16 + 2800000000*x
^17) - 800000000*x^16*log(x - 3)^7) - log(x)^8*(50000000*x^23*log(x - 3)^7 - log(x - 3)^8*(431250000*x^22 - 14
3750000*x^23)) - log(x)^7*(350000000*x^22*log(x - 3)^7 - log(x - 3)^8*(2887500000*x^21 - 981250000*x^22 + 6250
000*x^23)) + log(x)^2*(log(x - 3)^8*(20400000000*x^16 - 19400000000*x^17 + 4200000000*x^18) - 3200000000*x^17*
log(x - 3)^7))/(log(x)^9*(x - 3)),x)
[Out]
390625*x^24*log(x - 3)^8 + (100000000*x^16*log(x - 3)^8)/log(x)^8 + (400000000*x^17*log(x - 3)^8)/log(x)^7 + (
700000000*x^18*log(x - 3)^8)/log(x)^6 + (700000000*x^19*log(x - 3)^8)/log(x)^5 + (437500000*x^20*log(x - 3)^8)
/log(x)^4 + (175000000*x^21*log(x - 3)^8)/log(x)^3 + (43750000*x^22*log(x - 3)^8)/log(x)^2 + (6250000*x^23*log
(x - 3)^8)/log(x)
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sympy [B] time = 1.16, size = 95, normalized size = 4.52 \begin {gather*} \frac {\left (390625 x^{24} \log {\relax (x )}^{8} + 6250000 x^{23} \log {\relax (x )}^{7} + 43750000 x^{22} \log {\relax (x )}^{6} + 175000000 x^{21} \log {\relax (x )}^{5} + 437500000 x^{20} \log {\relax (x )}^{4} + 700000000 x^{19} \log {\relax (x )}^{3} + 700000000 x^{18} \log {\relax (x )}^{2} + 400000000 x^{17} \log {\relax (x )} + 100000000 x^{16}\right ) \log {\left (x - 3 \right )}^{8}}{\log {\relax (x )}^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((((9375000*x**24-28125000*x**23)*ln(x-3)**8+3125000*x**24*ln(x-3)**7)*ln(x)**9+((143750000*x**23-431
250000*x**22)*ln(x-3)**8+50000000*x**23*ln(x-3)**7)*ln(x)**8+((-6250000*x**23+981250000*x**22-2887500000*x**21
)*ln(x-3)**8+350000000*x**22*ln(x-3)**7)*ln(x)**7+((-87500000*x**22+3937500000*x**21-11025000000*x**20)*ln(x-3
)**8+1400000000*x**21*ln(x-3)**7)*ln(x)**6+((-525000000*x**21+10325000000*x**20-26250000000*x**19)*ln(x-3)**8+
3500000000*x**20*ln(x-3)**7)*ln(x)**5+((-1750000000*x**20+18550000000*x**19-39900000000*x**18)*ln(x-3)**8+5600
000000*x**19*ln(x-3)**7)*ln(x)**4+((-3500000000*x**19+23100000000*x**18-37800000000*x**17)*ln(x-3)**8+56000000
00*x**18*ln(x-3)**7)*ln(x)**3+((-4200000000*x**18+19400000000*x**17-20400000000*x**16)*ln(x-3)**8+3200000000*x
**17*ln(x-3)**7)*ln(x)**2+((-2800000000*x**17+10000000000*x**16-4800000000*x**15)*ln(x-3)**8+800000000*x**16*l
n(x-3)**7)*ln(x)+(-800000000*x**16+2400000000*x**15)*ln(x-3)**8)/(x-3)/ln(x)**9,x)
[Out]
(390625*x**24*log(x)**8 + 6250000*x**23*log(x)**7 + 43750000*x**22*log(x)**6 + 175000000*x**21*log(x)**5 + 437
500000*x**20*log(x)**4 + 700000000*x**19*log(x)**3 + 700000000*x**18*log(x)**2 + 400000000*x**17*log(x) + 1000
00000*x**16)*log(x - 3)**8/log(x)**8
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