3.73.16 \(\int \frac {x^7 \log ^9(x)+e^{\frac {1048576+(6291456 x-2097152 x^2) \log (x)+(16515072 x^2-11010048 x^3+1835008 x^4) \log ^2(x)+(24772608 x^3-24772608 x^4+8257536 x^5-917504 x^6) \log ^3(x)+(23224320 x^4-30965760 x^5+15482880 x^6-3440640 x^7+286720 x^8) \log ^4(x)+(13934592 x^5-23224320 x^6+15482880 x^7-5160960 x^8+860160 x^9-57344 x^{10}) \log ^5(x)+(5225472 x^6-10450944 x^7+8709120 x^8-3870720 x^9+967680 x^{10}-129024 x^{11}+7168 x^{12}) \log ^6(x)+(1119744 x^7-2612736 x^8+2612736 x^9-1451520 x^{10}+483840 x^{11}-96768 x^{12}+10752 x^{13}-512 x^{14}) \log ^7(x)+(104977 x^8-279936 x^9+326592 x^{10}-217728 x^{11}+90720 x^{12}-24192 x^{13}+4032 x^{14}-384 x^{15}+16 x^{16}) \log ^8(x)}{x^7 \log ^8(x)}} (-8388608+(-7340032-44040192 x+14680064 x^2) \log (x)+(-37748736 x-88604672 x^2+66060288 x^3-11010048 x^4) \log ^2(x)+(-82575360 x^2-79822848 x^3+118358016 x^4-41287680 x^5+4587520 x^6) \log ^3(x)+(-99090432 x^3-18579456 x^4+107347968 x^5-61014016 x^6+13762560 x^7-1146880 x^8) \log ^4(x)+(-69672960 x^4+20127744 x^5+54190080 x^6-46448640 x^7+15769600 x^8-2580480 x^9+172032 x^{10}) \log ^5(x)+(-27869184 x^5+12773376 x^6+20901888 x^7-22579200 x^8+9461760 x^9-2107392 x^{10}+258048 x^{11}-14336 x^{12}) \log ^6(x)+(-5225472 x^6-1119744 x^7+11321856 x^8-10354176 x^9+4354560 x^{10}-999936 x^{11}+132608 x^{12}-10752 x^{13}+512 x^{14}) \log ^7(x)+(-2612736 x^8+5225472 x^9-4354560 x^{10}+1935360 x^{11}-483840 x^{12}+64512 x^{13}-3584 x^{14}) \log ^8(x)+(x^7+104977 x^8-559872 x^9+979776 x^{10}-870912 x^{11}+453600 x^{12}-145152 x^{13}+28224 x^{14}-3072 x^{15}+144 x^{16}) \log ^9(x))}{x^8 \log ^9(x)+e^{\frac {1048576+(6291456 x-2097152 x^2) \log (x)+(16515072 x^2-11010048 x^3+1835008 x^4) \log ^2(x)+(24772608 x^3-24772608 x^4+8257536 x^5-917504 x^6) \log ^3(x)+(23224320 x^4-30965760 x^5+15482880 x^6-3440640 x^7+286720 x^8) \log ^4(x)+(13934592 x^5-23224320 x^6+15482880 x^7-5160960 x^8+860160 x^9-57344 x^{10}) \log ^5(x)+(5225472 x^6-10450944 x^7+8709120 x^8-3870720 x^9+967680 x^{10}-129024 x^{11}+7168 x^{12}) \log ^6(x)+(1119744 x^7-2612736 x^8+2612736 x^9-1451520 x^{10}+483840 x^{11}-96768 x^{12}+10752 x^{13}-512 x^{14}) \log ^7(x)+(104977 x^8-279936 x^9+326592 x^{10}-217728 x^{11}+90720 x^{12}-24192 x^{13}+4032 x^{14}-384 x^{15}+16 x^{16}) \log ^8(x)}{x^7 \log ^8(x)}} x^8 \log ^9(x)} \, dx\)

Optimal. Leaf size=28 \[ \log \left (x+e^{x+16 x \left (3-x+\frac {4}{x \log (x)}\right )^8} x\right ) \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x^7*Log[x]^9 + E^((1048576 + (6291456*x - 2097152*x^2)*Log[x] + (16515072*x^2 - 11010048*x^3 + 1835008*x^
4)*Log[x]^2 + (24772608*x^3 - 24772608*x^4 + 8257536*x^5 - 917504*x^6)*Log[x]^3 + (23224320*x^4 - 30965760*x^5
+ 15482880*x^6 - 3440640*x^7 + 286720*x^8)*Log[x]^4 + (13934592*x^5 - 23224320*x^6 + 15482880*x^7 - 5160960*x
^8 + 860160*x^9 - 57344*x^10)*Log[x]^5 + (5225472*x^6 - 10450944*x^7 + 8709120*x^8 - 3870720*x^9 + 967680*x^10
- 129024*x^11 + 7168*x^12)*Log[x]^6 + (1119744*x^7 - 2612736*x^8 + 2612736*x^9 - 1451520*x^10 + 483840*x^11 -
96768*x^12 + 10752*x^13 - 512*x^14)*Log[x]^7 + (104977*x^8 - 279936*x^9 + 326592*x^10 - 217728*x^11 + 90720*x
^12 - 24192*x^13 + 4032*x^14 - 384*x^15 + 16*x^16)*Log[x]^8)/(x^7*Log[x]^8))*(-8388608 + (-7340032 - 44040192*
x + 14680064*x^2)*Log[x] + (-37748736*x - 88604672*x^2 + 66060288*x^3 - 11010048*x^4)*Log[x]^2 + (-82575360*x^
2 - 79822848*x^3 + 118358016*x^4 - 41287680*x^5 + 4587520*x^6)*Log[x]^3 + (-99090432*x^3 - 18579456*x^4 + 1073
47968*x^5 - 61014016*x^6 + 13762560*x^7 - 1146880*x^8)*Log[x]^4 + (-69672960*x^4 + 20127744*x^5 + 54190080*x^6
- 46448640*x^7 + 15769600*x^8 - 2580480*x^9 + 172032*x^10)*Log[x]^5 + (-27869184*x^5 + 12773376*x^6 + 2090188
8*x^7 - 22579200*x^8 + 9461760*x^9 - 2107392*x^10 + 258048*x^11 - 14336*x^12)*Log[x]^6 + (-5225472*x^6 - 11197
44*x^7 + 11321856*x^8 - 10354176*x^9 + 4354560*x^10 - 999936*x^11 + 132608*x^12 - 10752*x^13 + 512*x^14)*Log[x
]^7 + (-2612736*x^8 + 5225472*x^9 - 4354560*x^10 + 1935360*x^11 - 483840*x^12 + 64512*x^13 - 3584*x^14)*Log[x]
^8 + (x^7 + 104977*x^8 - 559872*x^9 + 979776*x^10 - 870912*x^11 + 453600*x^12 - 145152*x^13 + 28224*x^14 - 307
2*x^15 + 144*x^16)*Log[x]^9))/(x^8*Log[x]^9 + E^((1048576 + (6291456*x - 2097152*x^2)*Log[x] + (16515072*x^2 -
11010048*x^3 + 1835008*x^4)*Log[x]^2 + (24772608*x^3 - 24772608*x^4 + 8257536*x^5 - 917504*x^6)*Log[x]^3 + (2
3224320*x^4 - 30965760*x^5 + 15482880*x^6 - 3440640*x^7 + 286720*x^8)*Log[x]^4 + (13934592*x^5 - 23224320*x^6
+ 15482880*x^7 - 5160960*x^8 + 860160*x^9 - 57344*x^10)*Log[x]^5 + (5225472*x^6 - 10450944*x^7 + 8709120*x^8 -
3870720*x^9 + 967680*x^10 - 129024*x^11 + 7168*x^12)*Log[x]^6 + (1119744*x^7 - 2612736*x^8 + 2612736*x^9 - 14
51520*x^10 + 483840*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14)*Log[x]^7 + (104977*x^8 - 279936*x^9 + 326592*x^
10 - 217728*x^11 + 90720*x^12 - 24192*x^13 + 4032*x^14 - 384*x^15 + 16*x^16)*Log[x]^8)/(x^7*Log[x]^8))*x^8*Log
[x]^9),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [B]  time = 15.31, size = 154, normalized size = 5.50 \begin {gather*} \log \left (1+e^{104977 x-279936 x^2+326592 x^3-217728 x^4+90720 x^5-24192 x^6+4032 x^7-384 x^8+16 x^9+\frac {1048576}{x^7 \log ^8(x)}-\frac {2097152 (-3+x)}{x^6 \log ^7(x)}+\frac {1835008 (-3+x)^2}{x^5 \log ^6(x)}-\frac {917504 (-3+x)^3}{x^4 \log ^5(x)}+\frac {286720 (-3+x)^4}{x^3 \log ^4(x)}-\frac {57344 (-3+x)^5}{x^2 \log ^3(x)}+\frac {7168 (-3+x)^6}{x \log ^2(x)}-\frac {512 (-3+x)^7}{\log (x)}}\right )+\log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(x^7*Log[x]^9 + E^((1048576 + (6291456*x - 2097152*x^2)*Log[x] + (16515072*x^2 - 11010048*x^3 + 1835
008*x^4)*Log[x]^2 + (24772608*x^3 - 24772608*x^4 + 8257536*x^5 - 917504*x^6)*Log[x]^3 + (23224320*x^4 - 309657
60*x^5 + 15482880*x^6 - 3440640*x^7 + 286720*x^8)*Log[x]^4 + (13934592*x^5 - 23224320*x^6 + 15482880*x^7 - 516
0960*x^8 + 860160*x^9 - 57344*x^10)*Log[x]^5 + (5225472*x^6 - 10450944*x^7 + 8709120*x^8 - 3870720*x^9 + 96768
0*x^10 - 129024*x^11 + 7168*x^12)*Log[x]^6 + (1119744*x^7 - 2612736*x^8 + 2612736*x^9 - 1451520*x^10 + 483840*
x^11 - 96768*x^12 + 10752*x^13 - 512*x^14)*Log[x]^7 + (104977*x^8 - 279936*x^9 + 326592*x^10 - 217728*x^11 + 9
0720*x^12 - 24192*x^13 + 4032*x^14 - 384*x^15 + 16*x^16)*Log[x]^8)/(x^7*Log[x]^8))*(-8388608 + (-7340032 - 440
40192*x + 14680064*x^2)*Log[x] + (-37748736*x - 88604672*x^2 + 66060288*x^3 - 11010048*x^4)*Log[x]^2 + (-82575
360*x^2 - 79822848*x^3 + 118358016*x^4 - 41287680*x^5 + 4587520*x^6)*Log[x]^3 + (-99090432*x^3 - 18579456*x^4
+ 107347968*x^5 - 61014016*x^6 + 13762560*x^7 - 1146880*x^8)*Log[x]^4 + (-69672960*x^4 + 20127744*x^5 + 541900
80*x^6 - 46448640*x^7 + 15769600*x^8 - 2580480*x^9 + 172032*x^10)*Log[x]^5 + (-27869184*x^5 + 12773376*x^6 + 2
0901888*x^7 - 22579200*x^8 + 9461760*x^9 - 2107392*x^10 + 258048*x^11 - 14336*x^12)*Log[x]^6 + (-5225472*x^6 -
1119744*x^7 + 11321856*x^8 - 10354176*x^9 + 4354560*x^10 - 999936*x^11 + 132608*x^12 - 10752*x^13 + 512*x^14)
*Log[x]^7 + (-2612736*x^8 + 5225472*x^9 - 4354560*x^10 + 1935360*x^11 - 483840*x^12 + 64512*x^13 - 3584*x^14)*
Log[x]^8 + (x^7 + 104977*x^8 - 559872*x^9 + 979776*x^10 - 870912*x^11 + 453600*x^12 - 145152*x^13 + 28224*x^14
- 3072*x^15 + 144*x^16)*Log[x]^9))/(x^8*Log[x]^9 + E^((1048576 + (6291456*x - 2097152*x^2)*Log[x] + (16515072
*x^2 - 11010048*x^3 + 1835008*x^4)*Log[x]^2 + (24772608*x^3 - 24772608*x^4 + 8257536*x^5 - 917504*x^6)*Log[x]^
3 + (23224320*x^4 - 30965760*x^5 + 15482880*x^6 - 3440640*x^7 + 286720*x^8)*Log[x]^4 + (13934592*x^5 - 2322432
0*x^6 + 15482880*x^7 - 5160960*x^8 + 860160*x^9 - 57344*x^10)*Log[x]^5 + (5225472*x^6 - 10450944*x^7 + 8709120
*x^8 - 3870720*x^9 + 967680*x^10 - 129024*x^11 + 7168*x^12)*Log[x]^6 + (1119744*x^7 - 2612736*x^8 + 2612736*x^
9 - 1451520*x^10 + 483840*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14)*Log[x]^7 + (104977*x^8 - 279936*x^9 + 326
592*x^10 - 217728*x^11 + 90720*x^12 - 24192*x^13 + 4032*x^14 - 384*x^15 + 16*x^16)*Log[x]^8)/(x^7*Log[x]^8))*x
^8*Log[x]^9),x]

[Out]

Log[1 + E^(104977*x - 279936*x^2 + 326592*x^3 - 217728*x^4 + 90720*x^5 - 24192*x^6 + 4032*x^7 - 384*x^8 + 16*x
^9 + 1048576/(x^7*Log[x]^8) - (2097152*(-3 + x))/(x^6*Log[x]^7) + (1835008*(-3 + x)^2)/(x^5*Log[x]^6) - (91750
4*(-3 + x)^3)/(x^4*Log[x]^5) + (286720*(-3 + x)^4)/(x^3*Log[x]^4) - (57344*(-3 + x)^5)/(x^2*Log[x]^3) + (7168*
(-3 + x)^6)/(x*Log[x]^2) - (512*(-3 + x)^7)/Log[x])] + Log[x]

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fricas [B]  time = 0.55, size = 274, normalized size = 9.79 \begin {gather*} \log \relax (x) + \log \left (e^{\left (\frac {{\left (16 \, x^{16} - 384 \, x^{15} + 4032 \, x^{14} - 24192 \, x^{13} + 90720 \, x^{12} - 217728 \, x^{11} + 326592 \, x^{10} - 279936 \, x^{9} + 104977 \, x^{8}\right )} \log \relax (x)^{8} - 512 \, {\left (x^{14} - 21 \, x^{13} + 189 \, x^{12} - 945 \, x^{11} + 2835 \, x^{10} - 5103 \, x^{9} + 5103 \, x^{8} - 2187 \, x^{7}\right )} \log \relax (x)^{7} + 7168 \, {\left (x^{12} - 18 \, x^{11} + 135 \, x^{10} - 540 \, x^{9} + 1215 \, x^{8} - 1458 \, x^{7} + 729 \, x^{6}\right )} \log \relax (x)^{6} - 57344 \, {\left (x^{10} - 15 \, x^{9} + 90 \, x^{8} - 270 \, x^{7} + 405 \, x^{6} - 243 \, x^{5}\right )} \log \relax (x)^{5} + 286720 \, {\left (x^{8} - 12 \, x^{7} + 54 \, x^{6} - 108 \, x^{5} + 81 \, x^{4}\right )} \log \relax (x)^{4} - 917504 \, {\left (x^{6} - 9 \, x^{5} + 27 \, x^{4} - 27 \, x^{3}\right )} \log \relax (x)^{3} + 1835008 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \relax (x)^{2} - 2097152 \, {\left (x^{2} - 3 \, x\right )} \log \relax (x) + 1048576}{x^{7} \log \relax (x)^{8}}\right )} + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((144*x^16-3072*x^15+28224*x^14-145152*x^13+453600*x^12-870912*x^11+979776*x^10-559872*x^9+104977*x
^8+x^7)*log(x)^9+(-3584*x^14+64512*x^13-483840*x^12+1935360*x^11-4354560*x^10+5225472*x^9-2612736*x^8)*log(x)^
8+(512*x^14-10752*x^13+132608*x^12-999936*x^11+4354560*x^10-10354176*x^9+11321856*x^8-1119744*x^7-5225472*x^6)
*log(x)^7+(-14336*x^12+258048*x^11-2107392*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^
5)*log(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20127744*x^5-69672960*x^4)*log(x)^
5+(-1146880*x^8+13762560*x^7-61014016*x^6+107347968*x^5-18579456*x^4-99090432*x^3)*log(x)^4+(4587520*x^6-41287
680*x^5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+66060288*x^3-88604672*x^2-37748736*x)
*log(x)^2+(14680064*x^2-44040192*x-7340032)*log(x)-8388608)*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^7*log(x)^9)/(x^8*log(x)^9*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorithm="fricas")

[Out]

log(x) + log(e^(((16*x^16 - 384*x^15 + 4032*x^14 - 24192*x^13 + 90720*x^12 - 217728*x^11 + 326592*x^10 - 27993
6*x^9 + 104977*x^8)*log(x)^8 - 512*(x^14 - 21*x^13 + 189*x^12 - 945*x^11 + 2835*x^10 - 5103*x^9 + 5103*x^8 - 2
187*x^7)*log(x)^7 + 7168*(x^12 - 18*x^11 + 135*x^10 - 540*x^9 + 1215*x^8 - 1458*x^7 + 729*x^6)*log(x)^6 - 5734
4*(x^10 - 15*x^9 + 90*x^8 - 270*x^7 + 405*x^6 - 243*x^5)*log(x)^5 + 286720*(x^8 - 12*x^7 + 54*x^6 - 108*x^5 +
81*x^4)*log(x)^4 - 917504*(x^6 - 9*x^5 + 27*x^4 - 27*x^3)*log(x)^3 + 1835008*(x^4 - 6*x^3 + 9*x^2)*log(x)^2 -
2097152*(x^2 - 3*x)*log(x) + 1048576)/(x^7*log(x)^8)) + 1)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((144*x^16-3072*x^15+28224*x^14-145152*x^13+453600*x^12-870912*x^11+979776*x^10-559872*x^9+104977*x
^8+x^7)*log(x)^9+(-3584*x^14+64512*x^13-483840*x^12+1935360*x^11-4354560*x^10+5225472*x^9-2612736*x^8)*log(x)^
8+(512*x^14-10752*x^13+132608*x^12-999936*x^11+4354560*x^10-10354176*x^9+11321856*x^8-1119744*x^7-5225472*x^6)
*log(x)^7+(-14336*x^12+258048*x^11-2107392*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^
5)*log(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20127744*x^5-69672960*x^4)*log(x)^
5+(-1146880*x^8+13762560*x^7-61014016*x^6+107347968*x^5-18579456*x^4-99090432*x^3)*log(x)^4+(4587520*x^6-41287
680*x^5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+66060288*x^3-88604672*x^2-37748736*x)
*log(x)^2+(14680064*x^2-44040192*x-7340032)*log(x)-8388608)*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^7*log(x)^9)/(x^8*log(x)^9*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [B]  time = 0.13, size = 1045, normalized size = 37.32

method	result	size
risch	\(16 x^{9}-384 x^{8}+4032 x^{7}-24192 x^{6}+90720 x^{5}-217728 x^{4}+326592 x^{3}-279936 x^{2}+104977 x +\ln \relax (x )-\frac {512 \left (-2048-27216 x^{5} \ln \relax (x )^{5}+45360 x^{6} \ln \relax (x )^{5}-10206 x^{6} \ln \relax (x )^{6}-30240 x^{7} \ln \relax (x )^{5}+20412 x^{7} \ln \relax (x )^{6}-2187 x^{7} \ln \relax (x )^{7}+10080 x^{8} \ln \relax (x )^{5}-17010 x^{8} \ln \relax (x )^{6}+5103 x^{8} \ln \relax (x )^{7}-1680 x^{9} \ln \relax (x )^{5}+7560 x^{9} \ln \relax (x )^{6}-5103 x^{9} \ln \relax (x )^{7}+112 x^{10} \ln \relax (x )^{5}-1890 x^{10} \ln \relax (x )^{6}+2835 x^{10} \ln \relax (x )^{7}+252 x^{11} \ln \relax (x )^{6}-945 x^{11} \ln \relax (x )^{7}-14 x^{12} \ln \relax (x )^{6}+189 x^{12} \ln \relax (x )^{7}-21 x^{13} \ln \relax (x )^{7}+4096 x^{2} \ln \relax (x )-30240 x^{6} \ln \relax (x )^{4}+6720 x^{7} \ln \relax (x )^{4}-32256 x^{2} \ln \relax (x )^{2}+48384 x^{4} \ln \relax (x )^{3}+1792 x^{6} \ln \relax (x )^{3}-16128 x^{5} \ln \relax (x )^{3}-48384 x^{3} \ln \relax (x )^{3}-3584 x^{4} \ln \relax (x )^{2}-12288 x \ln \relax (x )+60480 x^{5} \ln \relax (x )^{4}-560 x^{8} \ln \relax (x )^{4}-45360 x^{4} \ln \relax (x )^{4}+21504 x^{3} \ln \relax (x )^{2}+\ln \relax (x )^{7} x^{14}\right )}{x^{7} \ln \relax (x )^{8}}-\frac {\left (16 x^{16}-384 x^{15}+4032 x^{14}-24192 x^{13}+90720 x^{12}-217728 x^{11}+326592 x^{10}-279936 x^{9}+104977 x^{8}\right ) \ln \relax (x )^{8}+\left (-512 x^{14}+10752 x^{13}-96768 x^{12}+483840 x^{11}-1451520 x^{10}+2612736 x^{9}-2612736 x^{8}+1119744 x^{7}\right ) \ln \relax (x )^{7}+\left (7168 x^{12}-129024 x^{11}+967680 x^{10}-3870720 x^{9}+8709120 x^{8}-10450944 x^{7}+5225472 x^{6}\right ) \ln \relax (x )^{6}+\left (-57344 x^{10}+860160 x^{9}-5160960 x^{8}[phone] x^{7}-23224320 x^{6}[phone] x^{5}\right ) \ln \relax (x )^{5}+\left (286720 x^{8}-3440640 x^{7}[phone] x^{6}-30965760 x^{5}[phone] x^{4}\right ) \ln \relax (x )^{4}+\left (-917504 x^{6}+8257536 x^{5}-24772608 x^{4}[phone] x^{3}\right ) \ln \relax (x )^{3}+\left (1835008 x^{4}-11010048 x^{3}[phone] x^{2}\right ) \ln \relax (x )^{2}+\left (-2097152 x^{2}+6291456 x \right ) \ln \relax (x )+1048576}{x^{7} \ln \relax (x )^{8}}+\ln \left ({\mathrm e}^{\frac {1048576-24192 x^{13} \ln \relax (x )^{8}[phone] x^{5} \ln \relax (x )^{5}-23224320 x^{6} \ln \relax (x )^{5}+5225472 x^{6} \ln \relax (x )^{6}[phone] x^{7} \ln \relax (x )^{5}-10450944 x^{7} \ln \relax (x )^{6}+1119744 x^{7} \ln \relax (x )^{7}-5160960 x^{8} \ln \relax (x )^{5}+8709120 x^{8} \ln \relax (x )^{6}-2612736 x^{8} \ln \relax (x )^{7}+860160 x^{9} \ln \relax (x )^{5}+104977 x^{8} \ln \relax (x )^{8}-3870720 x^{9} \ln \relax (x )^{6}+2612736 x^{9} \ln \relax (x )^{7}-57344 x^{10} \ln \relax (x )^{5}-279936 x^{9} \ln \relax (x )^{8}+967680 x^{10} \ln \relax (x )^{6}-1451520 x^{10} \ln \relax (x )^{7}+326592 x^{10} \ln \relax (x )^{8}-129024 x^{11} \ln \relax (x )^{6}+483840 x^{11} \ln \relax (x )^{7}-217728 x^{11} \ln \relax (x )^{8}+7168 x^{12} \ln \relax (x )^{6}-96768 x^{12} \ln \relax (x )^{7}+90720 x^{12} \ln \relax (x )^{8}+10752 x^{13} \ln \relax (x )^{7}-2097152 x^{2} \ln \relax (x )[phone] x^{6} \ln \relax (x )^{4}-3440640 x^{7} \ln \relax (x )^{4}[phone] x^{2} \ln \relax (x )^{2}-24772608 x^{4} \ln \relax (x )^{3}-917504 x^{6} \ln \relax (x )^{3}+8257536 x^{5} \ln \relax (x )^{3}[phone] x^{3} \ln \relax (x )^{3}+1835008 x^{4} \ln \relax (x )^{2}+6291456 x \ln \relax (x )-30965760 x^{5} \ln \relax (x )^{4}+286720 x^{8} \ln \relax (x )^{4}[phone] x^{4} \ln \relax (x )^{4}-11010048 x^{3} \ln \relax (x )^{2}+16 \ln \relax (x )^{8} x^{16}-384 \ln \relax (x )^{8} x^{15}+4032 \ln \relax (x )^{8} x^{14}-512 \ln \relax (x )^{7} x^{14}}{x^{7} \ln \relax (x )^{8}}}+1\right )\)	\(1045\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((144*x^16-3072*x^15+28224*x^14-145152*x^13+453600*x^12-870912*x^11+979776*x^10-559872*x^9+104977*x^8+x^7
)*ln(x)^9+(-3584*x^14+64512*x^13-483840*x^12+1935360*x^11-4354560*x^10+5225472*x^9-2612736*x^8)*ln(x)^8+(512*x
^14-10752*x^13+132608*x^12-999936*x^11+4354560*x^10-10354176*x^9+11321856*x^8-1119744*x^7-5225472*x^6)*ln(x)^7
+(-14336*x^12+258048*x^11-2107392*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^5)*ln(x)^
6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20127744*x^5-69672960*x^4)*ln(x)^5+(-1146880
*x^8+13762560*x^7-61014016*x^6+107347968*x^5-18579456*x^4-99090432*x^3)*ln(x)^4+(4587520*x^6-41287680*x^5+1183
58016*x^4-79822848*x^3-82575360*x^2)*ln(x)^3+(-11010048*x^4+66060288*x^3-88604672*x^2-37748736*x)*ln(x)^2+(146
80064*x^2-44040192*x-7340032)*ln(x)-8388608)*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*x^12-217728*x^1
1+326592*x^10-279936*x^9+104977*x^8)*ln(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451520*x^10+2612736
*x^9-2612736*x^8+1119744*x^7)*ln(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*x^8-10450944*x^7+
5225472*x^6)*ln(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*x^5)*ln(x)^5+(2867
20*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*ln(x)^4+(-917504*x^6+8257536*x^5-24772608*x^4+24772
608*x^3)*ln(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*ln(x)^2+(-2097152*x^2+6291456*x)*ln(x)+1048576)/x^7/l
n(x)^8)+x^7*ln(x)^9)/(x^8*ln(x)^9*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*x^12-217728*x^11+326592*x^
10-279936*x^9+104977*x^8)*ln(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451520*x^10+2612736*x^9-261273
6*x^8+1119744*x^7)*ln(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*x^8-10450944*x^7+5225472*x^6
)*ln(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*x^5)*ln(x)^5+(286720*x^8-3440
640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*ln(x)^4+(-917504*x^6+8257536*x^5-24772608*x^4+24772608*x^3)*ln
(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*ln(x)^2+(-2097152*x^2+6291456*x)*ln(x)+1048576)/x^7/ln(x)^8)+x^8
*ln(x)^9),x,method=_RETURNVERBOSE)

[Out]

16*x^9-384*x^8+4032*x^7-24192*x^6+90720*x^5-217728*x^4+326592*x^3-279936*x^2+104977*x+ln(x)-512*(-2048-27216*x
^5*ln(x)^5+45360*x^6*ln(x)^5-10206*x^6*ln(x)^6-30240*x^7*ln(x)^5+20412*x^7*ln(x)^6-2187*x^7*ln(x)^7+10080*x^8*
ln(x)^5-17010*x^8*ln(x)^6+5103*x^8*ln(x)^7-1680*x^9*ln(x)^5+7560*x^9*ln(x)^6-5103*x^9*ln(x)^7+112*x^10*ln(x)^5
-1890*x^10*ln(x)^6+2835*x^10*ln(x)^7+252*x^11*ln(x)^6-945*x^11*ln(x)^7-14*x^12*ln(x)^6+189*x^12*ln(x)^7-21*x^1
3*ln(x)^7+4096*x^2*ln(x)-30240*x^6*ln(x)^4+6720*x^7*ln(x)^4-32256*x^2*ln(x)^2+48384*x^4*ln(x)^3+1792*x^6*ln(x)
^3-16128*x^5*ln(x)^3-48384*x^3*ln(x)^3-3584*x^4*ln(x)^2-12288*x*ln(x)+60480*x^5*ln(x)^4-560*x^8*ln(x)^4-45360*
x^4*ln(x)^4+21504*x^3*ln(x)^2+ln(x)^7*x^14)/x^7/ln(x)^8-((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*x^12-217
728*x^11+326592*x^10-279936*x^9+104977*x^8)*ln(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451520*x^10+
2612736*x^9-2612736*x^8+1119744*x^7)*ln(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*x^8-104509
44*x^7+5225472*x^6)*ln(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*x^5)*ln(x)^
5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*ln(x)^4+(-917504*x^6+8257536*x^5-24772608*x^
4+24772608*x^3)*ln(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*ln(x)^2+(-2097152*x^2+6291456*x)*ln(x)+1048576
)/x^7/ln(x)^8+ln(exp((1048576-24192*x^13*ln(x)^8+13934592*x^5*ln(x)^5-23224320*x^6*ln(x)^5+5225472*x^6*ln(x)^6
[phone]*x^7*ln(x)^5-10450944*x^7*ln(x)^6+1119744*x^7*ln(x)^7-5160960*x^8*ln(x)^5+8709120*x^8*ln(x)^6-2612736
*x^8*ln(x)^7+860160*x^9*ln(x)^5+104977*x^8*ln(x)^8-3870720*x^9*ln(x)^6+2612736*x^9*ln(x)^7-57344*x^10*ln(x)^5-
279936*x^9*ln(x)^8+967680*x^10*ln(x)^6-1451520*x^10*ln(x)^7+326592*x^10*ln(x)^8-129024*x^11*ln(x)^6+483840*x^1
1*ln(x)^7-217728*x^11*ln(x)^8+7168*x^12*ln(x)^6-96768*x^12*ln(x)^7+90720*x^12*ln(x)^8+10752*x^13*ln(x)^7-20971
52*x^2*ln(x)[phone]*x^6*ln(x)^4-3440640*x^7*ln(x)^4+16515072*x^2*ln(x)^2-24772608*x^4*ln(x)^3-917504*x^6*ln(
x)^3+8257536*x^5*ln(x)^3+24772608*x^3*ln(x)^3+1835008*x^4*ln(x)^2+6291456*x*ln(x)-30965760*x^5*ln(x)^4+286720*
x^8*ln(x)^4+23224320*x^4*ln(x)^4-11010048*x^3*ln(x)^2+16*ln(x)^8*x^16-384*ln(x)^8*x^15+4032*ln(x)^8*x^14-512*l
n(x)^7*x^14)/x^7/ln(x)^8)+1)

________________________________________________________________________________________

maxima [B]  time = 1.61, size = 807, normalized size = 28.82 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((144*x^16-3072*x^15+28224*x^14-145152*x^13+453600*x^12-870912*x^11+979776*x^10-559872*x^9+104977*x
^8+x^7)*log(x)^9+(-3584*x^14+64512*x^13-483840*x^12+1935360*x^11-4354560*x^10+5225472*x^9-2612736*x^8)*log(x)^
8+(512*x^14-10752*x^13+132608*x^12-999936*x^11+4354560*x^10-10354176*x^9+11321856*x^8-1119744*x^7-5225472*x^6)
*log(x)^7+(-14336*x^12+258048*x^11-2107392*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^
5)*log(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20127744*x^5-69672960*x^4)*log(x)^
5+(-1146880*x^8+13762560*x^7-61014016*x^6+107347968*x^5-18579456*x^4-99090432*x^3)*log(x)^4+(4587520*x^6-41287
680*x^5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+66060288*x^3-88604672*x^2-37748736*x)
*log(x)^2+(14680064*x^2-44040192*x-7340032)*log(x)-8388608)*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^7*log(x)^9)/(x^8*log(x)^9*exp(((16*x^16-384*x^15+4032*x^14-24192*x^13+90720*
x^12-217728*x^11+326592*x^10-279936*x^9+104977*x^8)*log(x)^8+(-512*x^14+10752*x^13-96768*x^12+483840*x^11-1451
520*x^10+2612736*x^9-2612736*x^8+1119744*x^7)*log(x)^7+(7168*x^12-129024*x^11+967680*x^10-3870720*x^9+8709120*
x^8-10450944*x^7+5225472*x^6)*log(x)^6+(-57344*x^10+860160*x^9-5160960*x^8+15482880*x^7-23224320*x^6+13934592*
x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^
5-24772608*x^4+24772608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-2097152*x^2+6291456*x
)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorithm="maxima")

[Out]

((16*x^16 - 384*x^15 + 4032*x^14 - 24192*x^13 + 90720*x^12 - 217728*x^11 + 326592*x^10 - 279936*x^9 + 104977*x
^8)*log(x)^8 - 512*(x^14 - 21*x^13 + 189*x^12 - 945*x^11 + 2835*x^10 - 5103*x^9 + 5103*x^8 - 2187*x^7)*log(x)^
7 - 64512*(2*x^11 - 15*x^10 + 60*x^9 - 135*x^8 + 162*x^7 - 81*x^6)*log(x)^6 - 57344*(x^10 - 15*x^9 + 90*x^8 -
270*x^7 + 405*x^6 - 243*x^5)*log(x)^5 + 286720*(x^8 - 12*x^7 + 54*x^6 - 108*x^5 + 81*x^4)*log(x)^4 - 917504*(x
^6 - 9*x^5 + 27*x^4 - 27*x^3)*log(x)^3 + 1835008*(x^4 - 6*x^3 + 9*x^2)*log(x)^2 - 2097152*(x^2 - 3*x)*log(x) +
1048576)/(x^7*log(x)^8) + log((e^(16*x^9 + 4032*x^7 + 90720*x^5 + 10752*x^6/log(x) + 326592*x^3 + 7168*x^5/lo
g(x)^2 + 483840*x^4/log(x) + 104977*x + 967680*x^3/log(x)^2 + 2612736*x^2/log(x) + 860160*x^2/log(x)^3 + 87091
20*x/log(x)^2 + 1119744/log(x) + 286720*x/log(x)^4 + 15482880/log(x)^3 + 5225472/(x*log(x)^2) + 15482880/(x*lo
g(x)^4) + 13934592/(x^2*log(x)^3) + 8257536/(x^2*log(x)^5) + 23224320/(x^3*log(x)^4) + 1835008/(x^3*log(x)^6)
+ 24772608/(x^4*log(x)^5) + 16515072/(x^5*log(x)^6) + 6291456/(x^6*log(x)^7) + 1048576/(x^7*log(x)^8)) + e^(38
4*x^8 + 24192*x^6 + 512*x^7/log(x) + 217728*x^4 + 96768*x^5/log(x) + 279936*x^2 + 129024*x^4/log(x)^2 + 145152
0*x^3/log(x) + 57344*x^3/log(x)^3 + 3870720*x^2/log(x)^2 + 2612736*x/log(x) + 5160960*x/log(x)^3 + 10450944/lo
g(x)^2 + 3440640/log(x)^4 + 23224320/(x*log(x)^3) + 917504/(x*log(x)^5) + 30965760/(x^2*log(x)^4) + 24772608/(
x^3*log(x)^5) + 11010048/(x^4*log(x)^6) + 2097152/(x^5*log(x)^7)))*e^(-16*x^9 - 4032*x^7 - 90720*x^5 - 10752*x
^6/log(x) - 326592*x^3 - 483840*x^4/log(x) - 104977*x - 967680*x^3/log(x)^2 - 2612736*x^2/log(x) - 860160*x^2/
log(x)^3 - 8709120*x/log(x)^2 - 1119744/log(x) - 286720*x/log(x)^4 - 15482880/log(x)^3 - 5225472/(x*log(x)^2)
- 15482880/(x*log(x)^4) - 13934592/(x^2*log(x)^3) - 8257536/(x^2*log(x)^5) - 23224320/(x^3*log(x)^4) - 1835008
/(x^3*log(x)^6) - 24772608/(x^4*log(x)^5) - 16515072/(x^5*log(x)^6) - 6291456/(x^6*log(x)^7) - 1048576/(x^7*lo
g(x)^8))) + log(x)

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mupad [B]  time = 7.22, size = 399, normalized size = 14.25 \begin {gather*} \ln \left ({\mathrm {e}}^{\frac {1119744}{\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {3440640}{{\ln \relax (x)}^4}}\,{\mathrm {e}}^{-\frac {10450944}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {15482880}{{\ln \relax (x)}^3}}\,{\mathrm {e}}^{104977\,x}\,{\mathrm {e}}^{\frac {286720\,x}{{\ln \relax (x)}^4}}\,{\mathrm {e}}^{-\frac {2612736\,x}{\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {5160960\,x}{{\ln \relax (x)}^3}}\,{\mathrm {e}}^{\frac {8709120\,x}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{16\,x^9}\,{\mathrm {e}}^{-384\,x^8}\,{\mathrm {e}}^{4032\,x^7}\,{\mathrm {e}}^{-24192\,x^6}\,{\mathrm {e}}^{90720\,x^5}\,{\mathrm {e}}^{-217728\,x^4}\,{\mathrm {e}}^{-279936\,x^2}\,{\mathrm {e}}^{326592\,x^3}\,{\mathrm {e}}^{-\frac {512\,x^7}{\ln \relax (x)}}\,{\mathrm {e}}^{\frac {7168\,x^5}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {10752\,x^6}{\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {57344\,x^3}{{\ln \relax (x)}^3}}\,{\mathrm {e}}^{-\frac {96768\,x^5}{\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {129024\,x^4}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {483840\,x^4}{\ln \relax (x)}}\,{\mathrm {e}}^{\frac {860160\,x^2}{{\ln \relax (x)}^3}}\,{\mathrm {e}}^{-\frac {917504}{x\,{\ln \relax (x)}^5}}\,{\mathrm {e}}^{\frac {967680\,x^3}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {1048576}{x^7\,{\ln \relax (x)}^8}}\,{\mathrm {e}}^{-\frac {1451520\,x^3}{\ln \relax (x)}}\,{\mathrm {e}}^{\frac {1835008}{x^3\,{\ln \relax (x)}^6}}\,{\mathrm {e}}^{-\frac {2097152}{x^5\,{\ln \relax (x)}^7}}\,{\mathrm {e}}^{\frac {2612736\,x^2}{\ln \relax (x)}}\,{\mathrm {e}}^{-\frac {3870720\,x^2}{{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {5225472}{x\,{\ln \relax (x)}^2}}\,{\mathrm {e}}^{\frac {6291456}{x^6\,{\ln \relax (x)}^7}}\,{\mathrm {e}}^{\frac {8257536}{x^2\,{\ln \relax (x)}^5}}\,{\mathrm {e}}^{-\frac {11010048}{x^4\,{\ln \relax (x)}^6}}\,{\mathrm {e}}^{\frac {13934592}{x^2\,{\ln \relax (x)}^3}}\,{\mathrm {e}}^{\frac {15482880}{x\,{\ln \relax (x)}^4}}\,{\mathrm {e}}^{\frac {16515072}{x^5\,{\ln \relax (x)}^6}}\,{\mathrm {e}}^{-\frac {23224320}{x\,{\ln \relax (x)}^3}}\,{\mathrm {e}}^{\frac {23224320}{x^3\,{\ln \relax (x)}^4}}\,{\mathrm {e}}^{-\frac {24772608}{x^3\,{\ln \relax (x)}^5}}\,{\mathrm {e}}^{\frac {24772608}{x^4\,{\ln \relax (x)}^5}}\,{\mathrm {e}}^{-\frac {30965760}{x^2\,{\ln \relax (x)}^4}}+1\right )+\ln \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((log(x)^4*(23224320*x^4 - 30965760*x^5 + 15482880*x^6 - 3440640*x^7 + 286720*x^8) + log(x)^5*(139345
92*x^5 - 23224320*x^6 + 15482880*x^7 - 5160960*x^8 + 860160*x^9 - 57344*x^10) + log(x)^6*(5225472*x^6 - 104509
44*x^7 + 8709120*x^8 - 3870720*x^9 + 967680*x^10 - 129024*x^11 + 7168*x^12) + log(x)^2*(16515072*x^2 - 1101004
8*x^3 + 1835008*x^4) + log(x)*(6291456*x - 2097152*x^2) + log(x)^7*(1119744*x^7 - 2612736*x^8 + 2612736*x^9 -
1451520*x^10 + 483840*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14) + log(x)^3*(24772608*x^3 - 24772608*x^4 + 825
7536*x^5 - 917504*x^6) + log(x)^8*(104977*x^8 - 279936*x^9 + 326592*x^10 - 217728*x^11 + 90720*x^12 - 24192*x^
13 + 4032*x^14 - 384*x^15 + 16*x^16) + 1048576)/(x^7*log(x)^8))*(log(x)^3*(82575360*x^2 + 79822848*x^3 - 11835
8016*x^4 + 41287680*x^5 - 4587520*x^6) + log(x)^4*(99090432*x^3 + 18579456*x^4 - 107347968*x^5 + 61014016*x^6
- 13762560*x^7 + 1146880*x^8) + log(x)^8*(2612736*x^8 - 5225472*x^9 + 4354560*x^10 - 1935360*x^11 + 483840*x^1
2 - 64512*x^13 + 3584*x^14) + log(x)^2*(37748736*x + 88604672*x^2 - 66060288*x^3 + 11010048*x^4) - log(x)^5*(2
0127744*x^5 - 69672960*x^4 + 54190080*x^6 - 46448640*x^7 + 15769600*x^8 - 2580480*x^9 + 172032*x^10) + log(x)*
(44040192*x - 14680064*x^2 + 7340032) + log(x)^6*(27869184*x^5 - 12773376*x^6 - 20901888*x^7 + 22579200*x^8 -
9461760*x^9 + 2107392*x^10 - 258048*x^11 + 14336*x^12) - log(x)^9*(x^7 + 104977*x^8 - 559872*x^9 + 979776*x^10
- 870912*x^11 + 453600*x^12 - 145152*x^13 + 28224*x^14 - 3072*x^15 + 144*x^16) + log(x)^7*(5225472*x^6 + 1119
744*x^7 - 11321856*x^8 + 10354176*x^9 - 4354560*x^10 + 999936*x^11 - 132608*x^12 + 10752*x^13 - 512*x^14) + 83
88608) - x^7*log(x)^9)/(x^8*log(x)^9 + x^8*exp((log(x)^4*(23224320*x^4 - 30965760*x^5 + 15482880*x^6 - 3440640
*x^7 + 286720*x^8) + log(x)^5*(13934592*x^5 - 23224320*x^6 + 15482880*x^7 - 5160960*x^8 + 860160*x^9 - 57344*x
^10) + log(x)^6*(5225472*x^6 - 10450944*x^7 + 8709120*x^8 - 3870720*x^9 + 967680*x^10 - 129024*x^11 + 7168*x^1
2) + log(x)^2*(16515072*x^2 - 11010048*x^3 + 1835008*x^4) + log(x)*(6291456*x - 2097152*x^2) + log(x)^7*(11197
44*x^7 - 2612736*x^8 + 2612736*x^9 - 1451520*x^10 + 483840*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14) + log(x)
^3*(24772608*x^3 - 24772608*x^4 + 8257536*x^5 - 917504*x^6) + log(x)^8*(104977*x^8 - 279936*x^9 + 326592*x^10
- 217728*x^11 + 90720*x^12 - 24192*x^13 + 4032*x^14 - 384*x^15 + 16*x^16) + 1048576)/(x^7*log(x)^8))*log(x)^9)
,x)

[Out]

log(exp(1119744/log(x))*exp(-3440640/log(x)^4)*exp(-10450944/log(x)^2)*exp(15482880/log(x)^3)*exp(104977*x)*ex
p((286720*x)/log(x)^4)*exp(-(2612736*x)/log(x))*exp(-(5160960*x)/log(x)^3)*exp((8709120*x)/log(x)^2)*exp(16*x^
9)*exp(-384*x^8)*exp(4032*x^7)*exp(-24192*x^6)*exp(90720*x^5)*exp(-217728*x^4)*exp(-279936*x^2)*exp(326592*x^3
)*exp(-(512*x^7)/log(x))*exp((7168*x^5)/log(x)^2)*exp((10752*x^6)/log(x))*exp(-(57344*x^3)/log(x)^3)*exp(-(967
68*x^5)/log(x))*exp(-(129024*x^4)/log(x)^2)*exp((483840*x^4)/log(x))*exp((860160*x^2)/log(x)^3)*exp(-917504/(x
*log(x)^5))*exp((967680*x^3)/log(x)^2)*exp(1048576/(x^7*log(x)^8))*exp(-(1451520*x^3)/log(x))*exp(1835008/(x^3
*log(x)^6))*exp(-2097152/(x^5*log(x)^7))*exp((2612736*x^2)/log(x))*exp(-(3870720*x^2)/log(x)^2)*exp(5225472/(x
*log(x)^2))*exp(6291456/(x^6*log(x)^7))*exp(8257536/(x^2*log(x)^5))*exp(-11010048/(x^4*log(x)^6))*exp(13934592
/(x^2*log(x)^3))*exp(15482880/(x*log(x)^4))*exp(16515072/(x^5*log(x)^6))*exp(-23224320/(x*log(x)^3))*exp(23224
320/(x^3*log(x)^4))*exp(-24772608/(x^3*log(x)^5))*exp(24772608/(x^4*log(x)^5))*exp(-30965760/(x^2*log(x)^4)) +
1) + log(x)

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sympy [B]  time = 10.48, size = 279, normalized size = 9.96 \begin {gather*} \log {\relax (x )} + \log {\left (e^{\frac {\left (- 2097152 x^{2} + 6291456 x\right ) \log {\relax (x )} + \left (1835008 x^{4} - 11010048 x^{3} + 16515072 x^{2}\right ) \log {\relax (x )}^{2} + \left (- 917504 x^{6} + 8257536 x^{5} - 24772608 x^{4} + 24772608 x^{3}\right ) \log {\relax (x )}^{3} + \left (286720 x^{8} - 3440640 x^{7} + 15482880 x^{6} - 30965760 x^{5} + 23224320 x^{4}\right ) \log {\relax (x )}^{4} + \left (- 57344 x^{10} + 860160 x^{9} - 5160960 x^{8} + 15482880 x^{7} - 23224320 x^{6} + 13934592 x^{5}\right ) \log {\relax (x )}^{5} + \left (7168 x^{12} - 129024 x^{11} + 967680 x^{10} - 3870720 x^{9} + 8709120 x^{8} - 10450944 x^{7} + 5225472 x^{6}\right ) \log {\relax (x )}^{6} + \left (- 512 x^{14} + 10752 x^{13} - 96768 x^{12} + 483840 x^{11} - 1451520 x^{10} + 2612736 x^{9} - 2612736 x^{8} + 1119744 x^{7}\right ) \log {\relax (x )}^{7} + \left (16 x^{16} - 384 x^{15} + 4032 x^{14} - 24192 x^{13} + 90720 x^{12} - 217728 x^{11} + 326592 x^{10} - 279936 x^{9} + 104977 x^{8}\right ) \log {\relax (x )}^{8} + 1048576}{x^{7} \log {\relax (x )}^{8}}} + 1 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((144*x**16-3072*x**15+28224*x**14-145152*x**13+453600*x**12-870912*x**11+979776*x**10-559872*x**9+
104977*x**8+x**7)*ln(x)**9+(-3584*x**14+64512*x**13-483840*x**12+1935360*x**11-4354560*x**10+5225472*x**9-2612
736*x**8)*ln(x)**8+(512*x**14-10752*x**13+132608*x**12-999936*x**11+4354560*x**10-10354176*x**9+11321856*x**8-
1119744*x**7-5225472*x**6)*ln(x)**7+(-14336*x**12+258048*x**11-2107392*x**10+9461760*x**9-22579200*x**8+209018
88*x**7+12773376*x**6-27869184*x**5)*ln(x)**6+(172032*x**10-2580480*x**9+15769600*x**8-46448640*x**7+54190080*
x**6+20127744*x**5-69672960*x**4)*ln(x)**5+(-1146880*x**8+13762560*x**7-61014016*x**6+107347968*x**5-18579456*
x**4-99090432*x**3)*ln(x)**4+(4587520*x**6-41287680*x**5+118358016*x**4-79822848*x**3-82575360*x**2)*ln(x)**3+
(-11010048*x**4+66060288*x**3-88604672*x**2-37748736*x)*ln(x)**2+(14680064*x**2-44040192*x-7340032)*ln(x)-8388
608)*exp(((16*x**16-384*x**15+4032*x**14-24192*x**13+90720*x**12-217728*x**11+326592*x**10-279936*x**9+104977*
x**8)*ln(x)**8+(-512*x**14+10752*x**13-96768*x**12+483840*x**11-1451520*x**10+2612736*x**9-2612736*x**8+111974
4*x**7)*ln(x)**7+(7168*x**12-129024*x**11+967680*x**10-3870720*x**9+8709120*x**8-10450944*x**7+5225472*x**6)*l
n(x)**6+(-57344*x**10+860160*x**9-5160960*x**8+15482880*x**7-23224320*x**6+13934592*x**5)*ln(x)**5+(286720*x**
8-3440640*x**7+15482880*x**6-30965760*x**5+23224320*x**4)*ln(x)**4+(-917504*x**6+8257536*x**5-24772608*x**4+24
772608*x**3)*ln(x)**3+(1835008*x**4-11010048*x**3+16515072*x**2)*ln(x)**2+(-2097152*x**2+6291456*x)*ln(x)+1048
576)/x**7/ln(x)**8)+x**7*ln(x)**9)/(x**8*ln(x)**9*exp(((16*x**16-384*x**15+4032*x**14-24192*x**13+90720*x**12-
217728*x**11+326592*x**10-279936*x**9+104977*x**8)*ln(x)**8+(-512*x**14+10752*x**13-96768*x**12+483840*x**11-1
451520*x**10+2612736*x**9-2612736*x**8+1119744*x**7)*ln(x)**7+(7168*x**12-129024*x**11+967680*x**10-3870720*x*
*9+8709120*x**8-10450944*x**7+5225472*x**6)*ln(x)**6+(-57344*x**10+860160*x**9-5160960*x**8+15482880*x**7-2322
4320*x**6+13934592*x**5)*ln(x)**5+(286720*x**8-3440640*x**7+15482880*x**6-30965760*x**5+23224320*x**4)*ln(x)**
4+(-917504*x**6+8257536*x**5-24772608*x**4+24772608*x**3)*ln(x)**3+(1835008*x**4-11010048*x**3+16515072*x**2)*
ln(x)**2+(-2097152*x**2+6291456*x)*ln(x)+1048576)/x**7/ln(x)**8)+x**8*ln(x)**9),x)

[Out]

log(x) + log(exp(((-2097152*x**2 + 6291456*x)*log(x) + (1835008*x**4 - 11010048*x**3 + 16515072*x**2)*log(x)**
2 + (-917504*x**6 + 8257536*x**5 - 24772608*x**4 + 24772608*x**3)*log(x)**3 + (286720*x**8 - 3440640*x**7 + 15
482880*x**6 - 30965760*x**5 + 23224320*x**4)*log(x)**4 + (-57344*x**10 + 860160*x**9 - 5160960*x**8 + 15482880
*x**7 - 23224320*x**6 + 13934592*x**5)*log(x)**5 + (7168*x**12 - 129024*x**11 + 967680*x**10 - 3870720*x**9 +
8709120*x**8 - 10450944*x**7 + 5225472*x**6)*log(x)**6 + (-512*x**14 + 10752*x**13 - 96768*x**12 + 483840*x**1
1 - 1451520*x**10 + 2612736*x**9 - 2612736*x**8 + 1119744*x**7)*log(x)**7 + (16*x**16 - 384*x**15 + 4032*x**14
- 24192*x**13 + 90720*x**12 - 217728*x**11 + 326592*x**10 - 279936*x**9 + 104977*x**8)*log(x)**8 + 1048576)/(
x**7*log(x)**8)) + 1)

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