Integrand size = 921, antiderivative size = 28 \[ \text {the integral} =\log \left (x+e^{x+16 x \left (3-x+\frac {4}{x \log (x)}\right )^8} x\right ) \]
Leaf count is larger than twice the leaf count of optimal. \(154\) vs. \(2(28)=56\).
Time = 15.48 (sec) , antiderivative size = 154, normalized size of antiderivative = 5.50 \[ \text {the integral} =\log \left (1+e^{104977 x-279936 x^2+326592 x^3-217728 x^4+90720 x^5-24192 x^6+4032 x^7-384 x^8+16 x^9+\frac {1048576}{x^7 \log ^8(x)}-\frac {2097152 (-3+x)}{x^6 \log ^7(x)}+\frac {1835008 (-3+x)^2}{x^5 \log ^6(x)}-\frac {917504 (-3+x)^3}{x^4 \log ^5(x)}+\frac {286720 (-3+x)^4}{x^3 \log ^4(x)}-\frac {57344 (-3+x)^5}{x^2 \log ^3(x)}+\frac {7168 (-3+x)^6}{x \log ^2(x)}-\frac {512 (-3+x)^7}{\log (x)}}\right )+\log (x) \]
Integrate[(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 - 24 772608*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 + 2612 736*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 + 107347968*x^5 - 61014016*x^6 + 13762560*x^7 - 1146880*x^8)*Log[x]^4 + (-69672960*x^4 + 20127744*x^5 + 54190080*x^6 - 4 6448640*x^7 + 15769600*x^8 - 2580480*x^9 + 172032*x^10)*Log[x]^5 + (-27869 184*x^5 + 12773376*x^6 + 20901888*x^7 - 22579200*x^8 + 9461760*x^9 - 21073 92*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 - 14 5152*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 - 3440 640*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 - 1045 0944*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 + 4 83840*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]
Log[1 + E^(104977*x - 279936*x^2 + 326592*x^3 - 217728*x^4 + 90720*x^5 - 2 4192*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) - (917504* (-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]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {x^7 \log ^9(x)+e^{\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 ^8(x)+\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 ^7(x)+\left (7168 x^{12}-129024 x^{11}+967680 x^{10}-3870720 x^9+8709120 x^8-10450944 x^7+5225472 x^6\right ) \log ^6(x)+\left (-57344 x^{10}+860160 x^9-5160960 x^8+15482880 x^7-23224320 x^6+13934592 x^5\right ) \log ^5(x)+\left (286720 x^8-3440640 x^7+15482880 x^6-30965760 x^5+23224320 x^4\right ) \log ^4(x)+\left (-917504 x^6+8257536 x^5-24772608 x^4+24772608 x^3\right ) \log ^3(x)+\left (1835008 x^4-11010048 x^3+16515072 x^2\right ) \log ^2(x)+\left (6291456 x-2097152 x^2\right ) \log (x)+1048576}{x^7 \log ^8(x)}} \left (\left (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\right ) \log ^9(x)+\left (-3584 x^{14}+64512 x^{13}-483840 x^{12}+1935360 x^{11}-4354560 x^{10}+5225472 x^9-2612736 x^8\right ) \log ^8(x)+\left (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\right ) \log ^7(x)+\left (-14336 x^{12}+258048 x^{11}-2107392 x^{10}+9461760 x^9-22579200 x^8+20901888 x^7+12773376 x^6-27869184 x^5\right ) \log ^6(x)+\left (172032 x^{10}-2580480 x^9+15769600 x^8-46448640 x^7+54190080 x^6+20127744 x^5-69672960 x^4\right ) \log ^5(x)+\left (-1146880 x^8+13762560 x^7-61014016 x^6+107347968 x^5-18579456 x^4-99090432 x^3\right ) \log ^4(x)+\left (4587520 x^6-41287680 x^5+118358016 x^4-79822848 x^3-82575360 x^2\right ) \log ^3(x)+\left (-11010048 x^4+66060288 x^3-88604672 x^2-37748736 x\right ) \log ^2(x)+\left (14680064 x^2-44040192 x-7340032\right ) \log (x)-8388608\right )}{e^{\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 ^8(x)+\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 ^7(x)+\left (7168 x^{12}-129024 x^{11}+967680 x^{10}-3870720 x^9+8709120 x^8-10450944 x^7+5225472 x^6\right ) \log ^6(x)+\left (-57344 x^{10}+860160 x^9-5160960 x^8+15482880 x^7-23224320 x^6+13934592 x^5\right ) \log ^5(x)+\left (286720 x^8-3440640 x^7+15482880 x^6-30965760 x^5+23224320 x^4\right ) \log ^4(x)+\left (-917504 x^6+8257536 x^5-24772608 x^4+24772608 x^3\right ) \log ^3(x)+\left (1835008 x^4-11010048 x^3+16515072 x^2\right ) \log ^2(x)+\left (6291456 x-2097152 x^2\right ) \log (x)+1048576}{x^7 \log ^8(x)}} x^8 \log ^9(x)+x^8 \log ^9(x)} \, dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \frac {x^7 \log ^9(x)+e^{\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 ^8(x)+\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 ^7(x)+\left (7168 x^{12}-129024 x^{11}+967680 x^{10}-3870720 x^9+8709120 x^8-10450944 x^7+5225472 x^6\right ) \log ^6(x)+\left (-57344 x^{10}+860160 x^9-5160960 x^8+15482880 x^7-23224320 x^6+13934592 x^5\right ) \log ^5(x)+\left (286720 x^8-3440640 x^7+15482880 x^6-30965760 x^5+23224320 x^4\right ) \log ^4(x)+\left (-917504 x^6+8257536 x^5-24772608 x^4+24772608 x^3\right ) \log ^3(x)+\left (1835008 x^4-11010048 x^3+16515072 x^2\right ) \log ^2(x)+\left (6291456 x-2097152 x^2\right ) \log (x)+1048576}{x^7 \log ^8(x)}} \left (\left (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\right ) \log ^9(x)+\left (-3584 x^{14}+64512 x^{13}-483840 x^{12}+1935360 x^{11}-4354560 x^{10}+5225472 x^9-2612736 x^8\right ) \log ^8(x)+\left (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\right ) \log ^7(x)+\left (-14336 x^{12}+258048 x^{11}-2107392 x^{10}+9461760 x^9-22579200 x^8+20901888 x^7+12773376 x^6-27869184 x^5\right ) \log ^6(x)+\left (172032 x^{10}-2580480 x^9+15769600 x^8-46448640 x^7+54190080 x^6+20127744 x^5-69672960 x^4\right ) \log ^5(x)+\left (-1146880 x^8+13762560 x^7-61014016 x^6+107347968 x^5-18579456 x^4-99090432 x^3\right ) \log ^4(x)+\left (4587520 x^6-41287680 x^5+118358016 x^4-79822848 x^3-82575360 x^2\right ) \log ^3(x)+\left (-11010048 x^4+66060288 x^3-88604672 x^2-37748736 x\right ) \log ^2(x)+\left (14680064 x^2-44040192 x-7340032\right ) \log (x)-8388608\right )}{e^{\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 ^8(x)+\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 ^7(x)+\left (7168 x^{12}-129024 x^{11}+967680 x^{10}-3870720 x^9+8709120 x^8-10450944 x^7+5225472 x^6\right ) \log ^6(x)+\left (-57344 x^{10}+860160 x^9-5160960 x^8+15482880 x^7-23224320 x^6+13934592 x^5\right ) \log ^5(x)+\left (286720 x^8-3440640 x^7+15482880 x^6-30965760 x^5+23224320 x^4\right ) \log ^4(x)+\left (-917504 x^6+8257536 x^5-24772608 x^4+24772608 x^3\right ) \log ^3(x)+\left (1835008 x^4-11010048 x^3+16515072 x^2\right ) \log ^2(x)+\left (6291456 x-2097152 x^2\right ) \log (x)+1048576}{x^7 \log ^8(x)}} x^8 \log ^9(x)+x^8 \log ^9(x)}dx\) |
Int[(x^7*Log[x]^9 + E^((1048576 + (6291456*x - 2097152*x^2)*Log[x] + (1651 5072*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 - 23224 320*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 - 1 29024*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))*(-8 388608 + (-7340032 - 44040192*x + 14680064*x^2)*Log[x] + (-37748736*x - 88 604672*x^2 + 66060288*x^3 - 11010048*x^4)*Log[x]^2 + (-82575360*x^2 - 7982 2848*x^3 + 118358016*x^4 - 41287680*x^5 + 4587520*x^6)*Log[x]^3 + (-990904 32*x^3 - 18579456*x^4 + 107347968*x^5 - 61014016*x^6 + 13762560*x^7 - 1146 880*x^8)*Log[x]^4 + (-69672960*x^4 + 20127744*x^5 + 54190080*x^6 - 4644864 0*x^7 + 15769600*x^8 - 2580480*x^9 + 172032*x^10)*Log[x]^5 + (-27869184*x^ 5 + 12773376*x^6 + 20901888*x^7 - 22579200*x^8 + 9461760*x^9 - 2107392*x^1 0 + 258048*x^11 - 14336*x^12)*Log[x]^6 + (-5225472*x^6 - 1119744*x^7 + 113 21856*x^8 - 10354176*x^9 + 4354560*x^10 - 999936*x^11 + 132608*x^12 - 1075 2*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 + 10 4977*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^((10 48576 + (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 - 91750 4*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 - 5 160960*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)*Lo g[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 - 3 84*x^15 + 16*x^16)*Log[x]^8)/(x^7*Log[x]^8))*x^8*Log[x]^9),x]
3.13.16.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(1044\) vs. \(2(27)=54\).
Time = 0.27 (sec) , antiderivative size = 1045, normalized size of antiderivative = 37.32
\[\text {Expression too large to display}\]
int((((144*x^16-3072*x^15+28224*x^14-145152*x^13+453600*x^12-870912*x^11+9 79776*x^10-559872*x^9+104977*x^8+x^7)*ln(x)^9+(-3584*x^14+64512*x^13-48384 0*x^12+1935360*x^11-4354560*x^10+5225472*x^9-2612736*x^8)*ln(x)^8+(512*x^1 4-10752*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+9 461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^5)*ln(x)^6+(1 72032*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^3-8860467 2*x^2-37748736*x)*ln(x)^2+(14680064*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^11+326592 *x^10-279936*x^9+104977*x^8)*ln(x)^8+(-512*x^14+10752*x^13-96768*x^12+4838 40*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+1 3934592*x^5)*ln(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-30965760*x^5+232 24320*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^7*ln(x)^9)/(x^8*ln(x)^9*exp(((16*x^16-38 4*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+1119744*x^7)*ln(x)^7+(7168*x^12-129024*x^11+96 7680*x^10-3870720*x^9+8709120*x^8-10450944*x^7+5225472*x^6)*ln(x)^6+(-5734 4*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)+x^8*ln(x)^9),x)
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+48384*x^4*ln(x)^3+252*x^11*ln(x)^6-945*x^11*l n(x)^7-14*x^12*ln(x)^6+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+45360*x^6*ln(x)^5-10206*x^6*ln(x)^6-30 240*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)^5-27216*x^5*ln(x)^5+6720*x^7* ln(x)^4-30240*x^6*ln(x)^4+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)^4-4536 0*x^4*ln(x)^4+21504*x^3*ln(x)^2-32256*x^2*ln(x)^2+4096*x^2*ln(x)+189*x^12* ln(x)^7-21*x^13*ln(x)^7+ln(x)^7*x^14)/x^7/ln(x)^8-((16*x^16-384*x^15+4032* x^14-24192*x^13+90720*x^12-217728*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+1119744*x^7)*ln(x)^7+(7168*x^12-129024*x^11+967680*x^10-38 70720*x^9+8709120*x^8-10450944*x^7+5225472*x^6)*ln(x)^6+(-57344*x^10+86016 0*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((1048576-24772608*x^4*ln(x)^3+326592*x^10*ln(x)^8-129024*x^11*ln( x)^6+483840*x^11*ln(x)^7-217728*x^11*ln(x)^8+7168*x^12*ln(x)^6+104977*x...
Leaf count of result is larger than twice the leaf count of optimal. 274 vs. \(2 (25) = 50\).
Time = 0.29 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.79 \[ \text {the integral} =\log \left (x\right ) + \log \left (e^{\left (\frac {{\left (16 \, x^{16} - 384 \, x^{15} + 4032 \, x^{14} - 24192 \, x^{13} + 90720 \, x^{12} - 217728 \, x^{11} + 326592 \, x^{10} - 279936 \, x^{9} + 104977 \, x^{8}\right )} \log \left (x\right )^{8} - 512 \, {\left (x^{14} - 21 \, x^{13} + 189 \, x^{12} - 945 \, x^{11} + 2835 \, x^{10} - 5103 \, x^{9} + 5103 \, x^{8} - 2187 \, x^{7}\right )} \log \left (x\right )^{7} + 7168 \, {\left (x^{12} - 18 \, x^{11} + 135 \, x^{10} - 540 \, x^{9} + 1215 \, x^{8} - 1458 \, x^{7} + 729 \, x^{6}\right )} \log \left (x\right )^{6} - 57344 \, {\left (x^{10} - 15 \, x^{9} + 90 \, x^{8} - 270 \, x^{7} + 405 \, x^{6} - 243 \, x^{5}\right )} \log \left (x\right )^{5} + 286720 \, {\left (x^{8} - 12 \, x^{7} + 54 \, x^{6} - 108 \, x^{5} + 81 \, x^{4}\right )} \log \left (x\right )^{4} - 917504 \, {\left (x^{6} - 9 \, x^{5} + 27 \, x^{4} - 27 \, x^{3}\right )} \log \left (x\right )^{3} + 1835008 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (x\right )^{2} - 2097152 \, {\left (x^{2} - 3 \, x\right )} \log \left (x\right ) + 1048576}{x^{7} \log \left (x\right )^{8}}\right )} + 1\right ) \]
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^1 3-483840*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+113 21856*x^8-1119744*x^7-5225472*x^6)*log(x)^7+(-14336*x^12+258048*x^11-21073 92*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^5)*l og(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20 127744*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^6-41287680*x^ 5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+6606028 8*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^12-217 728*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^11-1451520*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^8-104509 44*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^11-1451520*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^7-23 224320*x^6+13934592*x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-309 65760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^5-24772608*x^4+247 72608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-209 7152*x^2+6291456*x)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorit hm=\
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 - 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 - 218 7*x^7)*log(x)^7 + 7168*(x^12 - 18*x^11 + 135*x^10 - 540*x^9 + 1215*x^8 - 1 458*x^7 + 729*x^6)*log(x)^6 - 57344*(x^10 - 15*x^9 + 90*x^8 - 270*x^7 + 40 5*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)
Leaf count of result is larger than twice the leaf count of optimal. 279 vs. \(2 (22) = 44\).
Time = 2.89 (sec) , antiderivative size = 279, normalized size of antiderivative = 9.96 \[ \text {the integral} =\log {\left (x \right )} + \log {\left (e^{\frac {\left (- 2097152 x^{2} + 6291456 x\right ) \log {\left (x \right )} + \left (1835008 x^{4} - 11010048 x^{3} + 16515072 x^{2}\right ) \log {\left (x \right )}^{2} + \left (- 917504 x^{6} + 8257536 x^{5} - 24772608 x^{4} + 24772608 x^{3}\right ) \log {\left (x \right )}^{3} + \left (286720 x^{8} - 3440640 x^{7} + 15482880 x^{6} - 30965760 x^{5} + 23224320 x^{4}\right ) \log {\left (x \right )}^{4} + \left (- 57344 x^{10} + 860160 x^{9} - 5160960 x^{8} + 15482880 x^{7} - 23224320 x^{6} + 13934592 x^{5}\right ) \log {\left (x \right )}^{5} + \left (7168 x^{12} - 129024 x^{11} + 967680 x^{10} - 3870720 x^{9} + 8709120 x^{8} - 10450944 x^{7} + 5225472 x^{6}\right ) \log {\left (x \right )}^{6} + \left (- 512 x^{14} + 10752 x^{13} - 96768 x^{12} + 483840 x^{11} - 1451520 x^{10} + 2612736 x^{9} - 2612736 x^{8} + 1119744 x^{7}\right ) \log {\left (x \right )}^{7} + \left (16 x^{16} - 384 x^{15} + 4032 x^{14} - 24192 x^{13} + 90720 x^{12} - 217728 x^{11} + 326592 x^{10} - 279936 x^{9} + 104977 x^{8}\right ) \log {\left (x \right )}^{8} + 1048576}{x^{7} \log {\left (x \right )}^{8}}} + 1 \right )} \]
integrate((((144*x**16-3072*x**15+28224*x**14-145152*x**13+453600*x**12-87 0912*x**11+979776*x**10-559872*x**9+104977*x**8+x**7)*ln(x)**9+(-3584*x**1 4+64512*x**13-483840*x**12+1935360*x**11-4354560*x**10+5225472*x**9-261273 6*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+(-14 336*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+15769 600*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**4-9 9090432*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)-8388608)*exp (((16*x**16-384*x**15+4032*x**14-24192*x**13+90720*x**12-217728*x**11+3265 92*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**8-104 50944*x**7+5225472*x**6)*ln(x)**6+(-57344*x**10+860160*x**9-5160960*x**8+1 5482880*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+82575 36*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**7*ln(x)**9)/(x**8*ln(x)**9*exp(((16*x**16-384*x**15+4032*x**14-24 192*x**13+90720*x**12-217728*x**11+326592*x**10-279936*x**9+104977*x**8)*l n(x)**8+(-512*x**14+10752*x**13-96768*x**12+483840*x**11-1451520*x**10+261 2736*x**9-2612736*x**8+1119744*x**7)*ln(x)**7+(7168*x**12-129024*x**11+967 680*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**8-3440640*x**7+15482880*x**6-30965760*x**5+2322 4320*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)
log(x) + log(exp(((-2097152*x**2 + 6291456*x)*log(x) + (1835008*x**4 - 110 10048*x**3 + 16515072*x**2)*log(x)**2 + (-917504*x**6 + 8257536*x**5 - 247 72608*x**4 + 24772608*x**3)*log(x)**3 + (286720*x**8 - 3440640*x**7 + 1548 2880*x**6 - 30965760*x**5 + 23224320*x**4)*log(x)**4 + (-57344*x**10 + 860 160*x**9 - 5160960*x**8 + 15482880*x**7 - 23224320*x**6 + 13934592*x**5)*l og(x)**5 + (7168*x**12 - 129024*x**11 + 967680*x**10 - 3870720*x**9 + 8709 120*x**8 - 10450944*x**7 + 5225472*x**6)*log(x)**6 + (-512*x**14 + 10752*x **13 - 96768*x**12 + 483840*x**11 - 1451520*x**10 + 2612736*x**9 - 2612736 *x**8 + 1119744*x**7)*log(x)**7 + (16*x**16 - 384*x**15 + 4032*x**14 - 241 92*x**13 + 90720*x**12 - 217728*x**11 + 326592*x**10 - 279936*x**9 + 10497 7*x**8)*log(x)**8 + 1048576)/(x**7*log(x)**8)) + 1)
Leaf count of result is larger than twice the leaf count of optimal. 807 vs. \(2 (25) = 50\).
Time = 1.35 (sec) , antiderivative size = 807, normalized size of antiderivative = 28.82 \[ \text {the integral} =\text {Too large to display} \]
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^1 3-483840*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+113 21856*x^8-1119744*x^7-5225472*x^6)*log(x)^7+(-14336*x^12+258048*x^11-21073 92*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^5)*l og(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20 127744*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^6-41287680*x^ 5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+6606028 8*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^12-217 728*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^11-1451520*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^8-104509 44*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^11-1451520*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^7-23 224320*x^6+13934592*x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-309 65760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^5-24772608*x^4+247 72608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-209 7152*x^2+6291456*x)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorit hm=\
((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 + 1 89*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/log(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 + 8709120*x/log(x)^2 + 1119744/log(x) + 286720*x/lo g(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*log(x)^8)) + e^(384*x^8 + 24 192*x^6 + 512*x^7/log(x) + 217728*x^4 + 96768*x^5/log(x) + 279936*x^2 + 12 9024*x^4/log(x)^2 + 1451520*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/log(x)^2 + 344 0640/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) + 20971...
\[ \text {the integral} =\text {Too large to display} \]
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^1 3-483840*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+113 21856*x^8-1119744*x^7-5225472*x^6)*log(x)^7+(-14336*x^12+258048*x^11-21073 92*x^10+9461760*x^9-22579200*x^8+20901888*x^7+12773376*x^6-27869184*x^5)*l og(x)^6+(172032*x^10-2580480*x^9+15769600*x^8-46448640*x^7+54190080*x^6+20 127744*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^6-41287680*x^ 5+118358016*x^4-79822848*x^3-82575360*x^2)*log(x)^3+(-11010048*x^4+6606028 8*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^12-217 728*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^11-1451520*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^8-104509 44*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^11-1451520*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^7-23 224320*x^6+13934592*x^5)*log(x)^5+(286720*x^8-3440640*x^7+15482880*x^6-309 65760*x^5+23224320*x^4)*log(x)^4+(-917504*x^6+8257536*x^5-24772608*x^4+247 72608*x^3)*log(x)^3+(1835008*x^4-11010048*x^3+16515072*x^2)*log(x)^2+(-209 7152*x^2+6291456*x)*log(x)+1048576)/x^7/log(x)^8)+x^8*log(x)^9),x, algorit hm=\
Time = 16.42 (sec) , antiderivative size = 399, normalized size of antiderivative = 14.25 \[ \text {the integral} =\text {Too large to display} \]
int(-(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^12) + log(x)^2*(16515072*x^2 - 11010048*x^3 + 1835008*x^4) + log(x)*(6291456*x - 2097152*x^2) + log(x)^7*(1119744*x^7 - 2612736*x^8 + 2612736*x^9 - 1451 520*x^10 + 483840*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14) + log(x)^3*(2 4772608*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 + 4 032*x^14 - 384*x^15 + 16*x^16) + 1048576)/(x^7*log(x)^8))*(log(x)^3*(82575 360*x^2 + 79822848*x^3 - 118358016*x^4 + 41287680*x^5 - 4587520*x^6) + log (x)^4*(99090432*x^3 + 18579456*x^4 - 107347968*x^5 + 61014016*x^6 - 137625 60*x^7 + 1146880*x^8) + log(x)^8*(2612736*x^8 - 5225472*x^9 + 4354560*x^10 - 1935360*x^11 + 483840*x^12 - 64512*x^13 + 3584*x^14) + log(x)^2*(377487 36*x + 88604672*x^2 - 66060288*x^3 + 11010048*x^4) - log(x)^5*(20127744*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 + 1119744*x^7 - 1132 1856*x^8 + 10354176*x^9 - 4354560*x^10 + 999936*x^11 - 132608*x^12 + 10752 *x^13 - 512*x^14) + 8388608) - 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^12) + log(x)^2*(165 15072*x^2 - 11010048*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 + 4838 40*x^11 - 96768*x^12 + 10752*x^13 - 512*x^14) + log(x)^3*(24772608*x^3 - 2 4772608*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)
log(exp(1119744/log(x))*exp(-3440640/log(x)^4)*exp(-10450944/log(x)^2)*exp (15482880/log(x)^3)*exp(104977*x)*exp((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(-(96768*x ^5)/log(x))*exp(-(129024*x^4)/log(x)^2)*exp((483840*x^4)/log(x))*exp((8601 60*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*lo g(x)^3))*exp(15482880/(x*log(x)^4))*exp(16515072/(x^5*log(x)^6))*exp(-2322 4320/(x*log(x)^3))*exp(23224320/(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)