Integrand size = 268, antiderivative size = 29 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=2 x+\left (-2-x-(5+x)^2+\log \left (\frac {x}{3}\right )-4 \log (\log (3))\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(235\) vs. \(2(29)=58\).
Time = 0.17 (sec) , antiderivative size = 235, normalized size of antiderivative = 8.10 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=\log ^4\left (\frac {x}{3}\right )-4 \log (x) (27+4 \log (\log (3)))^3-4 \log ^3\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )+6 \log ^2\left (\frac {x}{3}\right ) \left (27+11 x+x^2+4 \log (\log (3))\right )^2-4 x (11+x) \log \left (\frac {x}{3}\right ) \left (22 x^3+x^4+33 x (27+4 \log (\log (3)))+3 (27+4 \log (\log (3)))^2+2 x^2 (101+6 \log (\log (3)))\right )+x \left (866054+44 x^6+x^7+384912 \log (\log (3))+57024 \log ^2(\log (3))+2816 \log ^3(\log (3))+88 x^4 (101+6 \log (\log (3)))+2 x^5 (417+8 \log (\log (3)))+2 x (27+4 \log (\log (3)))^2 (417+8 \log (\log (3)))+88 x^2 \left (2727+566 \log (\log (3))+24 \log ^2(\log (3))\right )+x^3 \left (58219+7104 \log (\log (3))+96 \log ^2(\log (3))\right )\right ) \]
Integrate[(-78732 + 769826*x + 1168020*x^2 + 707476*x^3 + 231100*x^4 + 443 08*x^5 + 5000*x^6 + 308*x^7 + 8*x^8 + (8748 - 89100*x - 93804*x^2 - 37092* x^3 - 7092*x^4 - 660*x^5 - 24*x^6)*Log[x/3] + (-324 + 3432*x + 2088*x^2 + 396*x^3 + 24*x^4)*Log[x/3]^2 + (4 - 44*x - 8*x^2)*Log[x/3]^3 + (-34992 + 3 56400*x + 375216*x^2 + 148368*x^3 + 28368*x^4 + 2640*x^5 + 96*x^6 + (2592 - 27456*x - 16704*x^2 - 3168*x^3 - 192*x^4)*Log[x/3] + (-48 + 528*x + 96*x ^2)*Log[x/3]^2)*Log[Log[3]] + (-5184 + 54912*x + 33408*x^2 + 6336*x^3 + 38 4*x^4 + (192 - 2112*x - 384*x^2)*Log[x/3])*Log[Log[3]]^2 + (-256 + 2816*x + 512*x^2)*Log[Log[3]]^3)/x,x]
Log[x/3]^4 - 4*Log[x]*(27 + 4*Log[Log[3]])^3 - 4*Log[x/3]^3*(27 + 11*x + x ^2 + 4*Log[Log[3]]) + 6*Log[x/3]^2*(27 + 11*x + x^2 + 4*Log[Log[3]])^2 - 4 *x*(11 + x)*Log[x/3]*(22*x^3 + x^4 + 33*x*(27 + 4*Log[Log[3]]) + 3*(27 + 4 *Log[Log[3]])^2 + 2*x^2*(101 + 6*Log[Log[3]])) + x*(866054 + 44*x^6 + x^7 + 384912*Log[Log[3]] + 57024*Log[Log[3]]^2 + 2816*Log[Log[3]]^3 + 88*x^4*( 101 + 6*Log[Log[3]]) + 2*x^5*(417 + 8*Log[Log[3]]) + 2*x*(27 + 4*Log[Log[3 ]])^2*(417 + 8*Log[Log[3]]) + 88*x^2*(2727 + 566*Log[Log[3]] + 24*Log[Log[ 3]]^2) + x^3*(58219 + 7104*Log[Log[3]] + 96*Log[Log[3]]^2))
Leaf count is larger than twice the leaf count of optimal. \(599\) vs. \(2(29)=58\).
Time = 1.12 (sec) , antiderivative size = 599, normalized size of antiderivative = 20.66, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {2010, 2009}
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.
| \(\displaystyle \int \frac {8 x^8+308 x^7+5000 x^6+44308 x^5+231100 x^4+707476 x^3+1168020 x^2+\left (-8 x^2-44 x+4\right ) \log ^3\left (\frac {x}{3}\right )+\left (512 x^2+2816 x-256\right ) \log ^3(\log (3))+\left (24 x^4+396 x^3+2088 x^2+3432 x-324\right ) \log ^2\left (\frac {x}{3}\right )+\log ^2(\log (3)) \left (384 x^4+6336 x^3+33408 x^2+\left (-384 x^2-2112 x+192\right ) \log \left (\frac {x}{3}\right )+54912 x-5184\right )+\log (\log (3)) \left (96 x^6+2640 x^5+28368 x^4+148368 x^3+375216 x^2+\left (96 x^2+528 x-48\right ) \log ^2\left (\frac {x}{3}\right )+\left (-192 x^4-3168 x^3-16704 x^2-27456 x+2592\right ) \log \left (\frac {x}{3}\right )+356400 x-34992\right )+\left (-24 x^6-660 x^5-7092 x^4-37092 x^3-93804 x^2-89100 x+8748\right ) \log \left (\frac {x}{3}\right )+769826 x-78732}{x} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (-\frac {4 \left (2 x^2+11 x-1\right ) \log ^3\left (\frac {x}{3}\right )}{x}+\frac {12 \left (2 x^2+11 x-1\right ) \left (x^2+11 x+27+4 \log (\log (3))\right ) \log ^2\left (\frac {x}{3}\right )}{x}-\frac {12 \left (2 x^2+11 x-1\right ) \left (x^2+11 x+27+4 \log (\log (3))\right )^2 \log \left (\frac {x}{3}\right )}{x}+\frac {2 \left (4 x^8+154 x^7+2500 x^6 \left (1+\frac {12}{625} \log (\log (3))\right )+22154 x^5 \left (1+\frac {60 \log (\log (3))}{1007}\right )+115550 x^4 \left (1+\frac {12 \log (\log (3)) (591+8 \log (\log (3)))}{57775}\right )+353738 x^3 \left (1+\frac {12 \log (\log (3)) (281+12 \log (\log (3)))}{16079}\right )+584010 x^2 \left (1+\frac {4 \log (\log (3)) \left (23451+32 \log ^2(\log (3))+2088 \log (\log (3))\right )}{292005}\right )+384913 x \left (1+\frac {88 \log (\log (3)) \left (2025+16 \log ^2(\log (3))+312 \log (\log (3))\right )}{384913}\right )-39366 \left (1+\frac {4}{9} \log (\log (3)) \left (1+\frac {4 \log (\log (3)) (81+4 \log (\log (3)))}{2187}\right )\right )\right )}{x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^8+44 x^7+\frac {2 x^6}{3}-4 x^6 \log \left (\frac {x}{3}\right )+\frac {4}{3} x^6 (625+12 \log (\log (3)))+\frac {132 x^5}{5}-132 x^5 \log \left (\frac {x}{3}\right )+\frac {44}{5} x^5 (1007+60 \log (\log (3)))+\frac {3 x^4}{4}+6 x^4 \log ^2\left (\frac {x}{3}\right )+x^4 \left (57775+96 \log ^2(\log (3))+7092 \log (\log (3))\right )-3 x^4 \log \left (\frac {x}{3}\right )-3 x^4 (591+16 \log (\log (3))) \log \left (\frac {x}{3}\right )+\frac {3}{4} x^4 (591+16 \log (\log (3)))+\frac {88 x^3}{3}+132 x^3 \log ^2\left (\frac {x}{3}\right )+\frac {44}{3} x^3 \left (16079+144 \log ^2(\log (3))+3372 \log (\log (3))\right )-88 x^3 \log \left (\frac {x}{3}\right )-44 x^3 (281+24 \log (\log (3))) \log \left (\frac {x}{3}\right )+\frac {44}{3} x^3 (281+24 \log (\log (3)))+3 x^2-4 x^2 \log ^3\left (\frac {x}{3}\right )+6 x^2 \log ^2\left (\frac {x}{3}\right )-6 x^2 \left (7817+32 \log ^2(\log (3))+1392 \log (\log (3))\right ) \log \left (\frac {x}{3}\right )+3 x^2 \left (7817+32 \log ^2(\log (3))+1392 \log (\log (3))\right )+12 x^2 (87+4 \log (\log (3))) \log ^2\left (\frac {x}{3}\right )+2 x^2 \left (292005+128 \log ^3(\log (3))+8352 \log ^2(\log (3))+93804 \log (\log (3))\right )-6 x^2 \log \left (\frac {x}{3}\right )-12 x^2 (87+4 \log (\log (3))) \log \left (\frac {x}{3}\right )+6 x^2 (87+4 \log (\log (3)))+264 x+\log ^4\left (\frac {x}{3}\right )-44 x \log ^3\left (\frac {x}{3}\right )-4 (27+4 \log (\log (3))) \log ^3\left (\frac {x}{3}\right )+132 x \log ^2\left (\frac {x}{3}\right )-132 x \left (675+16 \log ^2(\log (3))+208 \log (\log (3))\right ) \log \left (\frac {x}{3}\right )+132 x \left (675+16 \log ^2(\log (3))+208 \log (\log (3))\right )+264 x (13+2 \log (\log (3))) \log ^2\left (\frac {x}{3}\right )+6 (27+4 \log (\log (3)))^2 \log ^2\left (\frac {x}{3}\right )+2 x \left (384913+1408 \log ^3(\log (3))+27456 \log ^2(\log (3))+178200 \log (\log (3))\right )-264 x \log \left (\frac {x}{3}\right )-528 x (13+2 \log (\log (3))) \log \left (\frac {x}{3}\right )+528 x (13+2 \log (\log (3)))-4 (27+4 \log (\log (3)))^3 \log (x)\) |
Int[(-78732 + 769826*x + 1168020*x^2 + 707476*x^3 + 231100*x^4 + 44308*x^5 + 5000*x^6 + 308*x^7 + 8*x^8 + (8748 - 89100*x - 93804*x^2 - 37092*x^3 - 7092*x^4 - 660*x^5 - 24*x^6)*Log[x/3] + (-324 + 3432*x + 2088*x^2 + 396*x^ 3 + 24*x^4)*Log[x/3]^2 + (4 - 44*x - 8*x^2)*Log[x/3]^3 + (-34992 + 356400* x + 375216*x^2 + 148368*x^3 + 28368*x^4 + 2640*x^5 + 96*x^6 + (2592 - 2745 6*x - 16704*x^2 - 3168*x^3 - 192*x^4)*Log[x/3] + (-48 + 528*x + 96*x^2)*Lo g[x/3]^2)*Log[Log[3]] + (-5184 + 54912*x + 33408*x^2 + 6336*x^3 + 384*x^4 + (192 - 2112*x - 384*x^2)*Log[x/3])*Log[Log[3]]^2 + (-256 + 2816*x + 512* x^2)*Log[Log[3]]^3)/x,x]
264*x + 3*x^2 + (88*x^3)/3 + (3*x^4)/4 + (132*x^5)/5 + (2*x^6)/3 + 44*x^7 + x^8 - 264*x*Log[x/3] - 6*x^2*Log[x/3] - 88*x^3*Log[x/3] - 3*x^4*Log[x/3] - 132*x^5*Log[x/3] - 4*x^6*Log[x/3] + 132*x*Log[x/3]^2 + 6*x^2*Log[x/3]^2 + 132*x^3*Log[x/3]^2 + 6*x^4*Log[x/3]^2 - 44*x*Log[x/3]^3 - 4*x^2*Log[x/3 ]^3 + Log[x/3]^4 + 528*x*(13 + 2*Log[Log[3]]) - 528*x*Log[x/3]*(13 + 2*Log [Log[3]]) + 264*x*Log[x/3]^2*(13 + 2*Log[Log[3]]) - 4*Log[x/3]^3*(27 + 4*L og[Log[3]]) + 6*Log[x/3]^2*(27 + 4*Log[Log[3]])^2 - 4*Log[x]*(27 + 4*Log[L og[3]])^3 + 6*x^2*(87 + 4*Log[Log[3]]) - 12*x^2*Log[x/3]*(87 + 4*Log[Log[3 ]]) + 12*x^2*Log[x/3]^2*(87 + 4*Log[Log[3]]) + (4*x^6*(625 + 12*Log[Log[3] ]))/3 + (3*x^4*(591 + 16*Log[Log[3]]))/4 - 3*x^4*Log[x/3]*(591 + 16*Log[Lo g[3]]) + (44*x^3*(281 + 24*Log[Log[3]]))/3 - 44*x^3*Log[x/3]*(281 + 24*Log [Log[3]]) + (44*x^5*(1007 + 60*Log[Log[3]]))/5 + 132*x*(675 + 208*Log[Log[ 3]] + 16*Log[Log[3]]^2) - 132*x*Log[x/3]*(675 + 208*Log[Log[3]] + 16*Log[L og[3]]^2) + 3*x^2*(7817 + 1392*Log[Log[3]] + 32*Log[Log[3]]^2) - 6*x^2*Log [x/3]*(7817 + 1392*Log[Log[3]] + 32*Log[Log[3]]^2) + x^4*(57775 + 7092*Log [Log[3]] + 96*Log[Log[3]]^2) + (44*x^3*(16079 + 3372*Log[Log[3]] + 144*Log [Log[3]]^2))/3 + 2*x^2*(292005 + 93804*Log[Log[3]] + 8352*Log[Log[3]]^2 + 128*Log[Log[3]]^3) + 2*x*(384913 + 178200*Log[Log[3]] + 27456*Log[Log[3]]^ 2 + 1408*Log[Log[3]]^3)
3.20.18.3.1 Defintions of rubi rules used
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Leaf count of result is larger than twice the leaf count of optimal. \(211\) vs. \(2(27)=54\).
Time = 0.20 (sec) , antiderivative size = 212, normalized size of antiderivative = 7.31
| method | result | size |
| risch | \(\ln \left (\frac {x}{3}\right )^{4}+\left (-4 x^{2}-16 \ln \left (\ln \left (3\right )\right )-44 x -108\right ) \ln \left (\frac {x}{3}\right )^{3}+6 \left (x^{2}+4 \ln \left (\ln \left (3\right )\right )+11 x +27\right )^{2} \ln \left (\frac {x}{3}\right )^{2}-4 \left (x^{2}+4 \ln \left (\ln \left (3\right )\right )+11 x +27\right )^{3} \ln \left (\frac {x}{3}\right )+x^{8}+16 \ln \left (\ln \left (3\right )\right ) x^{6}+44 x^{7}+96 \ln \left (\ln \left (3\right )\right )^{2} x^{4}+528 \ln \left (\ln \left (3\right )\right ) x^{5}+834 x^{6}+256 \ln \left (\ln \left (3\right )\right )^{3} x^{2}+2112 \ln \left (\ln \left (3\right )\right )^{2} x^{3}+7104 \ln \left (\ln \left (3\right )\right ) x^{4}+8888 x^{5}+2816 \ln \left (\ln \left (3\right )\right )^{3} x +16800 \ln \left (\ln \left (3\right )\right )^{2} x^{2}+49808 x^{3} \ln \left (\ln \left (3\right )\right )+58219 x^{4}+57024 \ln \left (\ln \left (3\right )\right )^{2} x +191808 x^{2} \ln \left (\ln \left (3\right )\right )+239976 x^{3}+384912 \ln \left (\ln \left (3\right )\right ) x +607986 x^{2}+866054 x\) | \(212\) |
| parallelrisch | \(866054 x -34992 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )+2816 \ln \left (\ln \left (3\right )\right )^{3} x -44 \ln \left (\frac {x}{3}\right )^{3} x -132 x^{5} \ln \left (\frac {x}{3}\right )-47952 x^{2} \ln \left (\frac {x}{3}\right )+191808 x^{2} \ln \left (\ln \left (3\right )\right )+1050 x^{2} \ln \left (\frac {x}{3}\right )^{2}+6 x^{4} \ln \left (\frac {x}{3}\right )^{2}-96228 x \ln \left (\frac {x}{3}\right )-1776 x^{4} \ln \left (\frac {x}{3}\right )+49808 x^{3} \ln \left (\ln \left (3\right )\right )+384912 \ln \left (\ln \left (3\right )\right ) x +132 x^{3} \ln \left (\frac {x}{3}\right )^{2}+3564 x \ln \left (\frac {x}{3}\right )^{2}-78732 \ln \left (\frac {x}{3}\right )+44 x^{7}+x^{8}+58219 x^{4}+239976 x^{3}+607986 x^{2}+834 x^{6}+8888 x^{5}-12452 x^{3} \ln \left (\frac {x}{3}\right )-256 \ln \left (\ln \left (3\right )\right )^{3} \ln \left (\frac {x}{3}\right )+48 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2} x^{2}-1056 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right ) x^{3}-8400 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right ) x^{2}-28512 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right ) x -2112 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right ) x +528 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2} x -16 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{3}+16 \ln \left (\ln \left (3\right )\right ) x^{6}-4 \ln \left (\frac {x}{3}\right ) x^{6}+96 \ln \left (\ln \left (3\right )\right )^{2} x^{4}+528 \ln \left (\ln \left (3\right )\right ) x^{5}+256 \ln \left (\ln \left (3\right )\right )^{3} x^{2}+2112 \ln \left (\ln \left (3\right )\right )^{2} x^{3}-4 \ln \left (\frac {x}{3}\right )^{3} x^{2}+16800 \ln \left (\ln \left (3\right )\right )^{2} x^{2}-48 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right ) x^{4}-192 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right ) x^{2}+4374 \ln \left (\frac {x}{3}\right )^{2}-108 \ln \left (\frac {x}{3}\right )^{3}+7104 \ln \left (\ln \left (3\right )\right ) x^{4}+96 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )^{2}-5184 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )+57024 \ln \left (\ln \left (3\right )\right )^{2} x +1296 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2}+\ln \left (\frac {x}{3}\right )^{4}\) | \(446\) |
| parts | \(866054 x +2816 \ln \left (\ln \left (3\right )\right )^{3} x -44 \ln \left (\frac {x}{3}\right )^{3} x -132 x^{5} \ln \left (\frac {x}{3}\right )-47952 x^{2} \ln \left (\frac {x}{3}\right )+187608 x^{2} \ln \left (\ln \left (3\right )\right )+1050 x^{2} \ln \left (\frac {x}{3}\right )^{2}+6 x^{4} \ln \left (\frac {x}{3}\right )^{2}-96228 x \ln \left (\frac {x}{3}\right )-1776 x^{4} \ln \left (\frac {x}{3}\right )+49456 x^{3} \ln \left (\ln \left (3\right )\right )+356400 \ln \left (\ln \left (3\right )\right ) x +132 x^{3} \ln \left (\frac {x}{3}\right )^{2}+3564 x \ln \left (\frac {x}{3}\right )^{2}+44 x^{7}+x^{8}+58219 x^{4}+239976 x^{3}+607986 x^{2}+834 x^{6}+8888 x^{5}-12452 x^{3} \ln \left (\frac {x}{3}\right )-85536 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{3} \ln \left (\frac {x}{3}\right )}{81}-\frac {x^{3}}{243}\right )-150336 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+1584 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )^{2}}{3}-\frac {2 x \ln \left (\frac {x}{3}\right )}{3}+\frac {2 x}{3}\right )-16 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{3}-82368 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+16 \ln \left (\ln \left (3\right )\right ) x^{6}-4 \ln \left (\frac {x}{3}\right ) x^{6}+96 \ln \left (\ln \left (3\right )\right )^{2} x^{4}+528 \ln \left (\ln \left (3\right )\right ) x^{5}+256 \ln \left (\ln \left (3\right )\right )^{3} x^{2}+2112 \ln \left (\ln \left (3\right )\right )^{2} x^{3}-4 \ln \left (\frac {x}{3}\right )^{3} x^{2}+16704 \ln \left (\ln \left (3\right )\right )^{2} x^{2}-15552 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{4} \ln \left (\frac {x}{3}\right )}{324}-\frac {x^{4}}{1296}\right )-6336 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+4374 \ln \left (\frac {x}{3}\right )^{2}-108 \ln \left (\frac {x}{3}\right )^{3}+7092 \ln \left (\ln \left (3\right )\right ) x^{4}+96 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )^{2}+54912 \ln \left (\ln \left (3\right )\right )^{2} x +1296 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2}+864 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )^{2}}{18}-\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}+\frac {x^{2}}{36}\right )-3456 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+\ln \left (\frac {x}{3}\right )^{4}+2 \left (-128 \ln \left (\ln \left (3\right )\right )^{3}-2592 \ln \left (\ln \left (3\right )\right )^{2}-17496 \ln \left (\ln \left (3\right )\right )-39366\right ) \ln \left (x \right )\) | \(508\) |
| derivativedivides | \(866054 x -34992 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )+2816 \ln \left (\ln \left (3\right )\right )^{3} x -44 \ln \left (\frac {x}{3}\right )^{3} x -132 x^{5} \ln \left (\frac {x}{3}\right )-47952 x^{2} \ln \left (\frac {x}{3}\right )+187608 x^{2} \ln \left (\ln \left (3\right )\right )+1050 x^{2} \ln \left (\frac {x}{3}\right )^{2}+6 x^{4} \ln \left (\frac {x}{3}\right )^{2}-96228 x \ln \left (\frac {x}{3}\right )-1776 x^{4} \ln \left (\frac {x}{3}\right )+49456 x^{3} \ln \left (\ln \left (3\right )\right )+356400 \ln \left (\ln \left (3\right )\right ) x +132 x^{3} \ln \left (\frac {x}{3}\right )^{2}+3564 x \ln \left (\frac {x}{3}\right )^{2}-78732 \ln \left (\frac {x}{3}\right )+44 x^{7}+x^{8}+58219 x^{4}+239976 x^{3}+607986 x^{2}+834 x^{6}+8888 x^{5}-12452 x^{3} \ln \left (\frac {x}{3}\right )-256 \ln \left (\ln \left (3\right )\right )^{3} \ln \left (\frac {x}{3}\right )-85536 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{3} \ln \left (\frac {x}{3}\right )}{81}-\frac {x^{3}}{243}\right )-150336 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+1584 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )^{2}}{3}-\frac {2 x \ln \left (\frac {x}{3}\right )}{3}+\frac {2 x}{3}\right )-16 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{3}-82368 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+16 \ln \left (\ln \left (3\right )\right ) x^{6}-4 \ln \left (\frac {x}{3}\right ) x^{6}+96 \ln \left (\ln \left (3\right )\right )^{2} x^{4}+528 \ln \left (\ln \left (3\right )\right ) x^{5}+256 \ln \left (\ln \left (3\right )\right )^{3} x^{2}+2112 \ln \left (\ln \left (3\right )\right )^{2} x^{3}-4 \ln \left (\frac {x}{3}\right )^{3} x^{2}+16704 \ln \left (\ln \left (3\right )\right )^{2} x^{2}-15552 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{4} \ln \left (\frac {x}{3}\right )}{324}-\frac {x^{4}}{1296}\right )-6336 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+4374 \ln \left (\frac {x}{3}\right )^{2}-108 \ln \left (\frac {x}{3}\right )^{3}+7092 \ln \left (\ln \left (3\right )\right ) x^{4}+96 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )^{2}-5184 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )+54912 \ln \left (\ln \left (3\right )\right )^{2} x +1296 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2}+864 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )^{2}}{18}-\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}+\frac {x^{2}}{36}\right )-3456 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+\ln \left (\frac {x}{3}\right )^{4}\) | \(520\) |
| default | \(866054 x -34992 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )+2816 \ln \left (\ln \left (3\right )\right )^{3} x -44 \ln \left (\frac {x}{3}\right )^{3} x -132 x^{5} \ln \left (\frac {x}{3}\right )-47952 x^{2} \ln \left (\frac {x}{3}\right )+187608 x^{2} \ln \left (\ln \left (3\right )\right )+1050 x^{2} \ln \left (\frac {x}{3}\right )^{2}+6 x^{4} \ln \left (\frac {x}{3}\right )^{2}-96228 x \ln \left (\frac {x}{3}\right )-1776 x^{4} \ln \left (\frac {x}{3}\right )+49456 x^{3} \ln \left (\ln \left (3\right )\right )+356400 \ln \left (\ln \left (3\right )\right ) x +132 x^{3} \ln \left (\frac {x}{3}\right )^{2}+3564 x \ln \left (\frac {x}{3}\right )^{2}-78732 \ln \left (\frac {x}{3}\right )+44 x^{7}+x^{8}+58219 x^{4}+239976 x^{3}+607986 x^{2}+834 x^{6}+8888 x^{5}-12452 x^{3} \ln \left (\frac {x}{3}\right )-256 \ln \left (\ln \left (3\right )\right )^{3} \ln \left (\frac {x}{3}\right )-85536 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{3} \ln \left (\frac {x}{3}\right )}{81}-\frac {x^{3}}{243}\right )-150336 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+1584 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )^{2}}{3}-\frac {2 x \ln \left (\frac {x}{3}\right )}{3}+\frac {2 x}{3}\right )-16 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{3}-82368 \ln \left (\ln \left (3\right )\right ) \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+16 \ln \left (\ln \left (3\right )\right ) x^{6}-4 \ln \left (\frac {x}{3}\right ) x^{6}+96 \ln \left (\ln \left (3\right )\right )^{2} x^{4}+528 \ln \left (\ln \left (3\right )\right ) x^{5}+256 \ln \left (\ln \left (3\right )\right )^{3} x^{2}+2112 \ln \left (\ln \left (3\right )\right )^{2} x^{3}-4 \ln \left (\frac {x}{3}\right )^{3} x^{2}+16704 \ln \left (\ln \left (3\right )\right )^{2} x^{2}-15552 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{4} \ln \left (\frac {x}{3}\right )}{324}-\frac {x^{4}}{1296}\right )-6336 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x \ln \left (\frac {x}{3}\right )}{3}-\frac {x}{3}\right )+4374 \ln \left (\frac {x}{3}\right )^{2}-108 \ln \left (\frac {x}{3}\right )^{3}+7092 \ln \left (\ln \left (3\right )\right ) x^{4}+96 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )^{2}-5184 \ln \left (\ln \left (3\right )\right )^{2} \ln \left (\frac {x}{3}\right )+54912 \ln \left (\ln \left (3\right )\right )^{2} x +1296 \ln \left (\ln \left (3\right )\right ) \ln \left (\frac {x}{3}\right )^{2}+864 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )^{2}}{18}-\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}+\frac {x^{2}}{36}\right )-3456 \ln \left (\ln \left (3\right )\right )^{2} \left (\frac {x^{2} \ln \left (\frac {x}{3}\right )}{18}-\frac {x^{2}}{36}\right )+\ln \left (\frac {x}{3}\right )^{4}\) | \(520\) |
int(((512*x^2+2816*x-256)*ln(ln(3))^3+((-384*x^2-2112*x+192)*ln(1/3*x)+384 *x^4+6336*x^3+33408*x^2+54912*x-5184)*ln(ln(3))^2+((96*x^2+528*x-48)*ln(1/ 3*x)^2+(-192*x^4-3168*x^3-16704*x^2-27456*x+2592)*ln(1/3*x)+96*x^6+2640*x^ 5+28368*x^4+148368*x^3+375216*x^2+356400*x-34992)*ln(ln(3))+(-8*x^2-44*x+4 )*ln(1/3*x)^3+(24*x^4+396*x^3+2088*x^2+3432*x-324)*ln(1/3*x)^2+(-24*x^6-66 0*x^5-7092*x^4-37092*x^3-93804*x^2-89100*x+8748)*ln(1/3*x)+8*x^8+308*x^7+5 000*x^6+44308*x^5+231100*x^4+707476*x^3+1168020*x^2+769826*x-78732)/x,x,me thod=_RETURNVERBOSE)
ln(1/3*x)^4+(-4*x^2-16*ln(ln(3))-44*x-108)*ln(1/3*x)^3+6*(x^2+4*ln(ln(3))+ 11*x+27)^2*ln(1/3*x)^2-4*(x^2+4*ln(ln(3))+11*x+27)^3*ln(1/3*x)+x^8+16*ln(l n(3))*x^6+44*x^7+96*ln(ln(3))^2*x^4+528*ln(ln(3))*x^5+834*x^6+256*ln(ln(3) )^3*x^2+2112*ln(ln(3))^2*x^3+7104*ln(ln(3))*x^4+8888*x^5+2816*ln(ln(3))^3* x+16800*ln(ln(3))^2*x^2+49808*x^3*ln(ln(3))+58219*x^4+57024*ln(ln(3))^2*x+ 191808*x^2*ln(ln(3))+239976*x^3+384912*ln(ln(3))*x+607986*x^2+866054*x
Leaf count of result is larger than twice the leaf count of optimal. 263 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 263, normalized size of antiderivative = 9.07 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=x^{8} + 44 \, x^{7} + 834 \, x^{6} + 8888 \, x^{5} + 58219 \, x^{4} - 4 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right )^{3} + \log \left (\frac {1}{3} \, x\right )^{4} + 256 \, {\left (x^{2} + 11 \, x - \log \left (\frac {1}{3} \, x\right )\right )} \log \left (\log \left (3\right )\right )^{3} + 239976 \, x^{3} + 6 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} + 594 \, x + 729\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 96 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} - 2 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right ) + \log \left (\frac {1}{3} \, x\right )^{2} + 594 \, x\right )} \log \left (\log \left (3\right )\right )^{2} + 607986 \, x^{2} - 4 \, {\left (x^{6} + 33 \, x^{5} + 444 \, x^{4} + 3113 \, x^{3} + 11988 \, x^{2} + 24057 \, x + 19683\right )} \log \left (\frac {1}{3} \, x\right ) + 16 \, {\left (x^{6} + 33 \, x^{5} + 444 \, x^{4} + 3113 \, x^{3} + 3 \, {\left (x^{2} + 11 \, x + 27\right )} \log \left (\frac {1}{3} \, x\right )^{2} - \log \left (\frac {1}{3} \, x\right )^{3} + 11988 \, x^{2} - 3 \, {\left (x^{4} + 22 \, x^{3} + 175 \, x^{2} + 594 \, x + 729\right )} \log \left (\frac {1}{3} \, x\right ) + 24057 \, x\right )} \log \left (\log \left (3\right )\right ) + 866054 \, x \]
integrate(((512*x^2+2816*x-256)*log(log(3))^3+((-384*x^2-2112*x+192)*log(1 /3*x)+384*x^4+6336*x^3+33408*x^2+54912*x-5184)*log(log(3))^2+((96*x^2+528* x-48)*log(1/3*x)^2+(-192*x^4-3168*x^3-16704*x^2-27456*x+2592)*log(1/3*x)+9 6*x^6+2640*x^5+28368*x^4+148368*x^3+375216*x^2+356400*x-34992)*log(log(3)) +(-8*x^2-44*x+4)*log(1/3*x)^3+(24*x^4+396*x^3+2088*x^2+3432*x-324)*log(1/3 *x)^2+(-24*x^6-660*x^5-7092*x^4-37092*x^3-93804*x^2-89100*x+8748)*log(1/3* x)+8*x^8+308*x^7+5000*x^6+44308*x^5+231100*x^4+707476*x^3+1168020*x^2+7698 26*x-78732)/x,x, algorithm=\
x^8 + 44*x^7 + 834*x^6 + 8888*x^5 + 58219*x^4 - 4*(x^2 + 11*x + 27)*log(1/ 3*x)^3 + log(1/3*x)^4 + 256*(x^2 + 11*x - log(1/3*x))*log(log(3))^3 + 2399 76*x^3 + 6*(x^4 + 22*x^3 + 175*x^2 + 594*x + 729)*log(1/3*x)^2 + 96*(x^4 + 22*x^3 + 175*x^2 - 2*(x^2 + 11*x + 27)*log(1/3*x) + log(1/3*x)^2 + 594*x) *log(log(3))^2 + 607986*x^2 - 4*(x^6 + 33*x^5 + 444*x^4 + 3113*x^3 + 11988 *x^2 + 24057*x + 19683)*log(1/3*x) + 16*(x^6 + 33*x^5 + 444*x^4 + 3113*x^3 + 3*(x^2 + 11*x + 27)*log(1/3*x)^2 - log(1/3*x)^3 + 11988*x^2 - 3*(x^4 + 22*x^3 + 175*x^2 + 594*x + 729)*log(1/3*x) + 24057*x)*log(log(3)) + 866054 *x
Leaf count of result is larger than twice the leaf count of optimal. 333 vs. \(2 (24) = 48\).
Time = 0.49 (sec) , antiderivative size = 333, normalized size of antiderivative = 11.48 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=x^{8} + 44 x^{7} + x^{6} \cdot \left (16 \log {\left (\log {\left (3 \right )} \right )} + 834\right ) + x^{5} \cdot \left (528 \log {\left (\log {\left (3 \right )} \right )} + 8888\right ) + x^{4} \cdot \left (96 \log {\left (\log {\left (3 \right )} \right )}^{2} + 7104 \log {\left (\log {\left (3 \right )} \right )} + 58219\right ) + x^{3} \cdot \left (2112 \log {\left (\log {\left (3 \right )} \right )}^{2} + 49808 \log {\left (\log {\left (3 \right )} \right )} + 239976\right ) + x^{2} \cdot \left (256 \log {\left (\log {\left (3 \right )} \right )}^{3} + 16800 \log {\left (\log {\left (3 \right )} \right )}^{2} + 191808 \log {\left (\log {\left (3 \right )} \right )} + 607986\right ) + x \left (2816 \log {\left (\log {\left (3 \right )} \right )}^{3} + 57024 \log {\left (\log {\left (3 \right )} \right )}^{2} + 384912 \log {\left (\log {\left (3 \right )} \right )} + 866054\right ) + \left (- 4 x^{2} - 44 x - 108 - 16 \log {\left (\log {\left (3 \right )} \right )}\right ) \log {\left (\frac {x}{3} \right )}^{3} + \left (6 x^{4} + 132 x^{3} + 48 x^{2} \log {\left (\log {\left (3 \right )} \right )} + 1050 x^{2} + 528 x \log {\left (\log {\left (3 \right )} \right )} + 3564 x + 96 \log {\left (\log {\left (3 \right )} \right )}^{2} + 1296 \log {\left (\log {\left (3 \right )} \right )} + 4374\right ) \log {\left (\frac {x}{3} \right )}^{2} + \left (- 4 x^{6} - 132 x^{5} - 1776 x^{4} - 48 x^{4} \log {\left (\log {\left (3 \right )} \right )} - 12452 x^{3} - 1056 x^{3} \log {\left (\log {\left (3 \right )} \right )} - 47952 x^{2} - 8400 x^{2} \log {\left (\log {\left (3 \right )} \right )} - 192 x^{2} \log {\left (\log {\left (3 \right )} \right )}^{2} - 96228 x - 28512 x \log {\left (\log {\left (3 \right )} \right )} - 2112 x \log {\left (\log {\left (3 \right )} \right )}^{2}\right ) \log {\left (\frac {x}{3} \right )} + \log {\left (\frac {x}{3} \right )}^{4} - 4 \left (4 \log {\left (\log {\left (3 \right )} \right )} + 27\right )^{3} \log {\left (x \right )} \]
integrate(((512*x**2+2816*x-256)*ln(ln(3))**3+((-384*x**2-2112*x+192)*ln(1 /3*x)+384*x**4+6336*x**3+33408*x**2+54912*x-5184)*ln(ln(3))**2+((96*x**2+5 28*x-48)*ln(1/3*x)**2+(-192*x**4-3168*x**3-16704*x**2-27456*x+2592)*ln(1/3 *x)+96*x**6+2640*x**5+28368*x**4+148368*x**3+375216*x**2+356400*x-34992)*l n(ln(3))+(-8*x**2-44*x+4)*ln(1/3*x)**3+(24*x**4+396*x**3+2088*x**2+3432*x- 324)*ln(1/3*x)**2+(-24*x**6-660*x**5-7092*x**4-37092*x**3-93804*x**2-89100 *x+8748)*ln(1/3*x)+8*x**8+308*x**7+5000*x**6+44308*x**5+231100*x**4+707476 *x**3+1168020*x**2+769826*x-78732)/x,x)
x**8 + 44*x**7 + x**6*(16*log(log(3)) + 834) + x**5*(528*log(log(3)) + 888 8) + x**4*(96*log(log(3))**2 + 7104*log(log(3)) + 58219) + x**3*(2112*log( log(3))**2 + 49808*log(log(3)) + 239976) + x**2*(256*log(log(3))**3 + 1680 0*log(log(3))**2 + 191808*log(log(3)) + 607986) + x*(2816*log(log(3))**3 + 57024*log(log(3))**2 + 384912*log(log(3)) + 866054) + (-4*x**2 - 44*x - 1 08 - 16*log(log(3)))*log(x/3)**3 + (6*x**4 + 132*x**3 + 48*x**2*log(log(3) ) + 1050*x**2 + 528*x*log(log(3)) + 3564*x + 96*log(log(3))**2 + 1296*log( log(3)) + 4374)*log(x/3)**2 + (-4*x**6 - 132*x**5 - 1776*x**4 - 48*x**4*lo g(log(3)) - 12452*x**3 - 1056*x**3*log(log(3)) - 47952*x**2 - 8400*x**2*lo g(log(3)) - 192*x**2*log(log(3))**2 - 96228*x - 28512*x*log(log(3)) - 2112 *x*log(log(3))**2)*log(x/3) + log(x/3)**4 - 4*(4*log(log(3)) + 27)**3*log( x)
Leaf count of result is larger than twice the leaf count of optimal. 569 vs. \(2 (25) = 50\).
Time = 0.23 (sec) , antiderivative size = 569, normalized size of antiderivative = 19.62 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=\text {Too large to display} \]
integrate(((512*x^2+2816*x-256)*log(log(3))^3+((-384*x^2-2112*x+192)*log(1 /3*x)+384*x^4+6336*x^3+33408*x^2+54912*x-5184)*log(log(3))^2+((96*x^2+528* x-48)*log(1/3*x)^2+(-192*x^4-3168*x^3-16704*x^2-27456*x+2592)*log(1/3*x)+9 6*x^6+2640*x^5+28368*x^4+148368*x^3+375216*x^2+356400*x-34992)*log(log(3)) +(-8*x^2-44*x+4)*log(1/3*x)^3+(24*x^4+396*x^3+2088*x^2+3432*x-324)*log(1/3 *x)^2+(-24*x^6-660*x^5-7092*x^4-37092*x^3-93804*x^2-89100*x+8748)*log(1/3* x)+8*x^8+308*x^7+5000*x^6+44308*x^5+231100*x^4+707476*x^3+1168020*x^2+7698 26*x-78732)/x,x, algorithm=\
x^8 + 44*x^7 - 4*x^6*log(1/3*x) + 16*x^6*log(log(3)) + 834*x^6 - 132*x^5*l og(1/3*x) + 528*x^5*log(log(3)) + 96*x^4*log(log(3))^2 + 3/4*(8*log(1/3*x) ^2 - 4*log(1/3*x) + 1)*x^4 + 8888*x^5 - 1773*x^4*log(1/3*x) + 7092*x^4*log (log(3)) + 2112*x^3*log(log(3))^2 + 256*x^2*log(log(3))^3 + 44/3*(9*log(1/ 3*x)^2 - 6*log(1/3*x) + 2)*x^3 + 232873/4*x^4 - 12364*x^3*log(1/3*x) + log (1/3*x)^4 + 24*(2*log(1/3*x)^2 - 2*log(1/3*x) + 1)*x^2*log(log(3)) + 49456 *x^3*log(log(3)) - 16*log(1/3*x)^3*log(log(3)) + 16704*x^2*log(log(3))^2 + 96*log(1/3*x)^2*log(log(3))^2 + 2816*x*log(log(3))^3 - 256*log(x)*log(log (3))^3 - (4*log(1/3*x)^3 - 6*log(1/3*x)^2 + 6*log(1/3*x) - 3)*x^2 + 522*(2 *log(1/3*x)^2 - 2*log(1/3*x) + 1)*x^2 + 719840/3*x^3 - 46902*x^2*log(1/3*x ) - 108*log(1/3*x)^3 + 528*(log(1/3*x)^2 - 2*log(1/3*x) + 2)*x*log(log(3)) + 187608*x^2*log(log(3)) + 1296*log(1/3*x)^2*log(log(3)) - 96*(2*x^2*log( 1/3*x) - x^2)*log(log(3))^2 - 2112*(x*log(1/3*x) - x)*log(log(3))^2 + 5491 2*x*log(log(3))^2 - 5184*log(x)*log(log(3))^2 - 44*(log(1/3*x)^3 - 3*log(1 /3*x)^2 + 6*log(1/3*x) - 6)*x + 3432*(log(1/3*x)^2 - 2*log(1/3*x) + 2)*x + 607461*x^2 - 89100*x*log(1/3*x) + 4374*log(1/3*x)^2 - 12*(4*x^4*log(1/3*x ) - x^4)*log(log(3)) - 352*(3*x^3*log(1/3*x) - x^3)*log(log(3)) - 4176*(2* x^2*log(1/3*x) - x^2)*log(log(3)) - 27456*(x*log(1/3*x) - x)*log(log(3)) + 356400*x*log(log(3)) - 34992*log(x)*log(log(3)) + 858926*x - 78732*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 298 vs. \(2 (25) = 50\).
Time = 0.27 (sec) , antiderivative size = 298, normalized size of antiderivative = 10.28 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=x^{8} + 44 \, x^{7} + 2 \, x^{6} {\left (8 \, \log \left (\log \left (3\right )\right ) + 417\right )} + 88 \, x^{5} {\left (6 \, \log \left (\log \left (3\right )\right ) + 101\right )} + {\left (96 \, \log \left (\log \left (3\right )\right )^{2} + 7104 \, \log \left (\log \left (3\right )\right ) + 58219\right )} x^{4} + 88 \, {\left (24 \, \log \left (\log \left (3\right )\right )^{2} + 566 \, \log \left (\log \left (3\right )\right ) + 2727\right )} x^{3} - 4 \, {\left (x^{2} + 11 \, x + 4 \, \log \left (\log \left (3\right )\right ) + 27\right )} \log \left (\frac {1}{3} \, x\right )^{3} + \log \left (\frac {1}{3} \, x\right )^{4} + 2 \, {\left (128 \, \log \left (\log \left (3\right )\right )^{3} + 8400 \, \log \left (\log \left (3\right )\right )^{2} + 95904 \, \log \left (\log \left (3\right )\right ) + 303993\right )} x^{2} + 6 \, {\left (x^{4} + 22 \, x^{3} + x^{2} {\left (8 \, \log \left (\log \left (3\right )\right ) + 175\right )} + 22 \, x {\left (4 \, \log \left (\log \left (3\right )\right ) + 27\right )} + 16 \, \log \left (\log \left (3\right )\right )^{2} + 216 \, \log \left (\log \left (3\right )\right ) + 729\right )} \log \left (\frac {1}{3} \, x\right )^{2} + 2 \, {\left (1408 \, \log \left (\log \left (3\right )\right )^{3} + 28512 \, \log \left (\log \left (3\right )\right )^{2} + 192456 \, \log \left (\log \left (3\right )\right ) + 433027\right )} x - 4 \, {\left (x^{6} + 33 \, x^{5} + 12 \, x^{4} {\left (\log \left (\log \left (3\right )\right ) + 37\right )} + 11 \, x^{3} {\left (24 \, \log \left (\log \left (3\right )\right ) + 283\right )} + 12 \, {\left (4 \, \log \left (\log \left (3\right )\right )^{2} + 175 \, \log \left (\log \left (3\right )\right ) + 999\right )} x^{2} + 33 \, {\left (16 \, \log \left (\log \left (3\right )\right )^{2} + 216 \, \log \left (\log \left (3\right )\right ) + 729\right )} x\right )} \log \left (\frac {1}{3} \, x\right ) - 4 \, {\left (64 \, \log \left (\log \left (3\right )\right )^{3} + 1296 \, \log \left (\log \left (3\right )\right )^{2} + 8748 \, \log \left (\log \left (3\right )\right ) + 19683\right )} \log \left (\frac {1}{3} \, x\right ) \]
integrate(((512*x^2+2816*x-256)*log(log(3))^3+((-384*x^2-2112*x+192)*log(1 /3*x)+384*x^4+6336*x^3+33408*x^2+54912*x-5184)*log(log(3))^2+((96*x^2+528* x-48)*log(1/3*x)^2+(-192*x^4-3168*x^3-16704*x^2-27456*x+2592)*log(1/3*x)+9 6*x^6+2640*x^5+28368*x^4+148368*x^3+375216*x^2+356400*x-34992)*log(log(3)) +(-8*x^2-44*x+4)*log(1/3*x)^3+(24*x^4+396*x^3+2088*x^2+3432*x-324)*log(1/3 *x)^2+(-24*x^6-660*x^5-7092*x^4-37092*x^3-93804*x^2-89100*x+8748)*log(1/3* x)+8*x^8+308*x^7+5000*x^6+44308*x^5+231100*x^4+707476*x^3+1168020*x^2+7698 26*x-78732)/x,x, algorithm=\
x^8 + 44*x^7 + 2*x^6*(8*log(log(3)) + 417) + 88*x^5*(6*log(log(3)) + 101) + (96*log(log(3))^2 + 7104*log(log(3)) + 58219)*x^4 + 88*(24*log(log(3))^2 + 566*log(log(3)) + 2727)*x^3 - 4*(x^2 + 11*x + 4*log(log(3)) + 27)*log(1 /3*x)^3 + log(1/3*x)^4 + 2*(128*log(log(3))^3 + 8400*log(log(3))^2 + 95904 *log(log(3)) + 303993)*x^2 + 6*(x^4 + 22*x^3 + x^2*(8*log(log(3)) + 175) + 22*x*(4*log(log(3)) + 27) + 16*log(log(3))^2 + 216*log(log(3)) + 729)*log (1/3*x)^2 + 2*(1408*log(log(3))^3 + 28512*log(log(3))^2 + 192456*log(log(3 )) + 433027)*x - 4*(x^6 + 33*x^5 + 12*x^4*(log(log(3)) + 37) + 11*x^3*(24* log(log(3)) + 283) + 12*(4*log(log(3))^2 + 175*log(log(3)) + 999)*x^2 + 33 *(16*log(log(3))^2 + 216*log(log(3)) + 729)*x)*log(1/3*x) - 4*(64*log(log( 3))^3 + 1296*log(log(3))^2 + 8748*log(log(3)) + 19683)*log(1/3*x)
Time = 10.83 (sec) , antiderivative size = 335, normalized size of antiderivative = 11.55 \[ \int \frac {-78732+769826 x+1168020 x^2+707476 x^3+231100 x^4+44308 x^5+5000 x^6+308 x^7+8 x^8+\left (8748-89100 x-93804 x^2-37092 x^3-7092 x^4-660 x^5-24 x^6\right ) \log \left (\frac {x}{3}\right )+\left (-324+3432 x+2088 x^2+396 x^3+24 x^4\right ) \log ^2\left (\frac {x}{3}\right )+\left (4-44 x-8 x^2\right ) \log ^3\left (\frac {x}{3}\right )+\left (-34992+356400 x+375216 x^2+148368 x^3+28368 x^4+2640 x^5+96 x^6+\left (2592-27456 x-16704 x^2-3168 x^3-192 x^4\right ) \log \left (\frac {x}{3}\right )+\left (-48+528 x+96 x^2\right ) \log ^2\left (\frac {x}{3}\right )\right ) \log (\log (3))+\left (-5184+54912 x+33408 x^2+6336 x^3+384 x^4+\left (192-2112 x-384 x^2\right ) \log \left (\frac {x}{3}\right )\right ) \log ^2(\log (3))+\left (-256+2816 x+512 x^2\right ) \log ^3(\log (3))}{x} \, dx=x^4\,\left (7104\,\ln \left (\ln \left (3\right )\right )+96\,{\ln \left (\ln \left (3\right )\right )}^2+58219\right )-\ln \left (x\right )\,\left (34992\,\ln \left (\ln \left (3\right )\right )+5184\,{\ln \left (\ln \left (3\right )\right )}^2+256\,{\ln \left (\ln \left (3\right )\right )}^3+78732\right )+x^3\,\left (49808\,\ln \left (\ln \left (3\right )\right )+2112\,{\ln \left (\ln \left (3\right )\right )}^2+239976\right )-44\,x\,{\ln \left (\frac {x}{3}\right )}^3-132\,x^5\,\ln \left (\frac {x}{3}\right )-4\,x^6\,\ln \left (\frac {x}{3}\right )-{\ln \left (\frac {x}{3}\right )}^3\,\left (16\,\ln \left (\ln \left (3\right )\right )+108\right )+x\,\left (384912\,\ln \left (\ln \left (3\right )\right )+57024\,{\ln \left (\ln \left (3\right )\right )}^2+2816\,{\ln \left (\ln \left (3\right )\right )}^3+866054\right )+{\ln \left (\frac {x}{3}\right )}^4+x^6\,\left (16\,\ln \left (\ln \left (3\right )\right )+834\right )+x^5\,\left (528\,\ln \left (\ln \left (3\right )\right )+8888\right )+44\,x^7+x^8-4\,x^2\,{\ln \left (\frac {x}{3}\right )}^3+132\,x^3\,{\ln \left (\frac {x}{3}\right )}^2+6\,x^4\,{\ln \left (\frac {x}{3}\right )}^2+6\,{\ln \left (\frac {x}{3}\right )}^2\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2-132\,x\,\ln \left (\frac {x}{3}\right )\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2-x^4\,\ln \left (\frac {x}{3}\right )\,\left (48\,\ln \left (\ln \left (3\right )\right )+1776\right )+x\,{\ln \left (\frac {x}{3}\right )}^2\,\left (528\,\ln \left (\ln \left (3\right )\right )+3564\right )-x^3\,\ln \left (\frac {x}{3}\right )\,\left (1056\,\ln \left (\ln \left (3\right )\right )+12452\right )+x^2\,{\ln \left (\frac {x}{3}\right )}^2\,\left (48\,\ln \left (\ln \left (3\right )\right )+1050\right )+2\,x^2\,{\left (4\,\ln \left (\ln \left (3\right )\right )+27\right )}^2\,\left (8\,\ln \left (\ln \left (3\right )\right )+417\right )-48\,x^2\,\ln \left (\frac {x}{3}\right )\,\left (\ln \left (\ln \left (3\right )\right )+37\right )\,\left (4\,\ln \left (\ln \left (3\right )\right )+27\right ) \]
int((769826*x + log(log(3))^3*(2816*x + 512*x^2 - 256) - log(x/3)^3*(44*x + 8*x^2 - 4) + log(log(3))*(356400*x + log(x/3)^2*(528*x + 96*x^2 - 48) - log(x/3)*(27456*x + 16704*x^2 + 3168*x^3 + 192*x^4 - 2592) + 375216*x^2 + 148368*x^3 + 28368*x^4 + 2640*x^5 + 96*x^6 - 34992) + log(log(3))^2*(54912 *x - log(x/3)*(2112*x + 384*x^2 - 192) + 33408*x^2 + 6336*x^3 + 384*x^4 - 5184) + 1168020*x^2 + 707476*x^3 + 231100*x^4 + 44308*x^5 + 5000*x^6 + 308 *x^7 + 8*x^8 + log(x/3)^2*(3432*x + 2088*x^2 + 396*x^3 + 24*x^4 - 324) - l og(x/3)*(89100*x + 93804*x^2 + 37092*x^3 + 7092*x^4 + 660*x^5 + 24*x^6 - 8 748) - 78732)/x,x)
x^4*(7104*log(log(3)) + 96*log(log(3))^2 + 58219) - log(x)*(34992*log(log( 3)) + 5184*log(log(3))^2 + 256*log(log(3))^3 + 78732) + x^3*(49808*log(log (3)) + 2112*log(log(3))^2 + 239976) - 44*x*log(x/3)^3 - 132*x^5*log(x/3) - 4*x^6*log(x/3) - log(x/3)^3*(16*log(log(3)) + 108) + x*(384912*log(log(3) ) + 57024*log(log(3))^2 + 2816*log(log(3))^3 + 866054) + log(x/3)^4 + x^6* (16*log(log(3)) + 834) + x^5*(528*log(log(3)) + 8888) + 44*x^7 + x^8 - 4*x ^2*log(x/3)^3 + 132*x^3*log(x/3)^2 + 6*x^4*log(x/3)^2 + 6*log(x/3)^2*(4*lo g(log(3)) + 27)^2 - 132*x*log(x/3)*(4*log(log(3)) + 27)^2 - x^4*log(x/3)*( 48*log(log(3)) + 1776) + x*log(x/3)^2*(528*log(log(3)) + 3564) - x^3*log(x /3)*(1056*log(log(3)) + 12452) + x^2*log(x/3)^2*(48*log(log(3)) + 1050) + 2*x^2*(4*log(log(3)) + 27)^2*(8*log(log(3)) + 417) - 48*x^2*log(x/3)*(log( log(3)) + 37)*(4*log(log(3)) + 27)