Integrand size = 139, antiderivative size = 28 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=\frac {x^3 \left (-(18+x)^2+\log (x)\right )^2}{-x+(5+x) \log (x)} \] Output:
(ln(x)-(18+x)^2)^2*x^3/(ln(x)*(5+x)-x)
Leaf count is larger than twice the leaf count of optimal. \(72\) vs. \(2(28)=56\).
Time = 0.04 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=\frac {x \left (-8375+104976 x^2+23328 x^3+1944 x^4+72 x^5+x^6\right )+\left (41875+8375 x-648 x^3-72 x^4-2 x^5\right ) \log (x)+x^3 \log ^2(x)}{-x+(5+x) \log (x)} \] Input:
Integrate[(-524880*x^2 - 430920*x^3 - 102960*x^4 - 10078*x^5 - 437*x^6 - 7 *x^7 + (1574640*x^2 + 677806*x^3 + 118800*x^4 + 9944*x^5 + 395*x^6 + 6*x^7 )*Log[x] + (-9715*x^2 - 2737*x^3 - 266*x^4 - 8*x^5)*Log[x]^2 + (15*x^2 + 2 *x^3)*Log[x]^3)/(x^2 + (-10*x - 2*x^2)*Log[x] + (25 + 10*x + x^2)*Log[x]^2 ),x]
Output:
(x*(-8375 + 104976*x^2 + 23328*x^3 + 1944*x^4 + 72*x^5 + x^6) + (41875 + 8 375*x - 648*x^3 - 72*x^4 - 2*x^5)*Log[x] + x^3*Log[x]^2)/(-x + (5 + 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.
| \(\displaystyle \int \frac {-7 x^7-437 x^6-10078 x^5-102960 x^4-430920 x^3-524880 x^2+\left (2 x^3+15 x^2\right ) \log ^3(x)+\left (-8 x^5-266 x^4-2737 x^3-9715 x^2\right ) \log ^2(x)+\left (6 x^7+395 x^6+9944 x^5+118800 x^4+677806 x^3+1574640 x^2\right ) \log (x)}{x^2+\left (x^2+10 x+25\right ) \log ^2(x)+\left (-2 x^2-10 x\right ) \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-7 x^7-437 x^6-10078 x^5-102960 x^4-430920 x^3-524880 x^2+\left (2 x^3+15 x^2\right ) \log ^3(x)+\left (-8 x^5-266 x^4-2737 x^3-9715 x^2\right ) \log ^2(x)+\left (6 x^7+395 x^6+9944 x^5+118800 x^4+677806 x^3+1574640 x^2\right ) \log (x)}{(x+x (-\log (x))-5 \log (x))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {(2 x+15) x^2 \log (x)}{(x+5)^2}-\frac {\left (x^2+5 x+25\right ) \left (x^3+41 x^2+503 x+1620\right )^2 x^2}{(x+5)^3 (-x+x \log (x)+5 \log (x))^2}-\frac {\left (8 x^4+306 x^3+4063 x^2+23370 x+48575\right ) x^2}{(x+5)^3}+\frac {\left (6 x^7+455 x^6+14028 x^5+227503 x^4+2106278 x^3+11275945 x^2+32594400 x+39366000\right ) x^2}{(x+5)^3 (-x+x \log (x)+5 \log (x))}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\int \frac {x^7}{(\log (x) x-x+5 \log (x))^2}dx-72 \int \frac {x^6}{(\log (x) x-x+5 \log (x))^2}dx+6 \int \frac {x^6}{\log (x) x-x+5 \log (x)}dx-1967 \int \frac {x^5}{(\log (x) x-x+5 \log (x))^2}dx+365 \int \frac {x^5}{\log (x) x-x+5 \log (x)}dx-24941 \int \frac {x^4}{(\log (x) x-x+5 \log (x))^2}dx+8103 \int \frac {x^4}{\log (x) x-x+5 \log (x)}dx-144814 \int \frac {x^3}{(\log (x) x-x+5 \log (x))^2}dx+77833 \int \frac {x^3}{\log (x) x-x+5 \log (x)}dx-382455 \int \frac {x^2}{(\log (x) x-x+5 \log (x))^2}dx+285433 \int \frac {x^2}{\log (x) x-x+5 \log (x)}dx+3476750 \int \frac {1}{(\log (x) x-x+5 \log (x))^2}dx-703725 \int \frac {x}{(\log (x) x-x+5 \log (x))^2}dx-15625 \int \frac {1}{(x+5)^3 (\log (x) x-x+5 \log (x))^2}dx-1040625 \int \frac {1}{(x+5)^2 (\log (x) x-x+5 \log (x))^2}dx-17175000 \int \frac {1}{(x+5) (\log (x) x-x+5 \log (x))^2}dx-703700 \int \frac {1}{\log (x) x-x+5 \log (x)}dx+144100 \int \frac {x}{\log (x) x-x+5 \log (x)}dx+9375 \int \frac {1}{(x+5)^3 (\log (x) x-x+5 \log (x))}dx+416250 \int \frac {1}{(x+5)^2 (\log (x) x-x+5 \log (x))}dx+3434875 \int \frac {1}{(x+5) (\log (x) x-x+5 \log (x))}dx-2 x^4-62 x^3-337 x^2+x^2 \log (x)+1680 x+\frac {41750}{x+5}+\frac {625}{(x+5)^2}+\frac {25 x \log (x)}{x+5}-5 x \log (x)\) |
Input:
Int[(-524880*x^2 - 430920*x^3 - 102960*x^4 - 10078*x^5 - 437*x^6 - 7*x^7 + (1574640*x^2 + 677806*x^3 + 118800*x^4 + 9944*x^5 + 395*x^6 + 6*x^7)*Log[ x] + (-9715*x^2 - 2737*x^3 - 266*x^4 - 8*x^5)*Log[x]^2 + (15*x^2 + 2*x^3)* Log[x]^3)/(x^2 + (-10*x - 2*x^2)*Log[x] + (25 + 10*x + x^2)*Log[x]^2),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(28)=56\).
Time = 4.02 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.46
| method | result | size |
| parallelrisch | \(\frac {x^{7}+72 x^{6}-2 x^{5} \ln \left (x \right )+1944 x^{5}-72 x^{4} \ln \left (x \right )+x^{3} \ln \left (x \right )^{2}+23328 x^{4}-648 x^{3} \ln \left (x \right )+104976 x^{3}}{x \ln \left (x \right )+5 \ln \left (x \right )-x}\) | \(69\) |
| risch | \(\frac {\left (x^{3}-25 x -125\right ) \ln \left (x \right )}{5+x}+\frac {-2 x^{6}-82 x^{5}-1007 x^{4}+25 x^{2} \ln \left (x \right )-3240 x^{3}+250 x \ln \left (x \right )+8375 x^{2}+625 \ln \left (x \right )+83750 x +209375}{x^{2}+10 x +25}+\frac {\left (x^{6}+82 x^{5}+2687 x^{4}+44486 x^{3}+385849 x^{2}+1629720 x +2624400\right ) x^{3}}{\left (x^{2}+10 x +25\right ) \left (x \ln \left (x \right )+5 \ln \left (x \right )-x \right )}\) | \(131\) |
| default | \(25 \ln \left (x \right )+\frac {695325 \ln \left (x \right )^{6}-3849400 \ln \left (x \right )^{5}+7975225 \ln \left (x \right )^{4}-7304150 \ln \left (x \right )^{3}+2448350 \ln \left (x \right )^{2}+58650 \ln \left (x \right )-8375}{\left (\ln \left (x \right )^{2}-2 \ln \left (x \right )+1\right ) \left (\ln \left (x \right )-1\right )^{5}}+\frac {x^{6}}{\ln \left (x \right )-1}+\frac {\left (67 \ln \left (x \right )-72\right ) x^{5}}{\left (\ln \left (x \right )-1\right )^{2}}-\frac {\left (2 \ln \left (x \right )^{3}-1613 \ln \left (x \right )^{2}+3530 \ln \left (x \right )-1944\right ) x^{4}}{\left (\ln \left (x \right )-1\right )^{3}}-\frac {\left (62 \ln \left (x \right )^{4}-15479 \ln \left (x \right )^{3}+52550 \ln \left (x \right )^{2}-60336 \ln \left (x \right )+23328\right ) x^{3}}{\left (\ln \left (x \right )-1\right )^{4}}+\frac {\left (\ln \left (x \right )^{6}-342 \ln \left (x \right )^{5}+30179 \ln \left (x \right )^{4}-161046 \ln \left (x \right )^{3}+330769 \ln \left (x \right )^{2}-303912 \ln \left (x \right )+104976\right ) x^{2}}{\left (\ln \left (x \right )-1\right )^{5}}-\frac {5 \ln \left (x \right ) \left (\ln \left (x \right )^{6}-342 \ln \left (x \right )^{5}+30179 \ln \left (x \right )^{4}-161046 \ln \left (x \right )^{3}+330769 \ln \left (x \right )^{2}-303912 \ln \left (x \right )+104976\right ) x}{\left (\ln \left (x \right )-1\right )^{6}}-\frac {125 \ln \left (x \right )^{3} \left (\ln \left (x \right )^{6}-342 \ln \left (x \right )^{5}+30179 \ln \left (x \right )^{4}-161046 \ln \left (x \right )^{3}+330769 \ln \left (x \right )^{2}-303912 \ln \left (x \right )+104976\right )}{\left (\ln \left (x \right )^{2}-2 \ln \left (x \right )+1\right ) \left (\ln \left (x \right )-1\right )^{5} \left (x \ln \left (x \right )+5 \ln \left (x \right )-x \right )}\) | \(312\) |
Input:
int(((2*x^3+15*x^2)*ln(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*ln(x)^2+(6* x^7+395*x^6+9944*x^5+118800*x^4+677806*x^3+1574640*x^2)*ln(x)-7*x^7-437*x^ 6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*ln(x)^2+(-2*x ^2-10*x)*ln(x)+x^2),x,method=_RETURNVERBOSE)
Output:
(x^7+72*x^6-2*x^5*ln(x)+1944*x^5-72*x^4*ln(x)+x^3*ln(x)^2+23328*x^4-648*x^ 3*ln(x)+104976*x^3)/(x*ln(x)+5*ln(x)-x)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (28) = 56\).
Time = 0.09 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=\frac {x^{7} + 72 \, x^{6} + 1944 \, x^{5} + x^{3} \log \left (x\right )^{2} + 23328 \, x^{4} + 104976 \, x^{3} - {\left (2 \, x^{5} + 72 \, x^{4} + 648 \, x^{3} - 8375 \, x - 41875\right )} \log \left (x\right ) - 8375 \, x}{{\left (x + 5\right )} \log \left (x\right ) - x} \] Input:
integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log( x)^2+(6*x^7+395*x^6+9944*x^5+118800*x^4+677806*x^3+1574640*x^2)*log(x)-7*x ^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*log( x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="fricas")
Output:
(x^7 + 72*x^6 + 1944*x^5 + x^3*log(x)^2 + 23328*x^4 + 104976*x^3 - (2*x^5 + 72*x^4 + 648*x^3 - 8375*x - 41875)*log(x) - 8375*x)/((x + 5)*log(x) - x)
Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (20) = 40\).
Time = 0.25 (sec) , antiderivative size = 116, normalized size of antiderivative = 4.14 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=- 2 x^{4} - 62 x^{3} - 337 x^{2} + 1680 x - \frac {- 41750 x - 209375}{x^{2} + 10 x + 25} + 25 \log {\left (x \right )} + \frac {x^{9} + 82 x^{8} + 2687 x^{7} + 44486 x^{6} + 385849 x^{5} + 1629720 x^{4} + 2624400 x^{3}}{- x^{3} - 10 x^{2} - 25 x + \left (x^{3} + 15 x^{2} + 75 x + 125\right ) \log {\left (x \right )}} + \frac {\left (x^{3} - 25 x - 125\right ) \log {\left (x \right )}}{x + 5} \] Input:
integrate(((2*x**3+15*x**2)*ln(x)**3+(-8*x**5-266*x**4-2737*x**3-9715*x**2 )*ln(x)**2+(6*x**7+395*x**6+9944*x**5+118800*x**4+677806*x**3+1574640*x**2 )*ln(x)-7*x**7-437*x**6-10078*x**5-102960*x**4-430920*x**3-524880*x**2)/(( x**2+10*x+25)*ln(x)**2+(-2*x**2-10*x)*ln(x)+x**2),x)
Output:
-2*x**4 - 62*x**3 - 337*x**2 + 1680*x - (-41750*x - 209375)/(x**2 + 10*x + 25) + 25*log(x) + (x**9 + 82*x**8 + 2687*x**7 + 44486*x**6 + 385849*x**5 + 1629720*x**4 + 2624400*x**3)/(-x**3 - 10*x**2 - 25*x + (x**3 + 15*x**2 + 75*x + 125)*log(x)) + (x**3 - 25*x - 125)*log(x)/(x + 5)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (28) = 56\).
Time = 0.08 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.57 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=\frac {x^{7} + 72 \, x^{6} + 1944 \, x^{5} + x^{3} \log \left (x\right )^{2} + 23328 \, x^{4} + 104976 \, x^{3} - {\left (2 \, x^{5} + 72 \, x^{4} + 648 \, x^{3} - 8375 \, x - 41875\right )} \log \left (x\right ) - 8375 \, x}{{\left (x + 5\right )} \log \left (x\right ) - x} \] Input:
integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log( x)^2+(6*x^7+395*x^6+9944*x^5+118800*x^4+677806*x^3+1574640*x^2)*log(x)-7*x ^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*log( x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="maxima")
Output:
(x^7 + 72*x^6 + 1944*x^5 + x^3*log(x)^2 + 23328*x^4 + 104976*x^3 - (2*x^5 + 72*x^4 + 648*x^3 - 8375*x - 41875)*log(x) - 8375*x)/((x + 5)*log(x) - x)
Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (28) = 56\).
Time = 0.13 (sec) , antiderivative size = 130, normalized size of antiderivative = 4.64 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=-2 \, x^{4} - 62 \, x^{3} - 337 \, x^{2} + {\left (x^{2} - 5 \, x - \frac {125}{x + 5}\right )} \log \left (x\right ) + 1680 \, x + \frac {x^{9} + 82 \, x^{8} + 2687 \, x^{7} + 44486 \, x^{6} + 385849 \, x^{5} + 1629720 \, x^{4} + 2624400 \, x^{3}}{x^{3} \log \left (x\right ) - x^{3} + 15 \, x^{2} \log \left (x\right ) - 10 \, x^{2} + 75 \, x \log \left (x\right ) - 25 \, x + 125 \, \log \left (x\right )} + \frac {125 \, {\left (334 \, x + 1675\right )}}{x^{2} + 10 \, x + 25} + 25 \, \log \left (x\right ) \] Input:
integrate(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log( x)^2+(6*x^7+395*x^6+9944*x^5+118800*x^4+677806*x^3+1574640*x^2)*log(x)-7*x ^7-437*x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*log( x)^2+(-2*x^2-10*x)*log(x)+x^2),x, algorithm="giac")
Output:
-2*x^4 - 62*x^3 - 337*x^2 + (x^2 - 5*x - 125/(x + 5))*log(x) + 1680*x + (x ^9 + 82*x^8 + 2687*x^7 + 44486*x^6 + 385849*x^5 + 1629720*x^4 + 2624400*x^ 3)/(x^3*log(x) - x^3 + 15*x^2*log(x) - 10*x^2 + 75*x*log(x) - 25*x + 125*l og(x)) + 125*(334*x + 1675)/(x^2 + 10*x + 25) + 25*log(x)
Time = 2.75 (sec) , antiderivative size = 122, normalized size of antiderivative = 4.36 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=1680\,x+\frac {41750\,x+209375}{x^2+10\,x+25}-337\,x^2-62\,x^3-2\,x^4+\frac {x^3\,\ln \left (x\right )}{x+5}-\frac {x^{12}+87\,x^{11}+3122\,x^{10}+59971\,x^9+675454\,x^8+4671115\,x^7+20419225\,x^6+53865000\,x^5+65610000\,x^4}{{\left (x+5\right )}^2\,\left (x-\ln \left (x\right )\,\left (x+5\right )\right )\,\left (x^3+5\,x^2+25\,x\right )} \] Input:
int(-(524880*x^2 - log(x)^3*(15*x^2 + 2*x^3) + 430920*x^3 + 102960*x^4 + 1 0078*x^5 + 437*x^6 + 7*x^7 + log(x)^2*(9715*x^2 + 2737*x^3 + 266*x^4 + 8*x ^5) - log(x)*(1574640*x^2 + 677806*x^3 + 118800*x^4 + 9944*x^5 + 395*x^6 + 6*x^7))/(log(x)^2*(10*x + x^2 + 25) - log(x)*(10*x + 2*x^2) + x^2),x)
Output:
1680*x + (41750*x + 209375)/(10*x + x^2 + 25) - 337*x^2 - 62*x^3 - 2*x^4 + (x^3*log(x))/(x + 5) - (65610000*x^4 + 53865000*x^5 + 20419225*x^6 + 4671 115*x^7 + 675454*x^8 + 59971*x^9 + 3122*x^10 + 87*x^11 + x^12)/((x + 5)^2* (x - log(x)*(x + 5))*(25*x + 5*x^2 + x^3))
Time = 0.18 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00 \[ \int \frac {-524880 x^2-430920 x^3-102960 x^4-10078 x^5-437 x^6-7 x^7+\left (1574640 x^2+677806 x^3+118800 x^4+9944 x^5+395 x^6+6 x^7\right ) \log (x)+\left (-9715 x^2-2737 x^3-266 x^4-8 x^5\right ) \log ^2(x)+\left (15 x^2+2 x^3\right ) \log ^3(x)}{x^2+\left (-10 x-2 x^2\right ) \log (x)+\left (25+10 x+x^2\right ) \log ^2(x)} \, dx=\frac {x^{3} \left (\mathrm {log}\left (x \right )^{2}-2 \,\mathrm {log}\left (x \right ) x^{2}-72 \,\mathrm {log}\left (x \right ) x -648 \,\mathrm {log}\left (x \right )+x^{4}+72 x^{3}+1944 x^{2}+23328 x +104976\right )}{\mathrm {log}\left (x \right ) x +5 \,\mathrm {log}\left (x \right )-x} \] Input:
int(((2*x^3+15*x^2)*log(x)^3+(-8*x^5-266*x^4-2737*x^3-9715*x^2)*log(x)^2+( 6*x^7+395*x^6+9944*x^5+118800*x^4+677806*x^3+1574640*x^2)*log(x)-7*x^7-437 *x^6-10078*x^5-102960*x^4-430920*x^3-524880*x^2)/((x^2+10*x+25)*log(x)^2+( -2*x^2-10*x)*log(x)+x^2),x)
Output:
(x**3*(log(x)**2 - 2*log(x)*x**2 - 72*log(x)*x - 648*log(x) + x**4 + 72*x* *3 + 1944*x**2 + 23328*x + 104976))/(log(x)*x + 5*log(x) - x)