Integrand size = 190, antiderivative size = 24 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=2 x+\frac {x}{x+\frac {(-3-x)^4}{\log ^2(4 x)}} \] Output:
2*x+x/((-3-x)^4/ln(4*x)^2+x)
Time = 1.51 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.67 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=\frac {(3+x)^4 (-1+2 x)+2 x^2 \log ^2(4 x)}{(3+x)^4+x \log ^2(4 x)} \] Input:
Integrate[(13122 + 34992*x + 40824*x^2 + 27216*x^3 + 11340*x^4 + 3024*x^5 + 504*x^6 + 48*x^7 + 2*x^8 + (162 + 216*x + 108*x^2 + 24*x^3 + 2*x^4)*Log[ 4*x] + (81 + 324*x + 378*x^2 + 192*x^3 + 45*x^4 + 4*x^5)*Log[4*x]^2 + 2*x^ 2*Log[4*x]^4)/(6561 + 17496*x + 20412*x^2 + 13608*x^3 + 5670*x^4 + 1512*x^ 5 + 252*x^6 + 24*x^7 + x^8 + (162*x + 216*x^2 + 108*x^3 + 24*x^4 + 2*x^5)* Log[4*x]^2 + x^2*Log[4*x]^4),x]
Output:
((3 + x)^4*(-1 + 2*x) + 2*x^2*Log[4*x]^2)/((3 + x)^4 + x*Log[4*x]^2)
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.
| \(\displaystyle \int \frac {2 x^8+48 x^7+504 x^6+3024 x^5+11340 x^4+27216 x^3+40824 x^2+2 x^2 \log ^4(4 x)+\left (2 x^4+24 x^3+108 x^2+216 x+162\right ) \log (4 x)+\left (4 x^5+45 x^4+192 x^3+378 x^2+324 x+81\right ) \log ^2(4 x)+34992 x+13122}{x^8+24 x^7+252 x^6+1512 x^5+5670 x^4+13608 x^3+20412 x^2+x^2 \log ^4(4 x)+\left (2 x^5+24 x^4+108 x^3+216 x^2+162 x\right ) \log ^2(4 x)+17496 x+6561} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^2 \log ^4(4 x)+\left (4 x^2+9 x+3\right ) (x+3)^3 \log ^2(4 x)+2 (x+3)^8+2 (x+3)^4 \log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {3 (x-1) (x+3)^3}{x \left (x^4+12 x^3+54 x^2+108 x+x \log ^2(4 x)+81\right )}+\frac {3 x^8+60 x^7+504 x^6+2268 x^5+2 x^5 \log (4 x)+5670 x^4+24 x^4 \log (4 x)+6804 x^3+108 x^3 \log (4 x)+216 x^2 \log (4 x)-8748 x+162 x \log (4 x)-6561}{x \left (x^4+12 x^3+54 x^2+108 x+x \log ^2(4 x)+81\right )^2}+2\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 3 \int \frac {x^7}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+60 \int \frac {x^6}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+504 \int \frac {x^5}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+2268 \int \frac {x^4}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+2 \int \frac {x^4 \log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+5670 \int \frac {x^3}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+24 \int \frac {x^3 \log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx-3 \int \frac {x^3}{(x+3)^4+x \log ^2(4 x)}dx+6804 \int \frac {x^2}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+108 \int \frac {x^2 \log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx-24 \int \frac {x^2}{(x+3)^4+x \log ^2(4 x)}dx-8748 \int \frac {1}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx-6561 \int \frac {1}{x \left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+162 \int \frac {\log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+216 \int \frac {x \log (4 x)}{\left ((x+3)^4+x \log ^2(4 x)\right )^2}dx+81 \int \frac {1}{x \left ((x+3)^4+x \log ^2(4 x)\right )}dx-54 \int \frac {x}{(x+3)^4+x \log ^2(4 x)}dx+2 x\) |
Input:
Int[(13122 + 34992*x + 40824*x^2 + 27216*x^3 + 11340*x^4 + 3024*x^5 + 504* x^6 + 48*x^7 + 2*x^8 + (162 + 216*x + 108*x^2 + 24*x^3 + 2*x^4)*Log[4*x] + (81 + 324*x + 378*x^2 + 192*x^3 + 45*x^4 + 4*x^5)*Log[4*x]^2 + 2*x^2*Log[ 4*x]^4)/(6561 + 17496*x + 20412*x^2 + 13608*x^3 + 5670*x^4 + 1512*x^5 + 25 2*x^6 + 24*x^7 + x^8 + (162*x + 216*x^2 + 108*x^3 + 24*x^4 + 2*x^5)*Log[4* x]^2 + x^2*Log[4*x]^4),x]
Output:
$Aborted
Time = 9.94 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.88
| method | result | size |
| derivativedivides | \(2 x +\frac {256 \ln \left (4 x \right )^{2} x}{256 x^{4}+3072 x^{3}+256 x \ln \left (4 x \right )^{2}+13824 x^{2}+27648 x +20736}\) | \(45\) |
| default | \(2 x +\frac {256 \ln \left (4 x \right )^{2} x}{256 x^{4}+3072 x^{3}+256 x \ln \left (4 x \right )^{2}+13824 x^{2}+27648 x +20736}\) | \(45\) |
| risch | \(2 x -\frac {x^{4}+12 x^{3}+54 x^{2}+108 x +81}{x^{4}+x \ln \left (4 x \right )^{2}+12 x^{3}+54 x^{2}+108 x +81}\) | \(53\) |
| parallelrisch | \(\frac {-81+54 x +2 \ln \left (4 x \right )^{2} x^{2}+2 x^{5}+162 x^{2}+96 x^{3}+23 x^{4}}{x^{4}+x \ln \left (4 x \right )^{2}+12 x^{3}+54 x^{2}+108 x +81}\) | \(66\) |
Input:
int((2*x^2*ln(4*x)^4+(4*x^5+45*x^4+192*x^3+378*x^2+324*x+81)*ln(4*x)^2+(2* x^4+24*x^3+108*x^2+216*x+162)*ln(4*x)+2*x^8+48*x^7+504*x^6+3024*x^5+11340* x^4+27216*x^3+40824*x^2+34992*x+13122)/(x^2*ln(4*x)^4+(2*x^5+24*x^4+108*x^ 3+216*x^2+162*x)*ln(4*x)^2+x^8+24*x^7+252*x^6+1512*x^5+5670*x^4+13608*x^3+ 20412*x^2+17496*x+6561),x,method=_RETURNVERBOSE)
Output:
2*x+256*ln(4*x)^2*x/(256*x^4+3072*x^3+256*x*ln(4*x)^2+13824*x^2+27648*x+20 736)
Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (22) = 44\).
Time = 0.09 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.71 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=\frac {2 \, x^{5} + 23 \, x^{4} + 2 \, x^{2} \log \left (4 \, x\right )^{2} + 96 \, x^{3} + 162 \, x^{2} + 54 \, x - 81}{x^{4} + 12 \, x^{3} + x \log \left (4 \, x\right )^{2} + 54 \, x^{2} + 108 \, x + 81} \] Input:
integrate((2*x^2*log(4*x)^4+(4*x^5+45*x^4+192*x^3+378*x^2+324*x+81)*log(4* x)^2+(2*x^4+24*x^3+108*x^2+216*x+162)*log(4*x)+2*x^8+48*x^7+504*x^6+3024*x ^5+11340*x^4+27216*x^3+40824*x^2+34992*x+13122)/(x^2*log(4*x)^4+(2*x^5+24* x^4+108*x^3+216*x^2+162*x)*log(4*x)^2+x^8+24*x^7+252*x^6+1512*x^5+5670*x^4 +13608*x^3+20412*x^2+17496*x+6561),x, algorithm="fricas")
Output:
(2*x^5 + 23*x^4 + 2*x^2*log(4*x)^2 + 96*x^3 + 162*x^2 + 54*x - 81)/(x^4 + 12*x^3 + x*log(4*x)^2 + 54*x^2 + 108*x + 81)
Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (19) = 38\).
Time = 0.17 (sec) , antiderivative size = 49, normalized size of antiderivative = 2.04 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=2 x + \frac {- x^{4} - 12 x^{3} - 54 x^{2} - 108 x - 81}{x^{4} + 12 x^{3} + 54 x^{2} + x \log {\left (4 x \right )}^{2} + 108 x + 81} \] Input:
integrate((2*x**2*ln(4*x)**4+(4*x**5+45*x**4+192*x**3+378*x**2+324*x+81)*l n(4*x)**2+(2*x**4+24*x**3+108*x**2+216*x+162)*ln(4*x)+2*x**8+48*x**7+504*x **6+3024*x**5+11340*x**4+27216*x**3+40824*x**2+34992*x+13122)/(x**2*ln(4*x )**4+(2*x**5+24*x**4+108*x**3+216*x**2+162*x)*ln(4*x)**2+x**8+24*x**7+252* x**6+1512*x**5+5670*x**4+13608*x**3+20412*x**2+17496*x+6561),x)
Output:
2*x + (-x**4 - 12*x**3 - 54*x**2 - 108*x - 81)/(x**4 + 12*x**3 + 54*x**2 + x*log(4*x)**2 + 108*x + 81)
Leaf count of result is larger than twice the leaf count of optimal. 91 vs. \(2 (22) = 44\).
Time = 0.16 (sec) , antiderivative size = 91, normalized size of antiderivative = 3.79 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=\frac {2 \, x^{5} + 23 \, x^{4} + 8 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 2 \, x^{2} \log \left (x\right )^{2} + 2 \, {\left (4 \, \log \left (2\right )^{2} + 81\right )} x^{2} + 96 \, x^{3} + 54 \, x - 81}{x^{4} + 12 \, x^{3} + 4 \, x \log \left (2\right ) \log \left (x\right ) + x \log \left (x\right )^{2} + 4 \, {\left (\log \left (2\right )^{2} + 27\right )} x + 54 \, x^{2} + 81} \] Input:
integrate((2*x^2*log(4*x)^4+(4*x^5+45*x^4+192*x^3+378*x^2+324*x+81)*log(4* x)^2+(2*x^4+24*x^3+108*x^2+216*x+162)*log(4*x)+2*x^8+48*x^7+504*x^6+3024*x ^5+11340*x^4+27216*x^3+40824*x^2+34992*x+13122)/(x^2*log(4*x)^4+(2*x^5+24* x^4+108*x^3+216*x^2+162*x)*log(4*x)^2+x^8+24*x^7+252*x^6+1512*x^5+5670*x^4 +13608*x^3+20412*x^2+17496*x+6561),x, algorithm="maxima")
Output:
(2*x^5 + 23*x^4 + 8*x^2*log(2)*log(x) + 2*x^2*log(x)^2 + 2*(4*log(2)^2 + 8 1)*x^2 + 96*x^3 + 54*x - 81)/(x^4 + 12*x^3 + 4*x*log(2)*log(x) + x*log(x)^ 2 + 4*(log(2)^2 + 27)*x + 54*x^2 + 81)
Leaf count of result is larger than twice the leaf count of optimal. 52 vs. \(2 (22) = 44\).
Time = 0.20 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.17 \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=2 \, x - \frac {x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81}{x^{4} + 12 \, x^{3} + x \log \left (4 \, x\right )^{2} + 54 \, x^{2} + 108 \, x + 81} \] Input:
integrate((2*x^2*log(4*x)^4+(4*x^5+45*x^4+192*x^3+378*x^2+324*x+81)*log(4* x)^2+(2*x^4+24*x^3+108*x^2+216*x+162)*log(4*x)+2*x^8+48*x^7+504*x^6+3024*x ^5+11340*x^4+27216*x^3+40824*x^2+34992*x+13122)/(x^2*log(4*x)^4+(2*x^5+24* x^4+108*x^3+216*x^2+162*x)*log(4*x)^2+x^8+24*x^7+252*x^6+1512*x^5+5670*x^4 +13608*x^3+20412*x^2+17496*x+6561),x, algorithm="giac")
Output:
2*x - (x^4 + 12*x^3 + 54*x^2 + 108*x + 81)/(x^4 + 12*x^3 + x*log(4*x)^2 + 54*x^2 + 108*x + 81)
Timed out. \[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=\int \frac {34992\,x+{\ln \left (4\,x\right )}^2\,\left (4\,x^5+45\,x^4+192\,x^3+378\,x^2+324\,x+81\right )+\ln \left (4\,x\right )\,\left (2\,x^4+24\,x^3+108\,x^2+216\,x+162\right )+40824\,x^2+27216\,x^3+11340\,x^4+3024\,x^5+504\,x^6+48\,x^7+2\,x^8+2\,x^2\,{\ln \left (4\,x\right )}^4+13122}{17496\,x+{\ln \left (4\,x\right )}^2\,\left (2\,x^5+24\,x^4+108\,x^3+216\,x^2+162\,x\right )+20412\,x^2+13608\,x^3+5670\,x^4+1512\,x^5+252\,x^6+24\,x^7+x^8+x^2\,{\ln \left (4\,x\right )}^4+6561} \,d x \] Input:
int((34992*x + log(4*x)^2*(324*x + 378*x^2 + 192*x^3 + 45*x^4 + 4*x^5 + 81 ) + log(4*x)*(216*x + 108*x^2 + 24*x^3 + 2*x^4 + 162) + 40824*x^2 + 27216* x^3 + 11340*x^4 + 3024*x^5 + 504*x^6 + 48*x^7 + 2*x^8 + 2*x^2*log(4*x)^4 + 13122)/(17496*x + log(4*x)^2*(162*x + 216*x^2 + 108*x^3 + 24*x^4 + 2*x^5) + 20412*x^2 + 13608*x^3 + 5670*x^4 + 1512*x^5 + 252*x^6 + 24*x^7 + x^8 + x^2*log(4*x)^4 + 6561),x)
Output:
int((34992*x + log(4*x)^2*(324*x + 378*x^2 + 192*x^3 + 45*x^4 + 4*x^5 + 81 ) + log(4*x)*(216*x + 108*x^2 + 24*x^3 + 2*x^4 + 162) + 40824*x^2 + 27216* x^3 + 11340*x^4 + 3024*x^5 + 504*x^6 + 48*x^7 + 2*x^8 + 2*x^2*log(4*x)^4 + 13122)/(17496*x + log(4*x)^2*(162*x + 216*x^2 + 108*x^3 + 24*x^4 + 2*x^5) + 20412*x^2 + 13608*x^3 + 5670*x^4 + 1512*x^5 + 252*x^6 + 24*x^7 + x^8 + x^2*log(4*x)^4 + 6561), x)
\[ \int \frac {13122+34992 x+40824 x^2+27216 x^3+11340 x^4+3024 x^5+504 x^6+48 x^7+2 x^8+\left (162+216 x+108 x^2+24 x^3+2 x^4\right ) \log (4 x)+\left (81+324 x+378 x^2+192 x^3+45 x^4+4 x^5\right ) \log ^2(4 x)+2 x^2 \log ^4(4 x)}{6561+17496 x+20412 x^2+13608 x^3+5670 x^4+1512 x^5+252 x^6+24 x^7+x^8+\left (162 x+216 x^2+108 x^3+24 x^4+2 x^5\right ) \log ^2(4 x)+x^2 \log ^4(4 x)} \, dx=\text {too large to display} \] Input:
int((2*x^2*log(4*x)^4+(4*x^5+45*x^4+192*x^3+378*x^2+324*x+81)*log(4*x)^2+( 2*x^4+24*x^3+108*x^2+216*x+162)*log(4*x)+2*x^8+48*x^7+504*x^6+3024*x^5+113 40*x^4+27216*x^3+40824*x^2+34992*x+13122)/(x^2*log(4*x)^4+(2*x^5+24*x^4+10 8*x^3+216*x^2+162*x)*log(4*x)^2+x^8+24*x^7+252*x^6+1512*x^5+5670*x^4+13608 *x^3+20412*x^2+17496*x+6561),x)
Output:
81*int(log(4*x)**2/(log(4*x)**4*x**2 + 2*log(4*x)**2*x**5 + 24*log(4*x)**2 *x**4 + 108*log(4*x)**2*x**3 + 216*log(4*x)**2*x**2 + 162*log(4*x)**2*x + x**8 + 24*x**7 + 252*x**6 + 1512*x**5 + 5670*x**4 + 13608*x**3 + 20412*x** 2 + 17496*x + 6561),x) + 2*int(x**8/(log(4*x)**4*x**2 + 2*log(4*x)**2*x**5 + 24*log(4*x)**2*x**4 + 108*log(4*x)**2*x**3 + 216*log(4*x)**2*x**2 + 162 *log(4*x)**2*x + x**8 + 24*x**7 + 252*x**6 + 1512*x**5 + 5670*x**4 + 13608 *x**3 + 20412*x**2 + 17496*x + 6561),x) + 48*int(x**7/(log(4*x)**4*x**2 + 2*log(4*x)**2*x**5 + 24*log(4*x)**2*x**4 + 108*log(4*x)**2*x**3 + 216*log( 4*x)**2*x**2 + 162*log(4*x)**2*x + x**8 + 24*x**7 + 252*x**6 + 1512*x**5 + 5670*x**4 + 13608*x**3 + 20412*x**2 + 17496*x + 6561),x) + 504*int(x**6/( log(4*x)**4*x**2 + 2*log(4*x)**2*x**5 + 24*log(4*x)**2*x**4 + 108*log(4*x) **2*x**3 + 216*log(4*x)**2*x**2 + 162*log(4*x)**2*x + x**8 + 24*x**7 + 252 *x**6 + 1512*x**5 + 5670*x**4 + 13608*x**3 + 20412*x**2 + 17496*x + 6561), x) + 3024*int(x**5/(log(4*x)**4*x**2 + 2*log(4*x)**2*x**5 + 24*log(4*x)**2 *x**4 + 108*log(4*x)**2*x**3 + 216*log(4*x)**2*x**2 + 162*log(4*x)**2*x + x**8 + 24*x**7 + 252*x**6 + 1512*x**5 + 5670*x**4 + 13608*x**3 + 20412*x** 2 + 17496*x + 6561),x) + 11340*int(x**4/(log(4*x)**4*x**2 + 2*log(4*x)**2* x**5 + 24*log(4*x)**2*x**4 + 108*log(4*x)**2*x**3 + 216*log(4*x)**2*x**2 + 162*log(4*x)**2*x + x**8 + 24*x**7 + 252*x**6 + 1512*x**5 + 5670*x**4 + 1 3608*x**3 + 20412*x**2 + 17496*x + 6561),x) + 27216*int(x**3/(log(4*x)*...