Integrand size = 208, antiderivative size = 37 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\log \left (5 \left (-x+4 \left (\frac {3}{x}+x+x^2 \left (-\frac {e^5}{3}+\log (\log (4-x))\right )^2\right )\right )\right ) \] Output:
ln(15*x+20*(ln(ln(4-x))-1/3*exp(5))^2*x^2+60/x)
\[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx \] Input:
Integrate[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4))*Log[4 - x] + (72*x^4 + E^5*(192*x^3 - 48*x^4)*Log[4 - x])*Log[Log [4 - x]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x + 10 8*x^2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^ 4 - 24*x^5)*Log[4 - x]*Log[Log[4 - x]] + (-144*x^4 + 36*x^5)*Log[4 - x]*Lo g[Log[4 - x]]^2),x]
Output:
Integrate[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4))*Log[4 - x] + (72*x^4 + E^5*(192*x^3 - 48*x^4)*Log[4 - x])*Log[Log [4 - x]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x + 10 8*x^2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^ 4 - 24*x^5)*Log[4 - x]*Log[Log[4 - x]] + (-144*x^4 + 36*x^5)*Log[4 - x]*Lo g[Log[4 - x]]^2), 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.
| \(\displaystyle \int \frac {-24 e^5 x^4+\left (72 x^4-288 x^3\right ) \log (4-x) \log ^2(\log (4-x))+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (27 x^3-108 x^2+e^{10} \left (8 x^4-32 x^3\right )-108 x+432\right ) \log (4-x)}{\left (36 x^5-144 x^4\right ) \log (4-x) \log ^2(\log (4-x))+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (27 x^4-108 x^3+108 x^2+e^{10} \left (4 x^5-16 x^4\right )-432 x\right ) \log (4-x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {24 e^5 x^4-\left (72 x^4-288 x^3\right ) \log (4-x) \log ^2(\log (4-x))-\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))-\left (27 x^3-108 x^2+e^{10} \left (8 x^4-32 x^3\right )-108 x+432\right ) \log (4-x)}{(4-x) x \log (4-x) \left (4 e^{10} x^3+36 x^3 \log ^2(\log (4-x))-24 e^5 x^3 \log (\log (4-x))+27 x^2+108\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2}{x}-\frac {3 \left (8 e^5 x^4-24 x^4 \log (\log (4-x))+9 x^3 \log (4-x)-36 x^2 \log (4-x)+108 x \log (4-x)-432 \log (4-x)\right )}{(x-4) x \log (4-x) \left (4 e^{10} x^3+36 x^3 \log ^2(\log (4-x))-24 e^5 x^3 \log (\log (4-x))+27 x^2+108\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {2}{x}-\frac {3 \left (8 e^5 x^4-24 x^4 \log (\log (4-x))+9 x^3 \log (4-x)-36 x^2 \log (4-x)+108 x \log (4-x)-432 \log (4-x)\right )}{(x-4) x \log (4-x) \left (4 e^{10} x^3+36 x^3 \log ^2(\log (4-x))-24 e^5 x^3 \log (\log (4-x))+27 x^2+108\right )}\right )dx\) |
Input:
Int[(-24*E^5*x^4 + (432 - 108*x - 108*x^2 + 27*x^3 + E^10*(-32*x^3 + 8*x^4 ))*Log[4 - x] + (72*x^4 + E^5*(192*x^3 - 48*x^4)*Log[4 - x])*Log[Log[4 - x ]] + (-288*x^3 + 72*x^4)*Log[4 - x]*Log[Log[4 - x]]^2)/((-432*x + 108*x^2 - 108*x^3 + 27*x^4 + E^10*(-16*x^4 + 4*x^5))*Log[4 - x] + E^5*(96*x^4 - 24 *x^5)*Log[4 - x]*Log[Log[4 - x]] + (-144*x^4 + 36*x^5)*Log[4 - x]*Log[Log[ 4 - x]]^2),x]
Output:
$Aborted
Time = 7.41 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.27
| method | result | size |
| risch | \(2 \ln \left (x \right )+\ln \left (\ln \left (\ln \left (-x +4\right )\right )^{2}-\frac {2 \,{\mathrm e}^{5} \ln \left (\ln \left (-x +4\right )\right )}{3}+\frac {4 x^{3} {\mathrm e}^{10}+27 x^{2}+108}{36 x^{3}}\right )\) | \(47\) |
| parallelrisch | \(\ln \left (\frac {x^{3} {\mathrm e}^{10}}{9}-\frac {2 \,{\mathrm e}^{5} \ln \left (\ln \left (-x +4\right )\right ) x^{3}}{3}+\ln \left (\ln \left (-x +4\right )\right )^{2} x^{3}+\frac {3 x^{2}}{4}+3\right )-\ln \left (x \right )\) | \(50\) |
Input:
int(((72*x^4-288*x^3)*ln(-x+4)*ln(ln(-x+4))^2+((-48*x^4+192*x^3)*exp(5)*ln (-x+4)+72*x^4)*ln(ln(-x+4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-108*x^2-108*x+ 432)*ln(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*ln(-x+4)*ln(ln(-x+4))^2+(-2 4*x^5+96*x^4)*exp(5)*ln(-x+4)*ln(ln(-x+4))+((4*x^5-16*x^4)*exp(5)^2+27*x^4 -108*x^3+108*x^2-432*x)*ln(-x+4)),x,method=_RETURNVERBOSE)
Output:
2*ln(x)+ln(ln(ln(-x+4))^2-2/3*exp(5)*ln(ln(-x+4))+1/36*(4*x^3*exp(10)+27*x ^2+108)/x^3)
Time = 0.08 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.43 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \, \log \left (x\right ) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{x^{3}}\right ) \] Input:
integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)* exp(5)*log(-x+4)+72*x^4)*log(log(-x+4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-10 8*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*log( log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x ^4)*exp(5)^2+27*x^4-108*x^3+108*x^2-432*x)*log(-x+4)),x, algorithm="fricas ")
Output:
2*log(x) + log(-(24*x^3*e^5*log(log(-x + 4)) - 36*x^3*log(log(-x + 4))^2 - 4*x^3*e^10 - 27*x^2 - 108)/x^3)
Time = 0.49 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.30 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \log {\left (x \right )} + \log {\left (\log {\left (\log {\left (4 - x \right )} \right )}^{2} - \frac {2 e^{5} \log {\left (\log {\left (4 - x \right )} \right )}}{3} + \frac {4 x^{3} e^{10} + 27 x^{2} + 108}{36 x^{3}} \right )} \] Input:
integrate(((72*x**4-288*x**3)*ln(-x+4)*ln(ln(-x+4))**2+((-48*x**4+192*x**3 )*exp(5)*ln(-x+4)+72*x**4)*ln(ln(-x+4))+((8*x**4-32*x**3)*exp(5)**2+27*x** 3-108*x**2-108*x+432)*ln(-x+4)-24*x**4*exp(5))/((36*x**5-144*x**4)*ln(-x+4 )*ln(ln(-x+4))**2+(-24*x**5+96*x**4)*exp(5)*ln(-x+4)*ln(ln(-x+4))+((4*x**5 -16*x**4)*exp(5)**2+27*x**4-108*x**3+108*x**2-432*x)*ln(-x+4)),x)
Output:
2*log(x) + log(log(log(4 - x))**2 - 2*exp(5)*log(log(4 - x))/3 + (4*x**3*e xp(10) + 27*x**2 + 108)/(36*x**3))
Time = 0.12 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.43 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=2 \, \log \left (x\right ) + \log \left (-\frac {24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) - 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} - 4 \, x^{3} e^{10} - 27 \, x^{2} - 108}{36 \, x^{3}}\right ) \] Input:
integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)* exp(5)*log(-x+4)+72*x^4)*log(log(-x+4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-10 8*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*log( log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x ^4)*exp(5)^2+27*x^4-108*x^3+108*x^2-432*x)*log(-x+4)),x, algorithm="maxima ")
Output:
2*log(x) + log(-1/36*(24*x^3*e^5*log(log(-x + 4)) - 36*x^3*log(log(-x + 4) )^2 - 4*x^3*e^10 - 27*x^2 - 108)/x^3)
Time = 0.25 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.30 \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\log \left (-24 \, x^{3} e^{5} \log \left (\log \left (-x + 4\right )\right ) + 36 \, x^{3} \log \left (\log \left (-x + 4\right )\right )^{2} + 4 \, x^{3} e^{10} + 27 \, x^{2} + 108\right ) - \log \left (x\right ) \] Input:
integrate(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)* exp(5)*log(-x+4)+72*x^4)*log(log(-x+4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-10 8*x^2-108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*log( log(-x+4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x ^4)*exp(5)^2+27*x^4-108*x^3+108*x^2-432*x)*log(-x+4)),x, algorithm="giac")
Output:
log(-24*x^3*e^5*log(log(-x + 4)) + 36*x^3*log(log(-x + 4))^2 + 4*x^3*e^10 + 27*x^2 + 108) - log(x)
Timed out. \[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\int \frac {\ln \left (4-x\right )\,\left (108\,x+{\mathrm {e}}^{10}\,\left (32\,x^3-8\,x^4\right )+108\,x^2-27\,x^3-432\right )-\ln \left (\ln \left (4-x\right )\right )\,\left (72\,x^4+{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (192\,x^3-48\,x^4\right )\right )+24\,x^4\,{\mathrm {e}}^5+{\ln \left (\ln \left (4-x\right )\right )}^2\,\ln \left (4-x\right )\,\left (288\,x^3-72\,x^4\right )}{\ln \left (4-x\right )\,\left (144\,x^4-36\,x^5\right )\,{\ln \left (\ln \left (4-x\right )\right )}^2-{\mathrm {e}}^5\,\ln \left (4-x\right )\,\left (96\,x^4-24\,x^5\right )\,\ln \left (\ln \left (4-x\right )\right )+\ln \left (4-x\right )\,\left (432\,x+{\mathrm {e}}^{10}\,\left (16\,x^4-4\,x^5\right )-108\,x^2+108\,x^3-27\,x^4\right )} \,d x \] Input:
int((log(4 - x)*(108*x + exp(10)*(32*x^3 - 8*x^4) + 108*x^2 - 27*x^3 - 432 ) - log(log(4 - x))*(72*x^4 + exp(5)*log(4 - x)*(192*x^3 - 48*x^4)) + 24*x ^4*exp(5) + log(log(4 - x))^2*log(4 - x)*(288*x^3 - 72*x^4))/(log(4 - x)*( 432*x + exp(10)*(16*x^4 - 4*x^5) - 108*x^2 + 108*x^3 - 27*x^4) + log(log(4 - x))^2*log(4 - x)*(144*x^4 - 36*x^5) - log(log(4 - x))*exp(5)*log(4 - x) *(96*x^4 - 24*x^5)),x)
Output:
int((log(4 - x)*(108*x + exp(10)*(32*x^3 - 8*x^4) + 108*x^2 - 27*x^3 - 432 ) - log(log(4 - x))*(72*x^4 + exp(5)*log(4 - x)*(192*x^3 - 48*x^4)) + 24*x ^4*exp(5) + log(log(4 - x))^2*log(4 - x)*(288*x^3 - 72*x^4))/(log(4 - x)*( 432*x + exp(10)*(16*x^4 - 4*x^5) - 108*x^2 + 108*x^3 - 27*x^4) + log(log(4 - x))^2*log(4 - x)*(144*x^4 - 36*x^5) - log(log(4 - x))*exp(5)*log(4 - x) *(96*x^4 - 24*x^5)), x)
\[ \int \frac {-24 e^5 x^4+\left (432-108 x-108 x^2+27 x^3+e^{10} \left (-32 x^3+8 x^4\right )\right ) \log (4-x)+\left (72 x^4+e^5 \left (192 x^3-48 x^4\right ) \log (4-x)\right ) \log (\log (4-x))+\left (-288 x^3+72 x^4\right ) \log (4-x) \log ^2(\log (4-x))}{\left (-432 x+108 x^2-108 x^3+27 x^4+e^{10} \left (-16 x^4+4 x^5\right )\right ) \log (4-x)+e^5 \left (96 x^4-24 x^5\right ) \log (4-x) \log (\log (4-x))+\left (-144 x^4+36 x^5\right ) \log (4-x) \log ^2(\log (4-x))} \, dx=\text {too large to display} \] Input:
int(((72*x^4-288*x^3)*log(-x+4)*log(log(-x+4))^2+((-48*x^4+192*x^3)*exp(5) *log(-x+4)+72*x^4)*log(log(-x+4))+((8*x^4-32*x^3)*exp(5)^2+27*x^3-108*x^2- 108*x+432)*log(-x+4)-24*x^4*exp(5))/((36*x^5-144*x^4)*log(-x+4)*log(log(-x +4))^2+(-24*x^5+96*x^4)*exp(5)*log(-x+4)*log(log(-x+4))+((4*x^5-16*x^4)*ex p(5)^2+27*x^4-108*x^3+108*x^2-432*x)*log(-x+4)),x)
Output:
8*int(x**3/(36*log(log( - x + 4))**2*x**4 - 144*log(log( - x + 4))**2*x**3 - 24*log(log( - x + 4))*e**5*x**4 + 96*log(log( - x + 4))*e**5*x**3 + 4*e **10*x**4 - 16*e**10*x**3 + 27*x**3 - 108*x**2 + 108*x - 432),x)*e**10 - 2 4*int(x**3/(36*log(log( - x + 4))**2*log( - x + 4)*x**4 - 144*log(log( - x + 4))**2*log( - x + 4)*x**3 - 24*log(log( - x + 4))*log( - x + 4)*e**5*x* *4 + 96*log(log( - x + 4))*log( - x + 4)*e**5*x**3 + 4*log( - x + 4)*e**10 *x**4 - 16*log( - x + 4)*e**10*x**3 + 27*log( - x + 4)*x**3 - 108*log( - x + 4)*x**2 + 108*log( - x + 4)*x - 432*log( - x + 4)),x)*e**5 - 32*int(x** 2/(36*log(log( - x + 4))**2*x**4 - 144*log(log( - x + 4))**2*x**3 - 24*log (log( - x + 4))*e**5*x**4 + 96*log(log( - x + 4))*e**5*x**3 + 4*e**10*x**4 - 16*e**10*x**3 + 27*x**3 - 108*x**2 + 108*x - 432),x)*e**10 + 27*int(x** 2/(36*log(log( - x + 4))**2*x**4 - 144*log(log( - x + 4))**2*x**3 - 24*log (log( - x + 4))*e**5*x**4 + 96*log(log( - x + 4))*e**5*x**3 + 4*e**10*x**4 - 16*e**10*x**3 + 27*x**3 - 108*x**2 + 108*x - 432),x) + 72*int((log(log( - x + 4))**2*x**3)/(36*log(log( - x + 4))**2*x**4 - 144*log(log( - x + 4) )**2*x**3 - 24*log(log( - x + 4))*e**5*x**4 + 96*log(log( - x + 4))*e**5*x **3 + 4*e**10*x**4 - 16*e**10*x**3 + 27*x**3 - 108*x**2 + 108*x - 432),x) - 288*int((log(log( - x + 4))**2*x**2)/(36*log(log( - x + 4))**2*x**4 - 14 4*log(log( - x + 4))**2*x**3 - 24*log(log( - x + 4))*e**5*x**4 + 96*log(lo g( - x + 4))*e**5*x**3 + 4*e**10*x**4 - 16*e**10*x**3 + 27*x**3 - 108*x...