Integrand size = 182, antiderivative size = 28 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=e^{e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}}+x+2 x \log (x) \] Output:
2*x*ln(x)+x+exp(exp(2/ln(x)^4*(x-ln(x))^4*x^2))
Time = 0.23 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=e^{e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}}+x+2 x \log (x) \] Input:
Integrate[(3*Log[x]^5 + 2*Log[x]^6 + E^(E^((2*x^6 - 8*x^5*Log[x] + 12*x^4* Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4) + (2*x^6 - 8*x^5*Log [x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4)*(-8*x^5 + (24*x^4 + 12*x^5)*Log[x] + (-24*x^3 - 40*x^4)*Log[x]^2 + (8*x^2 + 48*x^ 3)*Log[x]^3 - 24*x^2*Log[x]^4 + 4*x*Log[x]^5))/Log[x]^5,x]
Output:
E^E^((2*x^2*(x - Log[x])^4)/Log[x]^4) + x + 2*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.
| \(\displaystyle \int \frac {\left (-8 x^5-24 x^2 \log ^4(x)+\left (12 x^5+24 x^4\right ) \log (x)+\left (-40 x^4-24 x^3\right ) \log ^2(x)+\left (48 x^3+8 x^2\right ) \log ^3(x)+4 x \log ^5(x)\right ) \exp \left (\exp \left (\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}\right )+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}\right )+2 \log ^6(x)+3 \log ^5(x)}{\log ^5(x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {4 x \left (-2 x-\log ^2(x)+3 x \log (x)\right ) (x-\log (x))^3 \exp \left (\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}+2 x^2+e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}\right )}{\log ^5(x)}+2 \log (x)+3\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {4 x \left (-2 x-\log ^2(x)+3 x \log (x)\right ) (x-\log (x))^3 \exp \left (\frac {2 x^6}{\log ^4(x)}-\frac {8 x^5}{\log ^3(x)}+\frac {12 x^4}{\log ^2(x)}-\frac {8 x^3}{\log (x)}+2 x^2+e^{\frac {2 x^2 (x-\log (x))^4}{\log ^4(x)}}\right )}{\log ^5(x)}+2 \log (x)+3\right )dx\) |
Input:
Int[(3*Log[x]^5 + 2*Log[x]^6 + E^(E^((2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x] ^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4) + (2*x^6 - 8*x^5*Log[x] + 12*x^4*Log[x]^2 - 8*x^3*Log[x]^3 + 2*x^2*Log[x]^4)/Log[x]^4)*(-8*x^5 + (24 *x^4 + 12*x^5)*Log[x] + (-24*x^3 - 40*x^4)*Log[x]^2 + (8*x^2 + 48*x^3)*Log [x]^3 - 24*x^2*Log[x]^4 + 4*x*Log[x]^5))/Log[x]^5,x]
Output:
$Aborted
Time = 11.38 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96
| method | result | size |
| risch | \(2 x \ln \left (x \right )+x +{\mathrm e}^{{\mathrm e}^{\frac {2 x^{2} \left (\ln \left (x \right )-x \right )^{4}}{\ln \left (x \right )^{4}}}}\) | \(27\) |
| parallelrisch | \(2 x \ln \left (x \right )+x +{\mathrm e}^{{\mathrm e}^{\frac {2 x^{2} \ln \left (x \right )^{4}-8 x^{3} \ln \left (x \right )^{3}+12 x^{4} \ln \left (x \right )^{2}-8 x^{5} \ln \left (x \right )+2 x^{6}}{\ln \left (x \right )^{4}}}}\) | \(55\) |
Input:
int(((4*x*ln(x)^5-24*x^2*ln(x)^4+(48*x^3+8*x^2)*ln(x)^3+(-40*x^4-24*x^3)*l n(x)^2+(12*x^5+24*x^4)*ln(x)-8*x^5)*exp((2*x^2*ln(x)^4-8*x^3*ln(x)^3+12*x^ 4*ln(x)^2-8*x^5*ln(x)+2*x^6)/ln(x)^4)*exp(exp((2*x^2*ln(x)^4-8*x^3*ln(x)^3 +12*x^4*ln(x)^2-8*x^5*ln(x)+2*x^6)/ln(x)^4))+2*ln(x)^6+3*ln(x)^5)/ln(x)^5, x,method=_RETURNVERBOSE)
Output:
2*x*ln(x)+x+exp(exp(2*x^2*(ln(x)-x)^4/ln(x)^4))
Leaf count of result is larger than twice the leaf count of optimal. 193 vs. \(2 (26) = 52\).
Time = 0.11 (sec) , antiderivative size = 193, normalized size of antiderivative = 6.89 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx={\left ({\left (2 \, x \log \left (x\right ) + x\right )} e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4}\right )}}{\log \left (x\right )^{4}}\right )} + e^{\left (\frac {2 \, x^{6} - 8 \, x^{5} \log \left (x\right ) + 12 \, x^{4} \log \left (x\right )^{2} - 8 \, x^{3} \log \left (x\right )^{3} + 2 \, x^{2} \log \left (x\right )^{4} + e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4}\right )}}{\log \left (x\right )^{4}}\right )} \log \left (x\right )^{4}}{\log \left (x\right )^{4}}\right )}\right )} e^{\left (-\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4}\right )}}{\log \left (x\right )^{4}}\right )} \] Input:
integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4- 24*x^3)*log(x)^2+(12*x^5+24*x^4)*log(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*l og(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log(x )^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x) ^6+3*log(x)^5)/log(x)^5,x, algorithm="fricas")
Output:
((2*x*log(x) + x)*e^(2*(x^6 - 4*x^5*log(x) + 6*x^4*log(x)^2 - 4*x^3*log(x) ^3 + x^2*log(x)^4)/log(x)^4) + e^((2*x^6 - 8*x^5*log(x) + 12*x^4*log(x)^2 - 8*x^3*log(x)^3 + 2*x^2*log(x)^4 + e^(2*(x^6 - 4*x^5*log(x) + 6*x^4*log(x )^2 - 4*x^3*log(x)^3 + x^2*log(x)^4)/log(x)^4)*log(x)^4)/log(x)^4))*e^(-2* (x^6 - 4*x^5*log(x) + 6*x^4*log(x)^2 - 4*x^3*log(x)^3 + x^2*log(x)^4)/log( x)^4)
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (27) = 54\).
Time = 1.14 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=2 x \log {\left (x \right )} + x + e^{e^{\frac {2 x^{6} - 8 x^{5} \log {\left (x \right )} + 12 x^{4} \log {\left (x \right )}^{2} - 8 x^{3} \log {\left (x \right )}^{3} + 2 x^{2} \log {\left (x \right )}^{4}}{\log {\left (x \right )}^{4}}}} \] Input:
integrate(((4*x*ln(x)**5-24*x**2*ln(x)**4+(48*x**3+8*x**2)*ln(x)**3+(-40*x **4-24*x**3)*ln(x)**2+(12*x**5+24*x**4)*ln(x)-8*x**5)*exp((2*x**2*ln(x)**4 -8*x**3*ln(x)**3+12*x**4*ln(x)**2-8*x**5*ln(x)+2*x**6)/ln(x)**4)*exp(exp(( 2*x**2*ln(x)**4-8*x**3*ln(x)**3+12*x**4*ln(x)**2-8*x**5*ln(x)+2*x**6)/ln(x )**4))+2*ln(x)**6+3*ln(x)**5)/ln(x)**5,x)
Output:
2*x*log(x) + x + exp(exp((2*x**6 - 8*x**5*log(x) + 12*x**4*log(x)**2 - 8*x **3*log(x)**3 + 2*x**2*log(x)**4)/log(x)**4))
Time = 0.78 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=2 \, x \log \left (x\right ) + x + e^{\left (e^{\left (2 \, x^{2} + \frac {2 \, x^{6}}{\log \left (x\right )^{4}} - \frac {8 \, x^{5}}{\log \left (x\right )^{3}} + \frac {12 \, x^{4}}{\log \left (x\right )^{2}} - \frac {8 \, x^{3}}{\log \left (x\right )}\right )}\right )} \] Input:
integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4- 24*x^3)*log(x)^2+(12*x^5+24*x^4)*log(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*l og(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log(x )^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x) ^6+3*log(x)^5)/log(x)^5,x, algorithm="maxima")
Output:
2*x*log(x) + x + e^(e^(2*x^2 + 2*x^6/log(x)^4 - 8*x^5/log(x)^3 + 12*x^4/lo g(x)^2 - 8*x^3/log(x)))
\[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=\int { \frac {2 \, \log \left (x\right )^{6} + 3 \, \log \left (x\right )^{5} - 4 \, {\left (6 \, x^{2} \log \left (x\right )^{4} - x \log \left (x\right )^{5} + 2 \, x^{5} - 2 \, {\left (6 \, x^{3} + x^{2}\right )} \log \left (x\right )^{3} + 2 \, {\left (5 \, x^{4} + 3 \, x^{3}\right )} \log \left (x\right )^{2} - 3 \, {\left (x^{5} + 2 \, x^{4}\right )} \log \left (x\right )\right )} e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4}\right )}}{\log \left (x\right )^{4}} + e^{\left (\frac {2 \, {\left (x^{6} - 4 \, x^{5} \log \left (x\right ) + 6 \, x^{4} \log \left (x\right )^{2} - 4 \, x^{3} \log \left (x\right )^{3} + x^{2} \log \left (x\right )^{4}\right )}}{\log \left (x\right )^{4}}\right )}\right )}}{\log \left (x\right )^{5}} \,d x } \] Input:
integrate(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4- 24*x^3)*log(x)^2+(12*x^5+24*x^4)*log(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*l og(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log(x )^4-8*x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x) ^6+3*log(x)^5)/log(x)^5,x, algorithm="giac")
Output:
undef
Time = 2.92 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.96 \[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=x+{\mathrm {e}}^{{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^{-\frac {8\,x^3}{\ln \left (x\right )}}\,{\mathrm {e}}^{\frac {2\,x^6}{{\ln \left (x\right )}^4}}\,{\mathrm {e}}^{-\frac {8\,x^5}{{\ln \left (x\right )}^3}}\,{\mathrm {e}}^{\frac {12\,x^4}{{\ln \left (x\right )}^2}}}+2\,x\,\ln \left (x\right ) \] Input:
int((3*log(x)^5 + 2*log(x)^6 + exp((2*x^2*log(x)^4 - 8*x^5*log(x) - 8*x^3* log(x)^3 + 12*x^4*log(x)^2 + 2*x^6)/log(x)^4)*exp(exp((2*x^2*log(x)^4 - 8* x^5*log(x) - 8*x^3*log(x)^3 + 12*x^4*log(x)^2 + 2*x^6)/log(x)^4))*(log(x)* (24*x^4 + 12*x^5) + 4*x*log(x)^5 + log(x)^3*(8*x^2 + 48*x^3) - log(x)^2*(2 4*x^3 + 40*x^4) - 24*x^2*log(x)^4 - 8*x^5))/log(x)^5,x)
Output:
x + exp(exp(2*x^2)*exp(-(8*x^3)/log(x))*exp((2*x^6)/log(x)^4)*exp(-(8*x^5) /log(x)^3)*exp((12*x^4)/log(x)^2)) + 2*x*log(x)
\[ \int \frac {3 \log ^5(x)+2 \log ^6(x)+e^{e^{\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}}+\frac {2 x^6-8 x^5 \log (x)+12 x^4 \log ^2(x)-8 x^3 \log ^3(x)+2 x^2 \log ^4(x)}{\log ^4(x)}} \left (-8 x^5+\left (24 x^4+12 x^5\right ) \log (x)+\left (-24 x^3-40 x^4\right ) \log ^2(x)+\left (8 x^2+48 x^3\right ) \log ^3(x)-24 x^2 \log ^4(x)+4 x \log ^5(x)\right )}{\log ^5(x)} \, dx=\text {too large to display} \] Input:
int(((4*x*log(x)^5-24*x^2*log(x)^4+(48*x^3+8*x^2)*log(x)^3+(-40*x^4-24*x^3 )*log(x)^2+(12*x^5+24*x^4)*log(x)-8*x^5)*exp((2*x^2*log(x)^4-8*x^3*log(x)^ 3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4)*exp(exp((2*x^2*log(x)^4-8* x^3*log(x)^3+12*x^4*log(x)^2-8*x^5*log(x)+2*x^6)/log(x)^4))+2*log(x)^6+3*l og(x)^5)/log(x)^5,x)
Output:
- 8*int((e**((e**((2*log(x)**4*x**2 + 12*log(x)**2*x**4 + 2*x**6)/log(x)* *4)*log(x)**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4*x** 2 + 12*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**2*x**4 + 2*e**(( 8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*x**6)/(e**((8*log(x)**2*x**3 + 8*x** 5)/log(x)**3)*log(x)**4))*x**5)/(e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3 )*log(x)**5),x) + 12*int((e**((e**((2*log(x)**4*x**2 + 12*log(x)**2*x**4 + 2*x**6)/log(x)**4)*log(x)**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)** 3)*log(x)**4*x**2 + 12*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)** 2*x**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*x**6)/(e**((8*log(x) **2*x**3 + 8*x**5)/log(x)**3)*log(x)**4))*x**5)/(e**((8*log(x)**2*x**3 + 8 *x**5)/log(x)**3)*log(x)**4),x) + 24*int((e**((e**((2*log(x)**4*x**2 + 12* log(x)**2*x**4 + 2*x**6)/log(x)**4)*log(x)**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4*x**2 + 12*e**((8*log(x)**2*x**3 + 8*x**5)/log (x)**3)*log(x)**2*x**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*x**6 )/(e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4))*x**4)/(e**((8*lo g(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4),x) - 40*int((e**((e**((2*log( x)**4*x**2 + 12*log(x)**2*x**4 + 2*x**6)/log(x)**4)*log(x)**4 + 2*e**((8*l og(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4*x**2 + 12*e**((8*log(x)**2*x* *3 + 8*x**5)/log(x)**3)*log(x)**2*x**4 + 2*e**((8*log(x)**2*x**3 + 8*x**5) /log(x)**3)*x**6)/(e**((8*log(x)**2*x**3 + 8*x**5)/log(x)**3)*log(x)**4...