\(\int \frac {-36 x-x^4+e^x (36+x^3)+(-e^x x^3+x^4) \log (x)+(2 x^5-2 e^x x^5+(-x^5+e^x x^5) \log (3 e^{\frac {9}{x^4}})+(x^4-e^x x^4) \log (x)) \log (\frac {-2 x+x \log (3 e^{\frac {9}{x^4}})-\log (x)}{x})}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+(e^{2 x} x^5-2 e^x x^6+x^7) \log (3 e^{\frac {9}{x^4}})+(-e^{2 x} x^4+2 e^x x^5-x^6) \log (x)} \, dx\) [1735]

Optimal result

Integrand size = 198, antiderivative size = 30 \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\frac {\log \left (-2+\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}\right )}{-e^x+x} \] Output:

ln(ln(3*exp(9/x^4))-ln(x)/x-2)/(x-exp(x))
 

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=-\frac {\log \left (-2+\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}\right )}{e^x-x} \] Input:

Integrate[(-36*x - x^4 + E^x*(36 + x^3) + (-(E^x*x^3) + x^4)*Log[x] + (2*x 
^5 - 2*E^x*x^5 + (-x^5 + E^x*x^5)*Log[3*E^(9/x^4)] + (x^4 - E^x*x^4)*Log[x 
])*Log[(-2*x + x*Log[3*E^(9/x^4)] - Log[x])/x])/(-2*E^(2*x)*x^5 + 4*E^x*x^ 
6 - 2*x^7 + (E^(2*x)*x^5 - 2*E^x*x^6 + x^7)*Log[3*E^(9/x^4)] + (-(E^(2*x)* 
x^4) + 2*E^x*x^5 - x^6)*Log[x]),x]
 

Output:

-(Log[-2 + Log[3*E^(9/x^4)] - Log[x]/x]/(E^x - x))
 

Rubi [F]

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.

\(\displaystyle \int \frac {-x^4+e^x \left (x^3+36\right )+\left (-2 e^x x^5+2 x^5+\left (x^4-e^x x^4\right ) \log (x)+\left (e^x x^5-x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )\right ) \log \left (\frac {x \log \left (3 e^{\frac {9}{x^4}}\right )-2 x-\log (x)}{x}\right )+\left (x^4-e^x x^3\right ) \log (x)-36 x}{-2 x^7+4 e^x x^6-2 e^{2 x} x^5+\left (-x^6+2 e^x x^5-e^{2 x} x^4\right ) \log (x)+\left (x^7-2 e^x x^6+e^{2 x} x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {x^4-e^x \left (x^3+36\right )-\left (-2 e^x x^5+2 x^5+\left (x^4-e^x x^4\right ) \log (x)+\left (e^x x^5-x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )\right ) \log \left (\frac {x \log \left (3 e^{\frac {9}{x^4}}\right )-2 x-\log (x)}{x}\right )-\left (x^4-e^x x^3\right ) \log (x)+36 x}{\left (e^x-x\right )^2 x^4 \left (x \left (-\log \left (3 e^{\frac {9}{x^4}}\right )\right )+2 x+\log (x)\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {(x-1) \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right )^2}+\frac {-x^4 \log (x) \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )+x^3-x^3 \log (x)+x^5 \log \left (3 e^{\frac {9}{x^4}}\right ) \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )-2 x^5 \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )+36}{\left (e^x-x\right ) x^4 \left (x \log \left (3 e^{\frac {9}{x^4}}\right )-2 x-\log (x)\right )}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 36 \int \frac {1}{\left (e^x-x\right ) x^4 \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx+\int \frac {1}{\left (e^x-x\right ) x \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx-\int \frac {\log (x)}{\left (e^x-x\right ) x \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx-\int \frac {\log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right )^2}dx+\int \frac {x \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right )^2}dx-2 \int \frac {x \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right ) \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx+\int \frac {x \log \left (3 e^{\frac {9}{x^4}}\right ) \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right ) \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx-\int \frac {\log (x) \log \left (\log \left (3 e^{\frac {9}{x^4}}\right )-\frac {\log (x)}{x}-2\right )}{\left (e^x-x\right ) \left (\log \left (3 e^{\frac {9}{x^4}}\right ) x-2 x-\log (x)\right )}dx\)

Input:

Int[(-36*x - x^4 + E^x*(36 + x^3) + (-(E^x*x^3) + x^4)*Log[x] + (2*x^5 - 2 
*E^x*x^5 + (-x^5 + E^x*x^5)*Log[3*E^(9/x^4)] + (x^4 - E^x*x^4)*Log[x])*Log 
[(-2*x + x*Log[3*E^(9/x^4)] - Log[x])/x])/(-2*E^(2*x)*x^5 + 4*E^x*x^6 - 2* 
x^7 + (E^(2*x)*x^5 - 2*E^x*x^6 + x^7)*Log[3*E^(9/x^4)] + (-(E^(2*x)*x^4) + 
 2*E^x*x^5 - x^6)*Log[x]),x]
 

Output:

$Aborted
 

Maple [F]

\[\int \frac {\left (\left (x^{5} {\mathrm e}^{x}-x^{5}\right ) \ln \left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )+\left (-{\mathrm e}^{x} x^{4}+x^{4}\right ) \ln \left (x \right )-2 x^{5} {\mathrm e}^{x}+2 x^{5}\right ) \ln \left (\frac {x \ln \left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )-2 x -\ln \left (x \right )}{x}\right )+\left (-{\mathrm e}^{x} x^{3}+x^{4}\right ) \ln \left (x \right )+\left (x^{3}+36\right ) {\mathrm e}^{x}-x^{4}-36 x}{\left (x^{5} {\mathrm e}^{2 x}-2 x^{6} {\mathrm e}^{x}+x^{7}\right ) \ln \left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )+\left (-x^{4} {\mathrm e}^{2 x}+2 x^{5} {\mathrm e}^{x}-x^{6}\right ) \ln \left (x \right )-2 x^{5} {\mathrm e}^{2 x}+4 x^{6} {\mathrm e}^{x}-2 x^{7}}d x\]

Input:

int((((x^5*exp(x)-x^5)*ln(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*ln(x)-2*x^5*exp( 
x)+2*x^5)*ln((x*ln(3*exp(9/x^4))-2*x-ln(x))/x)+(-exp(x)*x^3+x^4)*ln(x)+(x^ 
3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*ln(3*exp(9/x^4))+( 
-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*ln(x)-2*x^5*exp(x)^2+4*x^6*exp(x)-2*x^7),x 
)
 

Output:

int((((x^5*exp(x)-x^5)*ln(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*ln(x)-2*x^5*exp( 
x)+2*x^5)*ln((x*ln(3*exp(9/x^4))-2*x-ln(x))/x)+(-exp(x)*x^3+x^4)*ln(x)+(x^ 
3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*ln(3*exp(9/x^4))+( 
-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*ln(x)-2*x^5*exp(x)^2+4*x^6*exp(x)-2*x^7),x 
)
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\frac {\log \left (\frac {x^{4} \log \left (3\right ) - 2 \, x^{4} - x^{3} \log \left (x\right ) + 9}{x^{4}}\right )}{x - e^{x}} \] Input:

integrate((((x^5*exp(x)-x^5)*log(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*log(x)-2* 
x^5*exp(x)+2*x^5)*log((x*log(3*exp(9/x^4))-2*x-log(x))/x)+(-exp(x)*x^3+x^4 
)*log(x)+(x^3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*log(3* 
exp(9/x^4))+(-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*log(x)-2*x^5*exp(x)^2+4*x^6*e 
xp(x)-2*x^7),x, algorithm="fricas")
 

Output:

log((x^4*log(3) - 2*x^4 - x^3*log(x) + 9)/x^4)/(x - e^x)
 

Sympy [F(-1)]

Timed out. \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\text {Timed out} \] Input:

integrate((((x**5*exp(x)-x**5)*ln(3*exp(9/x**4))+(-exp(x)*x**4+x**4)*ln(x) 
-2*x**5*exp(x)+2*x**5)*ln((x*ln(3*exp(9/x**4))-2*x-ln(x))/x)+(-exp(x)*x**3 
+x**4)*ln(x)+(x**3+36)*exp(x)-x**4-36*x)/((x**5*exp(x)**2-2*x**6*exp(x)+x* 
*7)*ln(3*exp(9/x**4))+(-exp(x)**2*x**4+2*x**5*exp(x)-x**6)*ln(x)-2*x**5*ex 
p(x)**2+4*x**6*exp(x)-2*x**7),x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\frac {\log \left (x^{4} {\left (\log \left (3\right ) - 2\right )} - x^{3} \log \left (x\right ) + 9\right ) - 4 \, \log \left (x\right )}{x - e^{x}} \] Input:

integrate((((x^5*exp(x)-x^5)*log(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*log(x)-2* 
x^5*exp(x)+2*x^5)*log((x*log(3*exp(9/x^4))-2*x-log(x))/x)+(-exp(x)*x^3+x^4 
)*log(x)+(x^3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*log(3* 
exp(9/x^4))+(-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*log(x)-2*x^5*exp(x)^2+4*x^6*e 
xp(x)-2*x^7),x, algorithm="maxima")
 

Output:

(log(x^4*(log(3) - 2) - x^3*log(x) + 9) - 4*log(x))/(x - e^x)
 

Giac [F(-1)]

Timed out. \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\text {Timed out} \] Input:

integrate((((x^5*exp(x)-x^5)*log(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*log(x)-2* 
x^5*exp(x)+2*x^5)*log((x*log(3*exp(9/x^4))-2*x-log(x))/x)+(-exp(x)*x^3+x^4 
)*log(x)+(x^3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*log(3* 
exp(9/x^4))+(-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*log(x)-2*x^5*exp(x)^2+4*x^6*e 
xp(x)-2*x^7),x, algorithm="giac")
 

Output:

Timed out
 

Mupad [F(-1)]

Timed out. \[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=-\int -\frac {36\,x+\ln \left (-\frac {2\,x+\ln \left (x\right )-x\,\ln \left (3\,{\mathrm {e}}^{\frac {9}{x^4}}\right )}{x}\right )\,\left (2\,x^5\,{\mathrm {e}}^x-\ln \left (3\,{\mathrm {e}}^{\frac {9}{x^4}}\right )\,\left (x^5\,{\mathrm {e}}^x-x^5\right )-2\,x^5+\ln \left (x\right )\,\left (x^4\,{\mathrm {e}}^x-x^4\right )\right )-{\mathrm {e}}^x\,\left (x^3+36\right )+x^4+\ln \left (x\right )\,\left (x^3\,{\mathrm {e}}^x-x^4\right )}{\ln \left (x\right )\,\left (x^4\,{\mathrm {e}}^{2\,x}-2\,x^5\,{\mathrm {e}}^x+x^6\right )-4\,x^6\,{\mathrm {e}}^x+2\,x^5\,{\mathrm {e}}^{2\,x}-\ln \left (3\,{\mathrm {e}}^{\frac {9}{x^4}}\right )\,\left (x^5\,{\mathrm {e}}^{2\,x}-2\,x^6\,{\mathrm {e}}^x+x^7\right )+2\,x^7} \,d x \] Input:

int((36*x + log(-(2*x + log(x) - x*log(3*exp(9/x^4)))/x)*(2*x^5*exp(x) - l 
og(3*exp(9/x^4))*(x^5*exp(x) - x^5) - 2*x^5 + log(x)*(x^4*exp(x) - x^4)) - 
 exp(x)*(x^3 + 36) + x^4 + log(x)*(x^3*exp(x) - x^4))/(log(x)*(x^4*exp(2*x 
) - 2*x^5*exp(x) + x^6) - 4*x^6*exp(x) + 2*x^5*exp(2*x) - log(3*exp(9/x^4) 
)*(x^5*exp(2*x) - 2*x^6*exp(x) + x^7) + 2*x^7),x)
 

Output:

-int(-(36*x + log(-(2*x + log(x) - x*log(3*exp(9/x^4)))/x)*(2*x^5*exp(x) - 
 log(3*exp(9/x^4))*(x^5*exp(x) - x^5) - 2*x^5 + log(x)*(x^4*exp(x) - x^4)) 
 - exp(x)*(x^3 + 36) + x^4 + log(x)*(x^3*exp(x) - x^4))/(log(x)*(x^4*exp(2 
*x) - 2*x^5*exp(x) + x^6) - 4*x^6*exp(x) + 2*x^5*exp(2*x) - log(3*exp(9/x^ 
4))*(x^5*exp(2*x) - 2*x^6*exp(x) + x^7) + 2*x^7), x)
                                                                                    
                                                                                    
 

Reduce [F]

\[ \int \frac {-36 x-x^4+e^x \left (36+x^3\right )+\left (-e^x x^3+x^4\right ) \log (x)+\left (2 x^5-2 e^x x^5+\left (-x^5+e^x x^5\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (x^4-e^x x^4\right ) \log (x)\right ) \log \left (\frac {-2 x+x \log \left (3 e^{\frac {9}{x^4}}\right )-\log (x)}{x}\right )}{-2 e^{2 x} x^5+4 e^x x^6-2 x^7+\left (e^{2 x} x^5-2 e^x x^6+x^7\right ) \log \left (3 e^{\frac {9}{x^4}}\right )+\left (-e^{2 x} x^4+2 e^x x^5-x^6\right ) \log (x)} \, dx=\int \frac {\left (\left (x^{5} {\mathrm e}^{x}-x^{5}\right ) \mathrm {log}\left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )+\left (-{\mathrm e}^{x} x^{4}+x^{4}\right ) \mathrm {log}\left (x \right )-2 x^{5} {\mathrm e}^{x}+2 x^{5}\right ) \mathrm {log}\left (\frac {x \,\mathrm {log}\left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )-2 x -\mathrm {log}\left (x \right )}{x}\right )+\left (-{\mathrm e}^{x} x^{3}+x^{4}\right ) \mathrm {log}\left (x \right )+\left (x^{3}+36\right ) {\mathrm e}^{x}-x^{4}-36 x}{\left (x^{5} \left ({\mathrm e}^{x}\right )^{2}-2 x^{6} {\mathrm e}^{x}+x^{7}\right ) \mathrm {log}\left (3 \,{\mathrm e}^{\frac {9}{x^{4}}}\right )+\left (-\left ({\mathrm e}^{x}\right )^{2} x^{4}+2 x^{5} {\mathrm e}^{x}-x^{6}\right ) \mathrm {log}\left (x \right )-2 x^{5} \left ({\mathrm e}^{x}\right )^{2}+4 x^{6} {\mathrm e}^{x}-2 x^{7}}d x \] Input:

int((((x^5*exp(x)-x^5)*log(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*log(x)-2*x^5*ex 
p(x)+2*x^5)*log((x*log(3*exp(9/x^4))-2*x-log(x))/x)+(-exp(x)*x^3+x^4)*log( 
x)+(x^3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*log(3*exp(9/ 
x^4))+(-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*log(x)-2*x^5*exp(x)^2+4*x^6*exp(x)- 
2*x^7),x)
 

Output:

int((((x^5*exp(x)-x^5)*log(3*exp(9/x^4))+(-exp(x)*x^4+x^4)*log(x)-2*x^5*ex 
p(x)+2*x^5)*log((x*log(3*exp(9/x^4))-2*x-log(x))/x)+(-exp(x)*x^3+x^4)*log( 
x)+(x^3+36)*exp(x)-x^4-36*x)/((x^5*exp(x)^2-2*x^6*exp(x)+x^7)*log(3*exp(9/ 
x^4))+(-exp(x)^2*x^4+2*x^5*exp(x)-x^6)*log(x)-2*x^5*exp(x)^2+4*x^6*exp(x)- 
2*x^7),x)