\(\int \frac {e^{(4 x^4-4 x^5+x^6) \log ^2(x)} ((32 x^3-24 x^4+2 x^6) \log (x)+(64 x^3-64 x^4+4 x^5+6 x^6) \log ^2(x))+(-4-2 e^{(4 x^4-4 x^5+x^6) \log ^2(x)}-2 \log (4)) \log (2+e^{(4 x^4-4 x^5+x^6) \log ^2(x)}+\log (4))}{128+96 x+24 x^2+2 x^3+e^{(4 x^4-4 x^5+x^6) \log ^2(x)} (64+48 x+12 x^2+x^3)+(64+48 x+12 x^2+x^3) \log (4)} \, dx\) [1439]

Optimal result

Integrand size = 194, antiderivative size = 32 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log \left (2+e^{x^2 \left (2 x-x^2\right )^2 \log ^2(x)}+\log (4)\right )}{(4+x)^2} \] Output:

ln(exp(ln(x)^2*x^2*(-x^2+2*x)^2)+2*ln(2)+2)/(4+x)^2
 

Mathematica [A] (verified)

Time = 0.16 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log \left (2+e^{(-2+x)^2 x^4 \log ^2(x)}+\log (4)\right )}{(4+x)^2} \] Input:

Integrate[(E^((4*x^4 - 4*x^5 + x^6)*Log[x]^2)*((32*x^3 - 24*x^4 + 2*x^6)*L 
og[x] + (64*x^3 - 64*x^4 + 4*x^5 + 6*x^6)*Log[x]^2) + (-4 - 2*E^((4*x^4 - 
4*x^5 + x^6)*Log[x]^2) - 2*Log[4])*Log[2 + E^((4*x^4 - 4*x^5 + x^6)*Log[x] 
^2) + Log[4]])/(128 + 96*x + 24*x^2 + 2*x^3 + E^((4*x^4 - 4*x^5 + x^6)*Log 
[x]^2)*(64 + 48*x + 12*x^2 + x^3) + (64 + 48*x + 12*x^2 + x^3)*Log[4]),x]
 

Output:

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

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.

\(\displaystyle \int \frac {\left (-2 e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)}-4-2 \log (4)\right ) \log \left (e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)}+2+\log (4)\right )+e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)} \left (\left (2 x^6-24 x^4+32 x^3\right ) \log (x)+\left (6 x^6+4 x^5-64 x^4+64 x^3\right ) \log ^2(x)\right )}{2 x^3+24 x^2+\left (x^3+12 x^2+48 x+64\right ) \log (4)+\left (x^3+12 x^2+48 x+64\right ) e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)}+96 x+128} \, dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (-2 e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)}-4-2 \log (4)\right ) \log \left (e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)}+2+\log (4)\right )+e^{\left (x^6-4 x^5+4 x^4\right ) \log ^2(x)} \left (\left (2 x^6-24 x^4+32 x^3\right ) \log (x)+\left (6 x^6+4 x^5-64 x^4+64 x^3\right ) \log ^2(x)\right )}{(x+4)^3 \left (e^{(x-2)^2 x^4 \log ^2(x)}+2 (1+\log (2))\right )}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2 x^3 \log (x) \left (-6 x^3 (1+\log (2)) \log (x)-2 x^3 (1+\log (2))-4 x^2 (1+\log (2)) \log (x)+64 x (1+\log (2)) \log (x)+24 x (1+\log (2))-64 (1+\log (2)) \log (x)-32 (1+\log (2))\right )}{(x+4)^3 \left (e^{(x-2)^2 x^4 \log ^2(x)}+2 (1+\log (2))\right )}+\frac {2 \left (3 x^6 \log ^2(x)+x^6 \log (x)+2 x^5 \log ^2(x)-32 x^4 \log ^2(x)-\log \left (e^{(x-2)^2 x^4 \log ^2(x)}+2+\log (4)\right )-12 x^4 \log (x)+32 x^3 \log ^2(x)+16 x^3 \log (x)\right )}{(x+4)^3}\right )dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \left (\frac {2 \left (3 x^6 \log ^2(x)+x^6 \log (x)+2 x^5 \log ^2(x)-32 x^4 \log ^2(x)-\log \left (e^{(x-2)^2 x^4 \log ^2(x)}+2+\log (4)\right )-12 x^4 \log (x)+32 x^3 \log ^2(x)+16 x^3 \log (x)\right )}{(x+4)^3}-\frac {4 x^3 \left (x^2+2 x-8\right ) (1+\log (2)) \log (x) (x+3 x \log (x)-4 \log (x)-2)}{(x+4)^3 \left (e^{(x-2)^2 x^4 \log ^2(x)}+2 (1+\log (2))\right )}\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {4 (2-x) x^3 (1+\log (2)) \log (x) (x+3 x \log (x)-4 \log (x)-2)}{(x+4)^2 \left (e^{(x-2)^2 x^4 \log ^2(x)}+2 (1+\log (2))\right )}+\frac {2 \left (3 x^6 \log ^2(x)+x^6 \log (x)+2 x^5 \log ^2(x)-32 x^4 \log ^2(x)-\log \left (e^{(x-2)^2 x^4 \log ^2(x)}+2+\log (4)\right )-12 x^4 \log (x)+32 x^3 \log ^2(x)+16 x^3 \log (x)\right )}{(x+4)^3}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \int \left (\frac {4 (2-x) x^3 (1+\log (2)) \log (x) (x+3 x \log (x)-4 \log (x)-2)}{(x+4)^2 \left (e^{(x-2)^2 x^4 \log ^2(x)}+2 (1+\log (2))\right )}+\frac {2 \left (3 x^6 \log ^2(x)+x^6 \log (x)+2 x^5 \log ^2(x)-32 x^4 \log ^2(x)-\log \left (e^{(x-2)^2 x^4 \log ^2(x)}+2+\log (4)\right )-12 x^4 \log (x)+32 x^3 \log ^2(x)+16 x^3 \log (x)\right )}{(x+4)^3}\right )dx\)

Input:

Int[(E^((4*x^4 - 4*x^5 + x^6)*Log[x]^2)*((32*x^3 - 24*x^4 + 2*x^6)*Log[x] 
+ (64*x^3 - 64*x^4 + 4*x^5 + 6*x^6)*Log[x]^2) + (-4 - 2*E^((4*x^4 - 4*x^5 
+ x^6)*Log[x]^2) - 2*Log[4])*Log[2 + E^((4*x^4 - 4*x^5 + x^6)*Log[x]^2) + 
Log[4]])/(128 + 96*x + 24*x^2 + 2*x^3 + E^((4*x^4 - 4*x^5 + x^6)*Log[x]^2) 
*(64 + 48*x + 12*x^2 + x^3) + (64 + 48*x + 12*x^2 + x^3)*Log[4]),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.03

\[\frac {\ln \left ({\mathrm e}^{x^{4} \left (-2+x \right )^{2} \ln \left (x \right )^{2}}+2+2 \ln \left (2\right )\right )}{x^{2}+8 x +16}\]

Input:

int(((-2*exp((x^6-4*x^5+4*x^4)*ln(x)^2)-4*ln(2)-4)*ln(exp((x^6-4*x^5+4*x^4 
)*ln(x)^2)+2+2*ln(2))+((6*x^6+4*x^5-64*x^4+64*x^3)*ln(x)^2+(2*x^6-24*x^4+3 
2*x^3)*ln(x))*exp((x^6-4*x^5+4*x^4)*ln(x)^2))/((x^3+12*x^2+48*x+64)*exp((x 
^6-4*x^5+4*x^4)*ln(x)^2)+2*(x^3+12*x^2+48*x+64)*ln(2)+2*x^3+24*x^2+96*x+12 
8),x)
 

Output:

1/(x^2+8*x+16)*ln(exp(x^4*(-2+x)^2*ln(x)^2)+2+2*ln(2))
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.19 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log \left (e^{\left ({\left (x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} \log \left (x\right )^{2}\right )} + 2 \, \log \left (2\right ) + 2\right )}{x^{2} + 8 \, x + 16} \] Input:

integrate(((-2*exp((x^6-4*x^5+4*x^4)*log(x)^2)-4*log(2)-4)*log(exp((x^6-4* 
x^5+4*x^4)*log(x)^2)+2+2*log(2))+((6*x^6+4*x^5-64*x^4+64*x^3)*log(x)^2+(2* 
x^6-24*x^4+32*x^3)*log(x))*exp((x^6-4*x^5+4*x^4)*log(x)^2))/((x^3+12*x^2+4 
8*x+64)*exp((x^6-4*x^5+4*x^4)*log(x)^2)+2*(x^3+12*x^2+48*x+64)*log(2)+2*x^ 
3+24*x^2+96*x+128),x, algorithm="fricas")
 

Output:

log(e^((x^6 - 4*x^5 + 4*x^4)*log(x)^2) + 2*log(2) + 2)/(x^2 + 8*x + 16)
 

Sympy [A] (verification not implemented)

Time = 9.50 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log {\left (e^{\left (x^{6} - 4 x^{5} + 4 x^{4}\right ) \log {\left (x \right )}^{2}} + 2 \log {\left (2 \right )} + 2 \right )}}{x^{2} + 8 x + 16} \] Input:

integrate(((-2*exp((x**6-4*x**5+4*x**4)*ln(x)**2)-4*ln(2)-4)*ln(exp((x**6- 
4*x**5+4*x**4)*ln(x)**2)+2+2*ln(2))+((6*x**6+4*x**5-64*x**4+64*x**3)*ln(x) 
**2+(2*x**6-24*x**4+32*x**3)*ln(x))*exp((x**6-4*x**5+4*x**4)*ln(x)**2))/(( 
x**3+12*x**2+48*x+64)*exp((x**6-4*x**5+4*x**4)*ln(x)**2)+2*(x**3+12*x**2+4 
8*x+64)*ln(2)+2*x**3+24*x**2+96*x+128),x)
 

Output:

log(exp((x**6 - 4*x**5 + 4*x**4)*log(x)**2) + 2*log(2) + 2)/(x**2 + 8*x + 
16)
 

Maxima [A] (verification not implemented)

Time = 0.31 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.91 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log \left (2 \, {\left (\log \left (2\right ) + 1\right )} e^{\left (4 \, x^{5} \log \left (x\right )^{2}\right )} + e^{\left (x^{6} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right )^{2}\right )}\right ) - 4 \, \log \left (e^{\left (x^{5} \log \left (x\right )^{2}\right )}\right )}{x^{2} + 8 \, x + 16} \] Input:

integrate(((-2*exp((x^6-4*x^5+4*x^4)*log(x)^2)-4*log(2)-4)*log(exp((x^6-4* 
x^5+4*x^4)*log(x)^2)+2+2*log(2))+((6*x^6+4*x^5-64*x^4+64*x^3)*log(x)^2+(2* 
x^6-24*x^4+32*x^3)*log(x))*exp((x^6-4*x^5+4*x^4)*log(x)^2))/((x^3+12*x^2+4 
8*x+64)*exp((x^6-4*x^5+4*x^4)*log(x)^2)+2*(x^3+12*x^2+48*x+64)*log(2)+2*x^ 
3+24*x^2+96*x+128),x, algorithm="maxima")
 

Output:

(log(2*(log(2) + 1)*e^(4*x^5*log(x)^2) + e^(x^6*log(x)^2 + 4*x^4*log(x)^2) 
) - 4*log(e^(x^5*log(x)^2)))/(x^2 + 8*x + 16)
 

Giac [A] (verification not implemented)

Time = 0.87 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.44 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\log \left (e^{\left (x^{6} \log \left (x\right )^{2} - 4 \, x^{5} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right )^{2}\right )} + 2 \, \log \left (2\right ) + 2\right )}{x^{2} + 8 \, x + 16} \] Input:

integrate(((-2*exp((x^6-4*x^5+4*x^4)*log(x)^2)-4*log(2)-4)*log(exp((x^6-4* 
x^5+4*x^4)*log(x)^2)+2+2*log(2))+((6*x^6+4*x^5-64*x^4+64*x^3)*log(x)^2+(2* 
x^6-24*x^4+32*x^3)*log(x))*exp((x^6-4*x^5+4*x^4)*log(x)^2))/((x^3+12*x^2+4 
8*x+64)*exp((x^6-4*x^5+4*x^4)*log(x)^2)+2*(x^3+12*x^2+48*x+64)*log(2)+2*x^ 
3+24*x^2+96*x+128),x, algorithm="giac")
 

Output:

log(e^(x^6*log(x)^2 - 4*x^5*log(x)^2 + 4*x^4*log(x)^2) + 2*log(2) + 2)/(x^ 
2 + 8*x + 16)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\int \frac {{\mathrm {e}}^{{\ln \left (x\right )}^2\,\left (x^6-4\,x^5+4\,x^4\right )}\,\left (\left (6\,x^6+4\,x^5-64\,x^4+64\,x^3\right )\,{\ln \left (x\right )}^2+\left (2\,x^6-24\,x^4+32\,x^3\right )\,\ln \left (x\right )\right )-\ln \left (2\,\ln \left (2\right )+{\mathrm {e}}^{{\ln \left (x\right )}^2\,\left (x^6-4\,x^5+4\,x^4\right )}+2\right )\,\left (4\,\ln \left (2\right )+2\,{\mathrm {e}}^{{\ln \left (x\right )}^2\,\left (x^6-4\,x^5+4\,x^4\right )}+4\right )}{96\,x+2\,\ln \left (2\right )\,\left (x^3+12\,x^2+48\,x+64\right )+{\mathrm {e}}^{{\ln \left (x\right )}^2\,\left (x^6-4\,x^5+4\,x^4\right )}\,\left (x^3+12\,x^2+48\,x+64\right )+24\,x^2+2\,x^3+128} \,d x \] Input:

int((exp(log(x)^2*(4*x^4 - 4*x^5 + x^6))*(log(x)*(32*x^3 - 24*x^4 + 2*x^6) 
 + log(x)^2*(64*x^3 - 64*x^4 + 4*x^5 + 6*x^6)) - log(2*log(2) + exp(log(x) 
^2*(4*x^4 - 4*x^5 + x^6)) + 2)*(4*log(2) + 2*exp(log(x)^2*(4*x^4 - 4*x^5 + 
 x^6)) + 4))/(96*x + 2*log(2)*(48*x + 12*x^2 + x^3 + 64) + exp(log(x)^2*(4 
*x^4 - 4*x^5 + x^6))*(48*x + 12*x^2 + x^3 + 64) + 24*x^2 + 2*x^3 + 128),x)
 

Output:

int((exp(log(x)^2*(4*x^4 - 4*x^5 + x^6))*(log(x)*(32*x^3 - 24*x^4 + 2*x^6) 
 + log(x)^2*(64*x^3 - 64*x^4 + 4*x^5 + 6*x^6)) - log(2*log(2) + exp(log(x) 
^2*(4*x^4 - 4*x^5 + x^6)) + 2)*(4*log(2) + 2*exp(log(x)^2*(4*x^4 - 4*x^5 + 
 x^6)) + 4))/(96*x + 2*log(2)*(48*x + 12*x^2 + x^3 + 64) + exp(log(x)^2*(4 
*x^4 - 4*x^5 + x^6))*(48*x + 12*x^2 + x^3 + 64) + 24*x^2 + 2*x^3 + 128), x 
)
 

Reduce [B] (verification not implemented)

Time = 0.18 (sec) , antiderivative size = 75, normalized size of antiderivative = 2.34 \[ \int \frac {e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (\left (32 x^3-24 x^4+2 x^6\right ) \log (x)+\left (64 x^3-64 x^4+4 x^5+6 x^6\right ) \log ^2(x)\right )+\left (-4-2 e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}-2 \log (4)\right ) \log \left (2+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)}+\log (4)\right )}{128+96 x+24 x^2+2 x^3+e^{\left (4 x^4-4 x^5+x^6\right ) \log ^2(x)} \left (64+48 x+12 x^2+x^3\right )+\left (64+48 x+12 x^2+x^3\right ) \log (4)} \, dx=\frac {\mathrm {log}\left (\frac {e^{\mathrm {log}\left (x \right )^{2} x^{6}+4 \mathrm {log}\left (x \right )^{2} x^{4}}+2 e^{4 \mathrm {log}\left (x \right )^{2} x^{5}} \mathrm {log}\left (2\right )+2 e^{4 \mathrm {log}\left (x \right )^{2} x^{5}}}{e^{4 \mathrm {log}\left (x \right )^{2} x^{5}}}\right )}{x^{2}+8 x +16} \] Input:

int(((-2*exp((x^6-4*x^5+4*x^4)*log(x)^2)-4*log(2)-4)*log(exp((x^6-4*x^5+4* 
x^4)*log(x)^2)+2+2*log(2))+((6*x^6+4*x^5-64*x^4+64*x^3)*log(x)^2+(2*x^6-24 
*x^4+32*x^3)*log(x))*exp((x^6-4*x^5+4*x^4)*log(x)^2))/((x^3+12*x^2+48*x+64 
)*exp((x^6-4*x^5+4*x^4)*log(x)^2)+2*(x^3+12*x^2+48*x+64)*log(2)+2*x^3+24*x 
^2+96*x+128),x)
 

Output:

log((e**(log(x)**2*x**6 + 4*log(x)**2*x**4) + 2*e**(4*log(x)**2*x**5)*log( 
2) + 2*e**(4*log(x)**2*x**5))/e**(4*log(x)**2*x**5))/(x**2 + 8*x + 16)