\(\int \frac {(16-12 x^2+4 x^3+e^3 (-16 x^2-16 x^3+28 x^4-8 x^5)+e^3 (-16 x-16 x^2+28 x^3-8 x^4) \log (x)) \log (\log ^2(e^{-e^3 (2+x+x^2)} (x+\log (x))))+(-4 x^2+2 x^3+(-4 x+2 x^2) \log (x)) \log (e^{-e^3 (2+x+x^2)} (x+\log (x))) \log ^2(\log ^2(e^{-e^3 (2+x+x^2)} (x+\log (x))))}{(x^2+x \log (x)) \log (e^{-e^3 (2+x+x^2)} (x+\log (x)))} \, dx\) [2423]

Optimal result

Integrand size = 185, antiderivative size = 30 \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=(-2+x)^2 \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \] Output:

(-2+x)^2*ln(ln((x+ln(x))/exp((x^2+x+2)*exp(3)))^2)^2
 

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=(-2+x)^2 \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \] Input:

Integrate[((16 - 12*x^2 + 4*x^3 + E^3*(-16*x^2 - 16*x^3 + 28*x^4 - 8*x^5) 
+ E^3*(-16*x - 16*x^2 + 28*x^3 - 8*x^4)*Log[x])*Log[Log[(x + Log[x])/E^(E^ 
3*(2 + x + x^2))]^2] + (-4*x^2 + 2*x^3 + (-4*x + 2*x^2)*Log[x])*Log[(x + L 
og[x])/E^(E^3*(2 + x + x^2))]*Log[Log[(x + Log[x])/E^(E^3*(2 + x + x^2))]^ 
2]^2)/((x^2 + x*Log[x])*Log[(x + Log[x])/E^(E^3*(2 + x + x^2))]),x]
 

Output:

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

\(\displaystyle \int \frac {\left (2 x^3-4 x^2+\left (2 x^2-4 x\right ) \log (x)\right ) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )+\left (4 x^3-12 x^2+e^3 \left (-8 x^4+28 x^3-16 x^2-16 x\right ) \log (x)+e^3 \left (-8 x^5+28 x^4-16 x^3-16 x^2\right )+16\right ) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )} \, dx\)

\(\Big \downarrow \) 3041

\(\displaystyle \int \frac {\left (2 x^3-4 x^2+\left (2 x^2-4 x\right ) \log (x)\right ) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )+\left (4 x^3-12 x^2+e^3 \left (-8 x^4+28 x^3-16 x^2-16 x\right ) \log (x)+e^3 \left (-8 x^5+28 x^4-16 x^3-16 x^2\right )+16\right ) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx\)

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 2009

\(\displaystyle 16 \int \frac {\log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-16 e^3 \int \frac {x \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-12 \int \frac {x \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-16 e^3 \int \frac {x^2 \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx+4 \int \frac {x^2 \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-16 e^3 \int \frac {\log (x) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-16 e^3 \int \frac {x \log (x) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx+28 e^3 \int \frac {x^2 \log (x) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-4 \int \log ^2\left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )dx+2 \int x \log ^2\left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )dx-8 e^3 \int \frac {x^4 \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx+28 e^3 \int \frac {x^3 \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx-8 e^3 \int \frac {x^3 \log (x) \log \left (\log ^2\left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (x^2+x+2\right )} (x+\log (x))\right )}dx\)

Input:

Int[((16 - 12*x^2 + 4*x^3 + E^3*(-16*x^2 - 16*x^3 + 28*x^4 - 8*x^5) + E^3* 
(-16*x - 16*x^2 + 28*x^3 - 8*x^4)*Log[x])*Log[Log[(x + Log[x])/E^(E^3*(2 + 
 x + x^2))]^2] + (-4*x^2 + 2*x^3 + (-4*x + 2*x^2)*Log[x])*Log[(x + Log[x]) 
/E^(E^3*(2 + x + x^2))]*Log[Log[(x + Log[x])/E^(E^3*(2 + x + x^2))]^2]^2)/ 
((x^2 + x*Log[x])*Log[(x + Log[x])/E^(E^3*(2 + x + x^2))]),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs. \(2(29)=58\).

Time = 237.58 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.67

method	result	size
parallelrisch	\({\ln \left (\ln \left (\left (x +\ln \left (x \right )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )^{2}\right )}^{2} x^{2}-4 {\ln \left (\ln \left (\left (x +\ln \left (x \right )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )^{2}\right )}^{2} x +4 {\ln \left (\ln \left (\left (x +\ln \left (x \right )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )^{2}\right )}^{2}\)	\(80\)

Input:

int((((2*x^2-4*x)*ln(x)+2*x^3-4*x^2)*ln((x+ln(x))/exp((x^2+x+2)*exp(3)))*l 
n(ln((x+ln(x))/exp((x^2+x+2)*exp(3)))^2)^2+((-8*x^4+28*x^3-16*x^2-16*x)*ex 
p(3)*ln(x)+(-8*x^5+28*x^4-16*x^3-16*x^2)*exp(3)+4*x^3-12*x^2+16)*ln(ln((x+ 
ln(x))/exp((x^2+x+2)*exp(3)))^2))/(x*ln(x)+x^2)/ln((x+ln(x))/exp((x^2+x+2) 
*exp(3))),x,method=_RETURNVERBOSE)
 

Output:

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

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx={\left (x^{2} - 4 \, x + 4\right )} \log \left (\log \left (x e^{\left (-{\left (x^{2} + x + 2\right )} e^{3}\right )} + e^{\left (-{\left (x^{2} + x + 2\right )} e^{3}\right )} \log \left (x\right )\right )^{2}\right )^{2} \] Input:

integrate((((2*x^2-4*x)*log(x)+2*x^3-4*x^2)*log((x+log(x))/exp((x^2+x+2)*e 
xp(3)))*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2)^2+((-8*x^4+28*x^3-16* 
x^2-16*x)*exp(3)*log(x)+(-8*x^5+28*x^4-16*x^3-16*x^2)*exp(3)+4*x^3-12*x^2+ 
16)*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2))/(x*log(x)+x^2)/log((x+lo 
g(x))/exp((x^2+x+2)*exp(3))),x, algorithm="fricas")
 

Output:

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

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=\text {Exception raised: TypeError} \] Input:

integrate((((2*x**2-4*x)*ln(x)+2*x**3-4*x**2)*ln((x+ln(x))/exp((x**2+x+2)* 
exp(3)))*ln(ln((x+ln(x))/exp((x**2+x+2)*exp(3)))**2)**2+((-8*x**4+28*x**3- 
16*x**2-16*x)*exp(3)*ln(x)+(-8*x**5+28*x**4-16*x**3-16*x**2)*exp(3)+4*x**3 
-12*x**2+16)*ln(ln((x+ln(x))/exp((x**2+x+2)*exp(3)))**2))/(x*ln(x)+x**2)/l 
n((x+ln(x))/exp((x**2+x+2)*exp(3))),x)
 

Output:

Exception raised: TypeError >> '>' not supported between instances of 'Pol 
y' and 'int'
 

Maxima [A] (verification not implemented)

Time = 0.16 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=4 \, {\left (x^{2} - 4 \, x + 4\right )} \log \left (x^{2} e^{3} + x e^{3} + 2 \, e^{3} - \log \left (x + \log \left (x\right )\right )\right )^{2} \] Input:

integrate((((2*x^2-4*x)*log(x)+2*x^3-4*x^2)*log((x+log(x))/exp((x^2+x+2)*e 
xp(3)))*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2)^2+((-8*x^4+28*x^3-16* 
x^2-16*x)*exp(3)*log(x)+(-8*x^5+28*x^4-16*x^3-16*x^2)*exp(3)+4*x^3-12*x^2+ 
16)*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2))/(x*log(x)+x^2)/log((x+lo 
g(x))/exp((x^2+x+2)*exp(3))),x, algorithm="maxima")
 

Output:

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

Giac [F(-1)]

Timed out. \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx=\text {Timed out} \] Input:

integrate((((2*x^2-4*x)*log(x)+2*x^3-4*x^2)*log((x+log(x))/exp((x^2+x+2)*e 
xp(3)))*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2)^2+((-8*x^4+28*x^3-16* 
x^2-16*x)*exp(3)*log(x)+(-8*x^5+28*x^4-16*x^3-16*x^2)*exp(3)+4*x^3-12*x^2+ 
16)*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2))/(x*log(x)+x^2)/log((x+lo 
g(x))/exp((x^2+x+2)*exp(3))),x, algorithm="giac")
 

Output:

Timed out
 

Mupad [B] (verification not implemented)

Time = 3.65 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.20 \[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx={\ln \left ({\ln \left ({\mathrm {e}}^{-x^2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^3}\,\left (x+\ln \left (x\right )\right )\right )}^2\right )}^2\,{\left (x-2\right )}^2 \] Input:

int(-(log(log(exp(-exp(3)*(x + x^2 + 2))*(x + log(x)))^2)*(12*x^2 - 4*x^3 
+ exp(3)*(16*x^2 + 16*x^3 - 28*x^4 + 8*x^5) + exp(3)*log(x)*(16*x + 16*x^2 
 - 28*x^3 + 8*x^4) - 16) + log(log(exp(-exp(3)*(x + x^2 + 2))*(x + log(x)) 
)^2)^2*log(exp(-exp(3)*(x + x^2 + 2))*(x + log(x)))*(log(x)*(4*x - 2*x^2) 
+ 4*x^2 - 2*x^3))/(log(exp(-exp(3)*(x + x^2 + 2))*(x + log(x)))*(x*log(x) 
+ x^2)),x)
 

Output:

log(log(exp(-x^2*exp(3))*exp(-2*exp(3))*exp(-x*exp(3))*(x + log(x)))^2)^2* 
(x - 2)^2
 

Reduce [F]

\[ \int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx =\text {Too large to display} \] Input:

int((((2*x^2-4*x)*log(x)+2*x^3-4*x^2)*log((x+log(x))/exp((x^2+x+2)*exp(3)) 
)*log(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2)^2+((-8*x^4+28*x^3-16*x^2-16 
*x)*exp(3)*log(x)+(-8*x^5+28*x^4-16*x^3-16*x^2)*exp(3)+4*x^3-12*x^2+16)*lo 
g(log((x+log(x))/exp((x^2+x+2)*exp(3)))^2))/(x*log(x)+x^2)/log((x+log(x))/ 
exp((x^2+x+2)*exp(3))),x)
 

Output:

2*(8*int(log(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))**2)/(log(( 
log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))*log(x)*x + log((log(x) + x)/ 
e**(e**3*x**2 + e**3*x + 2*e**3))*x**2),x) + int((log(log((log(x) + x)/e** 
(e**3*x**2 + e**3*x + 2*e**3))**2)**2*x**2)/(log(x) + x),x) + int((log(log 
((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))**2)**2*log(x)*x)/(log(x) + 
 x),x) - 2*int((log(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))**2) 
**2*log(x))/(log(x) + x),x) - 2*int((log(log((log(x) + x)/e**(e**3*x**2 + 
e**3*x + 2*e**3))**2)**2*x)/(log(x) + x),x) - 4*int((log(log((log(x) + x)/ 
e**(e**3*x**2 + e**3*x + 2*e**3))**2)*x**4)/(log((log(x) + x)/e**(e**3*x** 
2 + e**3*x + 2*e**3))*log(x) + log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2 
*e**3))*x),x)*e**3 + 14*int((log(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 
 2*e**3))**2)*x**3)/(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))*lo 
g(x) + log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))*x),x)*e**3 - 8*i 
nt((log(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))**2)*x**2)/(log( 
(log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3))*log(x) + log((log(x) + x)/e 
**(e**3*x**2 + e**3*x + 2*e**3))*x),x)*e**3 + 2*int((log(log((log(x) + x)/ 
e**(e**3*x**2 + e**3*x + 2*e**3))**2)*x**2)/(log((log(x) + x)/e**(e**3*x** 
2 + e**3*x + 2*e**3))*log(x) + log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2 
*e**3))*x),x) - 4*int((log(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e** 
3))**2)*log(x)*x**3)/(log((log(x) + x)/e**(e**3*x**2 + e**3*x + 2*e**3)...