\(\int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} (-e^{x^6}+e^{e^x} (e^x x-6 x^6+(-e^x+6 x^5) \log (\log (3))))}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx\) [1232]

Optimal result

Integrand size = 113, antiderivative size = 30 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\frac {e^{e^{e^x-x^6}}-x+x^2}{x-\log (\log (3))} \] Output:

(exp(exp(exp(x))/exp(x^6))+x^2-x)/(x-ln(ln(3)))
 

Mathematica [A] (verified)

Time = 0.10 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.40 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\frac {e^{e^{e^x-x^6}}+x^2-x \log (\log (3))+(-1+\log (\log (3))) \log (\log (3))}{x-\log (\log (3))} \] Input:

Integrate[(E^x^6*x^2 + E^x^6*(1 - 2*x)*Log[Log[3]] + E^E^(E^x - x^6)*(-E^x 
^6 + E^E^x*(E^x*x - 6*x^6 + (-E^x + 6*x^5)*Log[Log[3]])))/(E^x^6*x^2 - 2*E 
^x^6*x*Log[Log[3]] + E^x^6*Log[Log[3]]^2),x]
 

Output:

(E^E^(E^x - x^6) + x^2 - x*Log[Log[3]] + (-1 + Log[Log[3]])*Log[Log[3]])/( 
x - Log[Log[3]])
 

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.

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

\(\Big \downarrow \) 7292

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

\(\Big \downarrow \) 7293

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

\(\Big \downarrow \) 2009

\(\displaystyle -6 \log ^5(\log (3)) \int \frac {e^{-x^6+e^x+e^{e^x-x^6}}}{x-\log (\log (3))}dx-6 \log ^4(\log (3)) \int e^{-x^6+e^x+e^{e^x-x^6}}dx-6 \log ^3(\log (3)) \int e^{-x^6+e^x+e^{e^x-x^6}} xdx-\int \frac {e^{e^{e^x-x^6}}}{(x-\log (\log (3)))^2}dx+\int \frac {e^{-x^6+x+e^x+e^{e^x-x^6}}}{x-\log (\log (3))}dx-6 \int e^{-x^6+e^x+e^{e^x-x^6}} x^4dx-6 \log (\log (3)) \int e^{-x^6+e^x+e^{e^x-x^6}} x^3dx-6 \log ^2(\log (3)) \int e^{-x^6+e^x+e^{e^x-x^6}} x^2dx+x-\frac {(1-\log (\log (3))) \log (\log (3))}{x-\log (\log (3))}\)

Input:

Int[(E^x^6*x^2 + E^x^6*(1 - 2*x)*Log[Log[3]] + E^E^(E^x - x^6)*(-E^x^6 + E 
^E^x*(E^x*x - 6*x^6 + (-E^x + 6*x^5)*Log[Log[3]])))/(E^x^6*x^2 - 2*E^x^6*x 
*Log[Log[3]] + E^x^6*Log[Log[3]]^2),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 247.20 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10

method	result	size
parallelrisch	\(\frac {-x^{2}+\ln \left (\ln \left (3\right )\right )-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}} {\mathrm e}^{-x^{6}}}}{\ln \left (\ln \left (3\right )\right )-x}\)	\(33\)
risch	\(x -\frac {\ln \left (\ln \left (3\right )\right )^{2}}{\ln \left (\ln \left (3\right )\right )-x}+\frac {\ln \left (\ln \left (3\right )\right )}{\ln \left (\ln \left (3\right )\right )-x}-\frac {{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}-x^{6}}}}{\ln \left (\ln \left (3\right )\right )-x}\)	\(53\)

Input:

int(((((-exp(x)+6*x^5)*ln(ln(3))+exp(x)*x-6*x^6)*exp(exp(x))-exp(x^6))*exp 
(exp(exp(x))/exp(x^6))+(1-2*x)*exp(x^6)*ln(ln(3))+x^2*exp(x^6))/(exp(x^6)* 
ln(ln(3))^2-2*x*exp(x^6)*ln(ln(3))+x^2*exp(x^6)),x,method=_RETURNVERBOSE)
 

Output:

(-x^2+ln(ln(3))-exp(exp(exp(x))/exp(x^6)))/(ln(ln(3))-x)
 

Fricas [A] (verification not implemented)

Time = 0.10 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\frac {x^{2} - {\left (x + 1\right )} \log \left (\log \left (3\right )\right ) + \log \left (\log \left (3\right )\right )^{2} + e^{\left (e^{\left (-x^{6} + e^{x}\right )}\right )}}{x - \log \left (\log \left (3\right )\right )} \] Input:

integrate(((((-exp(x)+6*x^5)*log(log(3))+exp(x)*x-6*x^6)*exp(exp(x))-exp(x 
^6))*exp(exp(exp(x))/exp(x^6))+(1-2*x)*exp(x^6)*log(log(3))+x^2*exp(x^6))/ 
(exp(x^6)*log(log(3))^2-2*x*exp(x^6)*log(log(3))+x^2*exp(x^6)),x, algorith 
m="fricas")
 

Output:

(x^2 - (x + 1)*log(log(3)) + log(log(3))^2 + e^(e^(-x^6 + e^x)))/(x - log( 
log(3)))
 

Sympy [A] (verification not implemented)

Time = 0.41 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.23 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=x + \frac {e^{e^{- x^{6}} e^{e^{x}}}}{x - \log {\left (\log {\left (3 \right )} \right )}} + \frac {- \log {\left (\log {\left (3 \right )} \right )} + \log {\left (\log {\left (3 \right )} \right )}^{2}}{x - \log {\left (\log {\left (3 \right )} \right )}} \] Input:

integrate(((((-exp(x)+6*x**5)*ln(ln(3))+exp(x)*x-6*x**6)*exp(exp(x))-exp(x 
**6))*exp(exp(exp(x))/exp(x**6))+(1-2*x)*exp(x**6)*ln(ln(3))+x**2*exp(x**6 
))/(exp(x**6)*ln(ln(3))**2-2*x*exp(x**6)*ln(ln(3))+x**2*exp(x**6)),x)
 

Output:

x + exp(exp(-x**6)*exp(exp(x)))/(x - log(log(3))) + (-log(log(3)) + log(lo 
g(3))**2)/(x - log(log(3)))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (27) = 54\).

Time = 0.18 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.47 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=2 \, {\left (\frac {\log \left (\log \left (3\right )\right )}{x - \log \left (\log \left (3\right )\right )} - \log \left (x - \log \left (\log \left (3\right )\right )\right )\right )} \log \left (\log \left (3\right )\right ) + 2 \, \log \left (x - \log \left (\log \left (3\right )\right )\right ) \log \left (\log \left (3\right )\right ) + \frac {x^{2} - x \log \left (\log \left (3\right )\right ) - \log \left (\log \left (3\right )\right )^{2}}{x - \log \left (\log \left (3\right )\right )} + \frac {e^{\left (e^{\left (-x^{6} + e^{x}\right )}\right )}}{x - \log \left (\log \left (3\right )\right )} - \frac {\log \left (\log \left (3\right )\right )}{x - \log \left (\log \left (3\right )\right )} \] Input:

integrate(((((-exp(x)+6*x^5)*log(log(3))+exp(x)*x-6*x^6)*exp(exp(x))-exp(x 
^6))*exp(exp(exp(x))/exp(x^6))+(1-2*x)*exp(x^6)*log(log(3))+x^2*exp(x^6))/ 
(exp(x^6)*log(log(3))^2-2*x*exp(x^6)*log(log(3))+x^2*exp(x^6)),x, algorith 
m="maxima")
 

Output:

2*(log(log(3))/(x - log(log(3))) - log(x - log(log(3))))*log(log(3)) + 2*l 
og(x - log(log(3)))*log(log(3)) + (x^2 - x*log(log(3)) - log(log(3))^2)/(x 
 - log(log(3))) + e^(e^(-x^6 + e^x))/(x - log(log(3))) - log(log(3))/(x - 
log(log(3)))
 

Giac [F]

\[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\int { \frac {x^{2} e^{\left (x^{6}\right )} - {\left (2 \, x - 1\right )} e^{\left (x^{6}\right )} \log \left (\log \left (3\right )\right ) - {\left ({\left (6 \, x^{6} - x e^{x} - {\left (6 \, x^{5} - e^{x}\right )} \log \left (\log \left (3\right )\right )\right )} e^{\left (e^{x}\right )} + e^{\left (x^{6}\right )}\right )} e^{\left (e^{\left (-x^{6} + e^{x}\right )}\right )}}{x^{2} e^{\left (x^{6}\right )} - 2 \, x e^{\left (x^{6}\right )} \log \left (\log \left (3\right )\right ) + e^{\left (x^{6}\right )} \log \left (\log \left (3\right )\right )^{2}} \,d x } \] Input:

integrate(((((-exp(x)+6*x^5)*log(log(3))+exp(x)*x-6*x^6)*exp(exp(x))-exp(x 
^6))*exp(exp(exp(x))/exp(x^6))+(1-2*x)*exp(x^6)*log(log(3))+x^2*exp(x^6))/ 
(exp(x^6)*log(log(3))^2-2*x*exp(x^6)*log(log(3))+x^2*exp(x^6)),x, algorith 
m="giac")
 

Output:

integrate((x^2*e^(x^6) - (2*x - 1)*e^(x^6)*log(log(3)) - ((6*x^6 - x*e^x - 
 (6*x^5 - e^x)*log(log(3)))*e^(e^x) + e^(x^6))*e^(e^(-x^6 + e^x)))/(x^2*e^ 
(x^6) - 2*x*e^(x^6)*log(log(3)) + e^(x^6)*log(log(3))^2), x)
 

Mupad [B] (verification not implemented)

Time = 7.53 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.37 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\frac {{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-x^6}}-\ln \left (\ln \left (3\right )\right )+{\ln \left (\ln \left (3\right )\right )}^2-x\,\ln \left (\ln \left (3\right )\right )+x^2}{x-\ln \left (\ln \left (3\right )\right )} \] Input:

int(-(exp(exp(exp(x))*exp(-x^6))*(exp(x^6) + exp(exp(x))*(log(log(3))*(exp 
(x) - 6*x^5) - x*exp(x) + 6*x^6)) - x^2*exp(x^6) + exp(x^6)*log(log(3))*(2 
*x - 1))/(x^2*exp(x^6) + exp(x^6)*log(log(3))^2 - 2*x*exp(x^6)*log(log(3)) 
),x)
 

Output:

(exp(exp(exp(x))*exp(-x^6)) - log(log(3)) + log(log(3))^2 - x*log(log(3)) 
+ x^2)/(x - log(log(3)))
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13 \[ \int \frac {e^{x^6} x^2+e^{x^6} (1-2 x) \log (\log (3))+e^{e^{e^x-x^6}} \left (-e^{x^6}+e^{e^x} \left (e^x x-6 x^6+\left (-e^x+6 x^5\right ) \log (\log (3))\right )\right )}{e^{x^6} x^2-2 e^{x^6} x \log (\log (3))+e^{x^6} \log ^2(\log (3))} \, dx=\frac {-e^{\frac {e^{e^{x}}}{e^{x^{6}}}}-x^{2}+x}{\mathrm {log}\left (\mathrm {log}\left (3\right )\right )-x} \] Input:

int(((((-exp(x)+6*x^5)*log(log(3))+exp(x)*x-6*x^6)*exp(exp(x))-exp(x^6))*e 
xp(exp(exp(x))/exp(x^6))+(1-2*x)*exp(x^6)*log(log(3))+x^2*exp(x^6))/(exp(x 
^6)*log(log(3))^2-2*x*exp(x^6)*log(log(3))+x^2*exp(x^6)),x)
 

Output:

( - e**(e**(e**x)/e**(x**6)) - x**2 + x)/(log(log(3)) - x)