\(\int \frac {2+x-2 x^2-x \log (16)+(-x+x^2+(-1+x) \log (16)-\log (x^2)) \log (x-x^2+(1-x) \log (16)+\log (x^2)) \log (\log (x-x^2+(1-x) \log (16)+\log (x^2)))+(-x+x^2+(-1+x) \log (16)-\log (x^2)) \log (x-x^2+(1-x) \log (16)+\log (x^2)) \log (\log (x-x^2+(1-x) \log (16)+\log (x^2))) \log (\log (\log (x-x^2+(1-x) \log (16)+\log (x^2))))}{(x^3-x^4+(x^2-x^3) \log (16)+x^2 \log (x^2)) \log (x-x^2+(1-x) \log (16)+\log (x^2)) \log (\log (x-x^2+(1-x) \log (16)+\log (x^2)))} \, dx\) [1890]

Optimal result

Integrand size = 234, antiderivative size = 24 \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\frac {1+\log \left (\log \left (\log \left ((1-x) (x+\log (16))+\log \left (x^2\right )\right )\right )\right )}{x} \] Output:

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

Mathematica [F]

\[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx \] Input:

Integrate[(2 + x - 2*x^2 - x*Log[16] + (-x + x^2 + (-1 + x)*Log[16] - Log[ 
x^2])*Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)* 
Log[16] + Log[x^2]]] + (-x + x^2 + (-1 + x)*Log[16] - Log[x^2])*Log[x - x^ 
2 + (1 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^ 
2]]]*Log[Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]])/((x^3 - x^4 + (x 
^2 - x^3)*Log[16] + x^2*Log[x^2])*Log[x - x^2 + (1 - x)*Log[16] + Log[x^2] 
]*Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]),x]
 

Output:

Integrate[(2 + x - 2*x^2 - x*Log[16] + (-x + x^2 + (-1 + x)*Log[16] - Log[ 
x^2])*Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)* 
Log[16] + Log[x^2]]] + (-x + x^2 + (-1 + x)*Log[16] - Log[x^2])*Log[x - x^ 
2 + (1 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^ 
2]]]*Log[Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]])/((x^3 - x^4 + (x 
^2 - x^3)*Log[16] + x^2*Log[x^2])*Log[x - x^2 + (1 - x)*Log[16] + Log[x^2] 
]*Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]), 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.

\(\displaystyle \int \frac {-2 x^2+\left (x^2-\log \left (x^2\right )-x+(x-1) \log (16)\right ) \log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right ) \log \left (\log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right )\right )+\left (x^2-\log \left (x^2\right )-x+(x-1) \log (16)\right ) \log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right ) \log \left (\log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right )\right ) \log \left (\log \left (\log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right )\right )\right )+x-x \log (16)+2}{\left (-x^4+x^3+x^2 \log \left (x^2\right )+\left (x^2-x^3\right ) \log (16)\right ) \log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right ) \log \left (\log \left (-x^2+\log \left (x^2\right )+x+(1-x) \log (16)\right )\right )} \, dx\)

\(\Big \downarrow \) 6

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

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {2 x^2+x^2 \left (-\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )+x (1-\log (16)) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )+\log \left (x^2\right ) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )+\log (16) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )-x (1-\log (16))-2}{x^2 \left (x^2-\log \left (16 x^2\right )-x (1-\log (16))\right ) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )}-\frac {\log \left (\log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )\right )}{x^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 2 \int \frac {1}{\left (x^2-(1-\log (16)) x-\log \left (16 x^2\right )\right ) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )}dx-(1-\log (16)) \int \frac {1}{x \left (x^2-(1-\log (16)) x-\log \left (16 x^2\right )\right ) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )}dx+2 \int \frac {1}{x^2 \left (-x^2+(1-\log (16)) x+\log \left (16 x^2\right )\right ) \log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right ) \log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )}dx-\int \frac {\log \left (\log \left (\log \left (\log \left (x^2\right )-(x-1) (x+\log (16))\right )\right )\right )}{x^2}dx+\frac {1}{x}\)

Input:

Int[(2 + x - 2*x^2 - x*Log[16] + (-x + x^2 + (-1 + x)*Log[16] - Log[x^2])* 
Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)*Log[16 
] + Log[x^2]]] + (-x + x^2 + (-1 + x)*Log[16] - Log[x^2])*Log[x - x^2 + (1 
 - x)*Log[16] + Log[x^2]]*Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]*L 
og[Log[Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]])/((x^3 - x^4 + (x^2 - x 
^3)*Log[16] + x^2*Log[x^2])*Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]*Log[ 
Log[x - x^2 + (1 - x)*Log[16] + Log[x^2]]]),x]
 

Output:

$Aborted
 

Maple [F]

\[\int \frac {\left (-\ln \left (x^{2}\right )+4 \left (-1+x \right ) \ln \left (2\right )+x^{2}-x \right ) \ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right ) \ln \left (\ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right )\right ) \ln \left (\ln \left (\ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right )\right )\right )+\left (-\ln \left (x^{2}\right )+4 \left (-1+x \right ) \ln \left (2\right )+x^{2}-x \right ) \ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right ) \ln \left (\ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right )\right )-4 x \ln \left (2\right )-2 x^{2}+x +2}{\left (x^{2} \ln \left (x^{2}\right )+4 \left (-x^{3}+x^{2}\right ) \ln \left (2\right )-x^{4}+x^{3}\right ) \ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right ) \ln \left (\ln \left (\ln \left (x^{2}\right )+4 \left (1-x \right ) \ln \left (2\right )-x^{2}+x \right )\right )}d x\]

Input:

int(((-ln(x^2)+4*(-1+x)*ln(2)+x^2-x)*ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)*ln(ln 
(ln(x^2)+4*(1-x)*ln(2)-x^2+x))*ln(ln(ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)))+(-l 
n(x^2)+4*(-1+x)*ln(2)+x^2-x)*ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)*ln(ln(ln(x^2) 
+4*(1-x)*ln(2)-x^2+x))-4*x*ln(2)-2*x^2+x+2)/(x^2*ln(x^2)+4*(-x^3+x^2)*ln(2 
)-x^4+x^3)/ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)/ln(ln(ln(x^2)+4*(1-x)*ln(2)-x^2 
+x)),x)
 

Output:

int(((-ln(x^2)+4*(-1+x)*ln(2)+x^2-x)*ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)*ln(ln 
(ln(x^2)+4*(1-x)*ln(2)-x^2+x))*ln(ln(ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)))+(-l 
n(x^2)+4*(-1+x)*ln(2)+x^2-x)*ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)*ln(ln(ln(x^2) 
+4*(1-x)*ln(2)-x^2+x))-4*x*ln(2)-2*x^2+x+2)/(x^2*ln(x^2)+4*(-x^3+x^2)*ln(2 
)-x^4+x^3)/ln(ln(x^2)+4*(1-x)*ln(2)-x^2+x)/ln(ln(ln(x^2)+4*(1-x)*ln(2)-x^2 
+x)),x)
 

Fricas [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\frac {\log \left (\log \left (\log \left (-x^{2} - 4 \, {\left (x - 1\right )} \log \left (2\right ) + x + \log \left (x^{2}\right )\right )\right )\right ) + 1}{x} \] Input:

integrate(((-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x 
^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))*log(log(log(log(x^2)+4*(1-x) 
*log(2)-x^2+x)))+(-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*lo 
g(2)-x^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))-4*x*log(2)-2*x^2+x+2)/ 
(x^2*log(x^2)+4*(-x^3+x^2)*log(2)-x^4+x^3)/log(log(x^2)+4*(1-x)*log(2)-x^2 
+x)/log(log(log(x^2)+4*(1-x)*log(2)-x^2+x)),x, algorithm="fricas")
 

Output:

(log(log(log(-x^2 - 4*(x - 1)*log(2) + x + log(x^2)))) + 1)/x
 

Sympy [F(-1)]

Timed out. \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\text {Timed out} \] Input:

integrate(((-ln(x**2)+4*(-1+x)*ln(2)+x**2-x)*ln(ln(x**2)+4*(1-x)*ln(2)-x** 
2+x)*ln(ln(ln(x**2)+4*(1-x)*ln(2)-x**2+x))*ln(ln(ln(ln(x**2)+4*(1-x)*ln(2) 
-x**2+x)))+(-ln(x**2)+4*(-1+x)*ln(2)+x**2-x)*ln(ln(x**2)+4*(1-x)*ln(2)-x** 
2+x)*ln(ln(ln(x**2)+4*(1-x)*ln(2)-x**2+x))-4*x*ln(2)-2*x**2+x+2)/(x**2*ln( 
x**2)+4*(-x**3+x**2)*ln(2)-x**4+x**3)/ln(ln(x**2)+4*(1-x)*ln(2)-x**2+x)/ln 
(ln(ln(x**2)+4*(1-x)*ln(2)-x**2+x)),x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\frac {\log \left (\log \left (\log \left (-x^{2} - x {\left (4 \, \log \left (2\right ) - 1\right )} + 4 \, \log \left (2\right ) + 2 \, \log \left (x\right )\right )\right )\right ) + 1}{x} \] Input:

integrate(((-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x 
^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))*log(log(log(log(x^2)+4*(1-x) 
*log(2)-x^2+x)))+(-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*lo 
g(2)-x^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))-4*x*log(2)-2*x^2+x+2)/ 
(x^2*log(x^2)+4*(-x^3+x^2)*log(2)-x^4+x^3)/log(log(x^2)+4*(1-x)*log(2)-x^2 
+x)/log(log(log(x^2)+4*(1-x)*log(2)-x^2+x)),x, algorithm="maxima")
 

Output:

(log(log(log(-x^2 - x*(4*log(2) - 1) + 4*log(2) + 2*log(x)))) + 1)/x
 

Giac [A] (verification not implemented)

Time = 2.93 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\frac {\log \left (\log \left (\log \left (-x^{2} - 4 \, x \log \left (2\right ) + x + 4 \, \log \left (2\right ) + \log \left (x^{2}\right )\right )\right )\right )}{x} + \frac {1}{x} \] Input:

integrate(((-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x 
^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))*log(log(log(log(x^2)+4*(1-x) 
*log(2)-x^2+x)))+(-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*lo 
g(2)-x^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))-4*x*log(2)-2*x^2+x+2)/ 
(x^2*log(x^2)+4*(-x^3+x^2)*log(2)-x^4+x^3)/log(log(x^2)+4*(1-x)*log(2)-x^2 
+x)/log(log(log(x^2)+4*(1-x)*log(2)-x^2+x)),x, algorithm="giac")
 

Output:

log(log(log(-x^2 - 4*x*log(2) + x + 4*log(2) + log(x^2))))/x + 1/x
 

Mupad [F(-1)]

Timed out. \[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\text {Hanged} \] Input:

int(-(4*x*log(2) - x + 2*x^2 + log(x + log(x^2) - 4*log(2)*(x - 1) - x^2)* 
log(log(x + log(x^2) - 4*log(2)*(x - 1) - x^2))*(x + log(x^2) - 4*log(2)*( 
x - 1) - x^2) + log(log(log(x + log(x^2) - 4*log(2)*(x - 1) - x^2)))*log(x 
 + log(x^2) - 4*log(2)*(x - 1) - x^2)*log(log(x + log(x^2) - 4*log(2)*(x - 
 1) - x^2))*(x + log(x^2) - 4*log(2)*(x - 1) - x^2) - 2)/(log(x + log(x^2) 
 - 4*log(2)*(x - 1) - x^2)*log(log(x + log(x^2) - 4*log(2)*(x - 1) - x^2)) 
*(4*log(2)*(x^2 - x^3) + x^2*log(x^2) + x^3 - x^4)),x)
 

Output:

\text{Hanged}
 

Reduce [F]

\[ \int \frac {2+x-2 x^2-x \log (16)+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )+\left (-x+x^2+(-1+x) \log (16)-\log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right ) \log \left (\log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )\right )}{\left (x^3-x^4+\left (x^2-x^3\right ) \log (16)+x^2 \log \left (x^2\right )\right ) \log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right ) \log \left (\log \left (x-x^2+(1-x) \log (16)+\log \left (x^2\right )\right )\right )} \, dx=\int \frac {\left (-\mathrm {log}\left (x^{2}\right )+4 \left (x -1\right ) \mathrm {log}\left (2\right )+x^{2}-x \right ) \mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right )\right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right )\right )\right )+\left (-\mathrm {log}\left (x^{2}\right )+4 \left (x -1\right ) \mathrm {log}\left (2\right )+x^{2}-x \right ) \mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right )\right )-4 \,\mathrm {log}\left (2\right ) x -2 x^{2}+x +2}{\left (\mathrm {log}\left (x^{2}\right ) x^{2}+4 \left (-x^{3}+x^{2}\right ) \mathrm {log}\left (2\right )-x^{4}+x^{3}\right ) \mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right ) \mathrm {log}\left (\mathrm {log}\left (\mathrm {log}\left (x^{2}\right )+4 \left (1-x \right ) \mathrm {log}\left (2\right )-x^{2}+x \right )\right )}d x \] Input:

int(((-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x^2+x)* 
log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))*log(log(log(log(x^2)+4*(1-x)*log(2 
)-x^2+x)))+(-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x 
^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))-4*x*log(2)-2*x^2+x+2)/(x^2*l 
og(x^2)+4*(-x^3+x^2)*log(2)-x^4+x^3)/log(log(x^2)+4*(1-x)*log(2)-x^2+x)/lo 
g(log(log(x^2)+4*(1-x)*log(2)-x^2+x)),x)
 

Output:

int(((-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x^2+x)* 
log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))*log(log(log(log(x^2)+4*(1-x)*log(2 
)-x^2+x)))+(-log(x^2)+4*(-1+x)*log(2)+x^2-x)*log(log(x^2)+4*(1-x)*log(2)-x 
^2+x)*log(log(log(x^2)+4*(1-x)*log(2)-x^2+x))-4*x*log(2)-2*x^2+x+2)/(x^2*l 
og(x^2)+4*(-x^3+x^2)*log(2)-x^4+x^3)/log(log(x^2)+4*(1-x)*log(2)-x^2+x)/lo 
g(log(log(x^2)+4*(1-x)*log(2)-x^2+x)),x)