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

3.19.90.1 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
 

3.19.90.2 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]
 

3.19.90.3 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.

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

\(\Big \downarrow \) 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
 

3.19.90.3.1 Defintions of rubi rules used

rule 6

Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v 
+ (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] &&  !FreeQ[Fx, x]
 

rule 2009

Int[u_, x_Symbol] :> Simp[IntSum[u, x], x] /; SumQ[u]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.19.90.4 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)
 

3.19.90.5 Fricas [A] (verification not implemented)

Time = 0.25 (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=\
 

output

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

3.19.90.6 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
 

3.19.90.7 Maxima [A] (verification not implemented)

Time = 0.35 (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=\
 

output

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

3.19.90.8 Giac [A] (verification not implemented)

Time = 3.09 (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=\
 

output

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

3.19.90.9 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}