Integrand size = 95, antiderivative size = 27 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=x+\log (x)-\frac {\left (x+\frac {4 x}{\log (x \log (4))}\right )^2}{4 (-1+x)^2} \]
Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(27)=54\).
Time = 0.36 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.30 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=\frac {1}{2} \left (-\frac {1}{2 (-1+x)^2}-\frac {1}{-1+x}+2 x+2 \log (x)-\frac {8 x^2}{(-1+x)^2 \log ^2(x \log (4))}-\frac {4 x^2}{(-1+x)^2 \log (x \log (4))}\right ) \]
Integrate[(-16*x^2 + 16*x^3 + (12*x^2 + 4*x^3)*Log[x*Log[4]] + 8*x^2*Log[x *Log[4]]^2 + (-2 + 4*x + x^2 - 4*x^3 + 2*x^4)*Log[x*Log[4]]^3)/((-2*x + 6* x^2 - 6*x^3 + 2*x^4)*Log[x*Log[4]]^3),x]
(-1/2*1/(-1 + x)^2 - (-1 + x)^(-1) + 2*x + 2*Log[x] - (8*x^2)/((-1 + x)^2* Log[x*Log[4]]^2) - (4*x^2)/((-1 + x)^2*Log[x*Log[4]]))/2
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.
| \(\displaystyle \int \frac {16 x^3-16 x^2+8 x^2 \log ^2(x \log (4))+\left (4 x^3+12 x^2\right ) \log (x \log (4))+\left (2 x^4-4 x^3+x^2+4 x-2\right ) \log ^3(x \log (4))}{\left (2 x^4-6 x^3+6 x^2-2 x\right ) \log ^3(x \log (4))} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {16 x^3-16 x^2+8 x^2 \log ^2(x \log (4))+\left (4 x^3+12 x^2\right ) \log (x \log (4))+\left (2 x^4-4 x^3+x^2+4 x-2\right ) \log ^3(x \log (4))}{x \left (2 x^3-6 x^2+6 x-2\right ) \log ^3(x \log (4))}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {16 x^3-16 x^2+8 x^2 \log ^2(x \log (4))+\left (4 x^3+12 x^2\right ) \log (x \log (4))+\left (2 x^4-4 x^3+x^2+4 x-2\right ) \log ^3(x \log (4))}{x \left (\sqrt [3]{2} x-\sqrt [3]{2}\right )^3 \log ^3(x \log (4))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 x^4-4 x^3+x^2+4 x-2}{2 (x-1)^3 x}+\frac {8 x}{(x-1)^2 \log ^3(x \log (4))}+\frac {2 (x+3) x}{(x-1)^3 \log ^2(x \log (4))}+\frac {4 x}{(x-1)^3 \log (x \log (4))}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 8 \int \frac {x}{(x-1)^2 \log ^3(x \log (4))}dx+2 \int \frac {x (x+3)}{(x-1)^3 \log ^2(x \log (4))}dx+4 \int \frac {x}{(x-1)^3 \log (x \log (4))}dx+x+\frac {1}{2 (1-x)}-\frac {1}{4 (1-x)^2}+\log (x)\) |
Int[(-16*x^2 + 16*x^3 + (12*x^2 + 4*x^3)*Log[x*Log[4]] + 8*x^2*Log[x*Log[4 ]]^2 + (-2 + 4*x + x^2 - 4*x^3 + 2*x^4)*Log[x*Log[4]]^3)/((-2*x + 6*x^2 - 6*x^3 + 2*x^4)*Log[x*Log[4]]^3),x]
3.8.34.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Leaf count of result is larger than twice the leaf count of optimal. \(75\) vs. \(2(28)=56\).
Time = 15.12 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.81
| method | result | size |
| risch | \(\frac {4 x^{2} \ln \left (x \right )+4 x^{3}-8 x \ln \left (x \right )-8 x^{2}+4 \ln \left (x \right )+2 x +1}{4 x^{2}-8 x +4}-\frac {2 \left (\ln \left (2 x \ln \left (2\right )\right )+2\right ) x^{2}}{\left (x^{2}-2 x +1\right ) \ln \left (2 x \ln \left (2\right )\right )^{2}}\) | \(76\) |
| norman | \(\frac {\ln \left (2 x \ln \left (2\right )\right )^{3}+\frac {9 \ln \left (2 x \ln \left (2\right )\right )^{2}}{4}+\ln \left (2 x \ln \left (2\right )\right )^{2} x^{3}-2 \ln \left (2 x \ln \left (2\right )\right )^{3} x +\ln \left (2 x \ln \left (2\right )\right )^{3} x^{2}-\frac {7 \ln \left (2 x \ln \left (2\right )\right )^{2} x}{2}-4 x^{2}-2 x^{2} \ln \left (2 x \ln \left (2\right )\right )}{\left (-1+x \right )^{2} \ln \left (2 x \ln \left (2\right )\right )^{2}}\) | \(96\) |
| parallelrisch | \(\frac {4 \ln \left (2 x \ln \left (2\right )\right )^{2} x^{3}+4 \ln \left (2 x \ln \left (2\right )\right )^{3} x^{2}-8 \ln \left (2 x \ln \left (2\right )\right )^{3} x -8 x^{2} \ln \left (2 x \ln \left (2\right )\right )-14 \ln \left (2 x \ln \left (2\right )\right )^{2} x +4 \ln \left (2 x \ln \left (2\right )\right )^{3}-16 x^{2}+9 \ln \left (2 x \ln \left (2\right )\right )^{2}}{4 \ln \left (2 x \ln \left (2\right )\right )^{2} \left (x^{2}-2 x +1\right )}\) | \(106\) |
| default | \(\frac {\frac {9 \ln \left (x \right )^{2}}{2}+\left (2 \ln \left (2\right )^{2}+4 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )+2 \ln \left (\ln \left (2\right )\right )^{2}\right ) x^{3}+\left (-6 \ln \left (2\right )^{2}-12 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )-6 \ln \left (\ln \left (2\right )\right )^{2}+9 \ln \left (2\right )+9 \ln \left (\ln \left (2\right )\right )\right ) \ln \left (x \right )+\left (-4 \ln \left (2\right )^{3}-12 \ln \left (2\right )^{2} \ln \left (\ln \left (2\right )\right )-12 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )^{2}-4 \ln \left (\ln \left (2\right )\right )^{3}-4 \ln \left (2\right )-4 \ln \left (\ln \left (2\right )\right )-8\right ) x^{2}+\left (8 \ln \left (2\right )^{3}+24 \ln \left (2\right )^{2} \ln \left (\ln \left (2\right )\right )+24 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )^{2}+8 \ln \left (\ln \left (2\right )\right )^{3}-7 \ln \left (2\right )^{2}-14 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )-7 \ln \left (\ln \left (2\right )\right )^{2}\right ) x -7 x \ln \left (x \right )^{2}+\left (4 \ln \left (2\right )+4 \ln \left (\ln \left (2\right )\right )\right ) \ln \left (x \right ) x^{3}+\left (-6 \ln \left (2\right )^{2}-12 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )-6 \ln \left (\ln \left (2\right )\right )^{2}-4\right ) \ln \left (x \right ) x^{2}+\left (12 \ln \left (2\right )^{2}+24 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )+12 \ln \left (\ln \left (2\right )\right )^{2}-14 \ln \left (2\right )-14 \ln \left (\ln \left (2\right )\right )\right ) \ln \left (x \right ) x +2 \ln \left (x \right )^{3}-4 x \ln \left (x \right )^{3}+2 x^{2} \ln \left (x \right )^{3}+2 x^{3} \ln \left (x \right )^{2}+\frac {9 \ln \left (2\right )^{2}}{2}+9 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )+\frac {9 \ln \left (\ln \left (2\right )\right )^{2}}{2}-4 \ln \left (2\right )^{3}-12 \ln \left (2\right )^{2} \ln \left (\ln \left (2\right )\right )-12 \ln \left (2\right ) \ln \left (\ln \left (2\right )\right )^{2}-4 \ln \left (\ln \left (2\right )\right )^{3}}{2 \left (-1+x \right )^{2} \left (\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+\ln \left (x \right )\right )^{2}}\) | \(350\) |
int(((2*x^4-4*x^3+x^2+4*x-2)*ln(2*x*ln(2))^3+8*x^2*ln(2*x*ln(2))^2+(4*x^3+ 12*x^2)*ln(2*x*ln(2))+16*x^3-16*x^2)/(2*x^4-6*x^3+6*x^2-2*x)/ln(2*x*ln(2)) ^3,x,method=_RETURNVERBOSE)
1/4*(4*x^2*ln(x)+4*x^3-8*x*ln(x)-8*x^2+4*ln(x)+2*x+1)/(x^2-2*x+1)-2*(ln(2* x*ln(2))+2)*x^2/(x^2-2*x+1)/ln(2*x*ln(2))^2
Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (26) = 52\).
Time = 0.47 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.93 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=\frac {4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, x \log \left (2\right )\right )^{3} - 8 \, x^{2} \log \left (2 \, x \log \left (2\right )\right ) + {\left (4 \, x^{3} - 8 \, x^{2} + 2 \, x + 1\right )} \log \left (2 \, x \log \left (2\right )\right )^{2} - 16 \, x^{2}}{4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, x \log \left (2\right )\right )^{2}} \]
integrate(((2*x^4-4*x^3+x^2+4*x-2)*log(2*x*log(2))^3+8*x^2*log(2*x*log(2)) ^2+(4*x^3+12*x^2)*log(2*x*log(2))+16*x^3-16*x^2)/(2*x^4-6*x^3+6*x^2-2*x)/l og(2*x*log(2))^3,x, algorithm=\
1/4*(4*(x^2 - 2*x + 1)*log(2*x*log(2))^3 - 8*x^2*log(2*x*log(2)) + (4*x^3 - 8*x^2 + 2*x + 1)*log(2*x*log(2))^2 - 16*x^2)/((x^2 - 2*x + 1)*log(2*x*lo g(2))^2)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (26) = 52\).
Time = 0.26 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.15 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=x + \frac {1 - 2 x}{4 x^{2} - 8 x + 4} + \frac {- 2 x^{2} \log {\left (2 x \log {\left (2 \right )} \right )} - 4 x^{2}}{\left (x^{2} - 2 x + 1\right ) \log {\left (2 x \log {\left (2 \right )} \right )}^{2}} + \log {\left (x \right )} \]
integrate(((2*x**4-4*x**3+x**2+4*x-2)*ln(2*x*ln(2))**3+8*x**2*ln(2*x*ln(2) )**2+(4*x**3+12*x**2)*ln(2*x*ln(2))+16*x**3-16*x**2)/(2*x**4-6*x**3+6*x**2 -2*x)/ln(2*x*ln(2))**3,x)
x + (1 - 2*x)/(4*x**2 - 8*x + 4) + (-2*x**2*log(2*x*log(2)) - 4*x**2)/((x* *2 - 2*x + 1)*log(2*x*log(2))**2) + log(x)
Leaf count of result is larger than twice the leaf count of optimal. 261 vs. \(2 (26) = 52\).
Time = 0.31 (sec) , antiderivative size = 261, normalized size of antiderivative = 9.67 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=\frac {4 \, {\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}\right )} x^{3} - 8 \, {\left ({\left (2 \, \log \left (\log \left (2\right )\right ) + 1\right )} \log \left (2\right ) + \log \left (2\right )^{2} + \log \left (\log \left (2\right )\right )^{2} + \log \left (\log \left (2\right )\right ) + 2\right )} x^{2} + {\left (4 \, x^{3} - 8 \, x^{2} + 2 \, x + 1\right )} \log \left (x\right )^{2} + 2 \, {\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}\right )} x + \log \left (2\right )^{2} + 2 \, {\left (4 \, x^{3} {\left (\log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} - 4 \, x^{2} {\left (2 \, \log \left (2\right ) + 2 \, \log \left (\log \left (2\right )\right ) + 1\right )} + 2 \, x {\left (\log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} + \log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} \log \left (x\right ) + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}}{4 \, {\left ({\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}\right )} x^{2} + {\left (x^{2} - 2 \, x + 1\right )} \log \left (x\right )^{2} - 2 \, {\left (\log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}\right )} x + \log \left (2\right )^{2} + 2 \, {\left (x^{2} {\left (\log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} - 2 \, x {\left (\log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} + \log \left (2\right ) + \log \left (\log \left (2\right )\right )\right )} \log \left (x\right ) + 2 \, \log \left (2\right ) \log \left (\log \left (2\right )\right ) + \log \left (\log \left (2\right )\right )^{2}\right )}} + \log \left (x\right ) \]
integrate(((2*x^4-4*x^3+x^2+4*x-2)*log(2*x*log(2))^3+8*x^2*log(2*x*log(2)) ^2+(4*x^3+12*x^2)*log(2*x*log(2))+16*x^3-16*x^2)/(2*x^4-6*x^3+6*x^2-2*x)/l og(2*x*log(2))^3,x, algorithm=\
1/4*(4*(log(2)^2 + 2*log(2)*log(log(2)) + log(log(2))^2)*x^3 - 8*((2*log(l og(2)) + 1)*log(2) + log(2)^2 + log(log(2))^2 + log(log(2)) + 2)*x^2 + (4* x^3 - 8*x^2 + 2*x + 1)*log(x)^2 + 2*(log(2)^2 + 2*log(2)*log(log(2)) + log (log(2))^2)*x + log(2)^2 + 2*(4*x^3*(log(2) + log(log(2))) - 4*x^2*(2*log( 2) + 2*log(log(2)) + 1) + 2*x*(log(2) + log(log(2))) + log(2) + log(log(2) ))*log(x) + 2*log(2)*log(log(2)) + log(log(2))^2)/((log(2)^2 + 2*log(2)*lo g(log(2)) + log(log(2))^2)*x^2 + (x^2 - 2*x + 1)*log(x)^2 - 2*(log(2)^2 + 2*log(2)*log(log(2)) + log(log(2))^2)*x + log(2)^2 + 2*(x^2*(log(2) + log( log(2))) - 2*x*(log(2) + log(log(2))) + log(2) + log(log(2)))*log(x) + 2*l og(2)*log(log(2)) + log(log(2))^2) + log(x)
Leaf count of result is larger than twice the leaf count of optimal. 125 vs. \(2 (26) = 52\).
Time = 0.35 (sec) , antiderivative size = 125, normalized size of antiderivative = 4.63 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=x - \frac {2 \, {\left (x^{2} \log \left (2\right ) + x^{2} \log \left (x \log \left (2\right )\right ) + 2 \, x^{2}\right )}}{x^{2} \log \left (2\right )^{2} + 2 \, x^{2} \log \left (2\right ) \log \left (x \log \left (2\right )\right ) + x^{2} \log \left (x \log \left (2\right )\right )^{2} - 2 \, x \log \left (2\right )^{2} - 4 \, x \log \left (2\right ) \log \left (x \log \left (2\right )\right ) - 2 \, x \log \left (x \log \left (2\right )\right )^{2} + \log \left (2\right )^{2} + 2 \, \log \left (2\right ) \log \left (x \log \left (2\right )\right ) + \log \left (x \log \left (2\right )\right )^{2}} - \frac {2 \, x - 1}{4 \, {\left (x^{2} - 2 \, x + 1\right )}} + \log \left (x\right ) \]
integrate(((2*x^4-4*x^3+x^2+4*x-2)*log(2*x*log(2))^3+8*x^2*log(2*x*log(2)) ^2+(4*x^3+12*x^2)*log(2*x*log(2))+16*x^3-16*x^2)/(2*x^4-6*x^3+6*x^2-2*x)/l og(2*x*log(2))^3,x, algorithm=\
x - 2*(x^2*log(2) + x^2*log(x*log(2)) + 2*x^2)/(x^2*log(2)^2 + 2*x^2*log(2 )*log(x*log(2)) + x^2*log(x*log(2))^2 - 2*x*log(2)^2 - 4*x*log(2)*log(x*lo g(2)) - 2*x*log(x*log(2))^2 + log(2)^2 + 2*log(2)*log(x*log(2)) + log(x*lo g(2))^2) - 1/4*(2*x - 1)/(x^2 - 2*x + 1) + log(x)
Time = 18.31 (sec) , antiderivative size = 203, normalized size of antiderivative = 7.52 \[ \int \frac {-16 x^2+16 x^3+\left (12 x^2+4 x^3\right ) \log (x \log (4))+8 x^2 \log ^2(x \log (4))+\left (-2+4 x+x^2-4 x^3+2 x^4\right ) \log ^3(x \log (4))}{\left (-2 x+6 x^2-6 x^3+2 x^4\right ) \log ^3(x \log (4))} \, dx=x+\ln \left (x\right )+\frac {\frac {x\,\left (5\,x-x^2\right )}{{\left (x-1\right )}^3}+\frac {2\,x^2\,{\ln \left (2\,x\,\ln \left (2\right )\right )}^2\,\left (x+2\right )}{{\left (x-1\right )}^4}+\frac {2\,x\,\ln \left (2\,x\,\ln \left (2\right )\right )\,\left (x^2+5\,x\right )}{{\left (x-1\right )}^4}}{\ln \left (2\,x\,\ln \left (2\right )\right )}-\frac {\frac {x^3}{2}+\frac {43\,x^2}{4}+x-\frac {1}{4}}{x^4-4\,x^3+6\,x^2-4\,x+1}-\frac {\frac {4\,x^2}{{\left (x-1\right )}^2}+\frac {2\,x^2\,{\ln \left (2\,x\,\ln \left (2\right )\right )}^2}{{\left (x-1\right )}^3}+\frac {x^2\,\ln \left (2\,x\,\ln \left (2\right )\right )\,\left (x+3\right )}{{\left (x-1\right )}^3}}{{\ln \left (2\,x\,\ln \left (2\right )\right )}^2}-\frac {\ln \left (2\,x\,\ln \left (2\right )\right )\,\left (2\,x^3+4\,x^2\right )}{x^4-4\,x^3+6\,x^2-4\,x+1} \]
int(-(8*x^2*log(2*x*log(2))^2 - 16*x^2 + 16*x^3 + log(2*x*log(2))*(12*x^2 + 4*x^3) + log(2*x*log(2))^3*(4*x + x^2 - 4*x^3 + 2*x^4 - 2))/(log(2*x*log (2))^3*(2*x - 6*x^2 + 6*x^3 - 2*x^4)),x)
x + log(x) + ((x*(5*x - x^2))/(x - 1)^3 + (2*x^2*log(2*x*log(2))^2*(x + 2) )/(x - 1)^4 + (2*x*log(2*x*log(2))*(5*x + x^2))/(x - 1)^4)/log(2*x*log(2)) - (x + (43*x^2)/4 + x^3/2 - 1/4)/(6*x^2 - 4*x - 4*x^3 + x^4 + 1) - ((4*x^ 2)/(x - 1)^2 + (2*x^2*log(2*x*log(2))^2)/(x - 1)^3 + (x^2*log(2*x*log(2))* (x + 3))/(x - 1)^3)/log(2*x*log(2))^2 - (log(2*x*log(2))*(4*x^2 + 2*x^3))/ (6*x^2 - 4*x - 4*x^3 + x^4 + 1)