Integrand size = 90, antiderivative size = 33 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {4+\log \left (-3+4 \left (\frac {3}{x}-\frac {x}{2}\right )+\frac {7 x}{4}-\frac {5}{\log (2)}\right )}{x} \] Output:
(4+ln(-1/4*x+12/x-3-5/ln(2)))/x
Leaf count is larger than twice the leaf count of optimal. \(96\) vs. \(2(33)=66\).
Time = 0.11 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.91 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {4}{x}+\frac {\text {arctanh}\left (\frac {10+x \log (2)+\log (64)}{2 \sqrt {12 \log ^2(2)+(5+\log (8))^2}}\right ) (-3 \log (2)+\log (8))}{2 \sqrt {12 \log ^2(2)+(5+\log (8))^2}}+\frac {\log \left (\frac {48 \log (2)-x^2 \log (2)-4 x (5+\log (8))}{x \log (16)}\right )}{x} \] Input:
Integrate[(-80*x + (240 - 48*x - 3*x^2)*Log[2] + (-20*x + (48 - 12*x - x^2 )*Log[2])*Log[(-20*x + (48 - 12*x - x^2)*Log[2])/(4*x*Log[2])])/(20*x^3 + (-48*x^2 + 12*x^3 + x^4)*Log[2]),x]
Output:
4/x + (ArcTanh[(10 + x*Log[2] + Log[64])/(2*Sqrt[12*Log[2]^2 + (5 + Log[8] )^2])]*(-3*Log[2] + Log[8]))/(2*Sqrt[12*Log[2]^2 + (5 + Log[8])^2]) + Log[ (48*Log[2] - x^2*Log[2] - 4*x*(5 + Log[8]))/(x*Log[16])]/x
Time = 1.03 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.94, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {2026, 7279, 2009}
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.
| \(\displaystyle \int \frac {\left (\left (-x^2-12 x+48\right ) \log (2)-20 x\right ) \log \left (\frac {\left (-x^2-12 x+48\right ) \log (2)-20 x}{4 x \log (2)}\right )+\left (-3 x^2-48 x+240\right ) \log (2)-80 x}{20 x^3+\left (x^4+12 x^3-48 x^2\right ) \log (2)} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (\left (-x^2-12 x+48\right ) \log (2)-20 x\right ) \log \left (\frac {\left (-x^2-12 x+48\right ) \log (2)-20 x}{4 x \log (2)}\right )+\left (-3 x^2-48 x+240\right ) \log (2)-80 x}{x^2 \left (x^2 \log (2)+4 x (5+\log (8))-48 \log (2)\right )}dx\) |
| \(\Big \downarrow \) 7279 |
| \(\displaystyle \int \left (\frac {x^2 \log (8)+16 x (5+\log (8))-240 \log (2)}{x^2 \left (x^2 (-\log (2))-4 x (5+\log (8))+48 \log (2)\right )}-\frac {\log \left (\frac {x^2 (-\log (2))-4 x (5+\log (8))+48 \log (2)}{x \log (16)}\right )}{x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\log \left (\frac {x^2 (-\log (2))-4 x (5+\log (8))+48 \log (2)}{x \log (16)}\right )}{x}+\frac {4}{x}-\frac {(5+\log (8)) \log (x)}{\log (4096)}+\frac {(5+\log (8)) \log (x)}{12 \log (2)}\) |
Input:
Int[(-80*x + (240 - 48*x - 3*x^2)*Log[2] + (-20*x + (48 - 12*x - x^2)*Log[ 2])*Log[(-20*x + (48 - 12*x - x^2)*Log[2])/(4*x*Log[2])])/(20*x^3 + (-48*x ^2 + 12*x^3 + x^4)*Log[2]),x]
Output:
4/x + ((5 + Log[8])*Log[x])/(12*Log[2]) - ((5 + Log[8])*Log[x])/Log[4096] + Log[(48*Log[2] - x^2*Log[2] - 4*x*(5 + Log[8]))/(x*Log[16])]/x
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])
Int[(u_)/((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.)), x_Symbol] :> With[ {v = RationalFunctionExpand[u/(a + b*x^n + c*x^(2*n)), x]}, Int[v, x] /; Su mQ[v]] /; FreeQ[{a, b, c}, x] && EqQ[n2, 2*n] && IGtQ[n, 0]
Time = 1.11 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.03
| method | result | size |
| norman | \(\frac {4+\ln \left (\frac {\left (-x^{2}-12 x +48\right ) \ln \left (2\right )-20 x}{4 x \ln \left (2\right )}\right )}{x}\) | \(34\) |
| risch | \(\frac {\ln \left (\frac {\left (-x^{2}-12 x +48\right ) \ln \left (2\right )-20 x}{4 x \ln \left (2\right )}\right )}{x}+\frac {4}{x}\) | \(38\) |
| parallelrisch | \(-\frac {-\ln \left (2\right )^{2} \ln \left (\frac {\left (-x^{2}-12 x +48\right ) \ln \left (2\right )-20 x}{4 x \ln \left (2\right )}\right )-4 \ln \left (2\right )^{2}}{x \ln \left (2\right )^{2}}\) | \(50\) |
| default | \(-\frac {\ln \left (\ln \left (2\right )\right )}{x}-\frac {2 \ln \left (2\right )-5}{x}+\frac {\left (-3 \ln \left (2\right )-5\right ) \ln \left (x \right )}{12 \ln \left (2\right )}+\frac {\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \ln \left (x^{2} \ln \left (2\right )+12 x \ln \left (2\right )-48 \ln \left (2\right )+20 x \right )}{2 \ln \left (2\right )}-\frac {\left (60 \ln \left (2\right )^{2}+120 \ln \left (2\right )+100-\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \left (12 \ln \left (2\right )+20\right )}{2 \ln \left (2\right )}\right ) \operatorname {arctanh}\left (\frac {2 x \ln \left (2\right )+12 \ln \left (2\right )+20}{4 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}\right )}{2 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}}{12 \ln \left (2\right )}+\frac {\ln \left (\frac {-x^{2} \ln \left (2\right )-12 x \ln \left (2\right )+48 \ln \left (2\right )-20 x}{x}\right )}{x}-\ln \left (2\right ) \left (\frac {1}{x \ln \left (2\right )}+\frac {\left (-3 \ln \left (2\right )-5\right ) \ln \left (x \right )}{12 \ln \left (2\right )^{2}}+\frac {\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \ln \left (x^{2} \ln \left (2\right )+12 x \ln \left (2\right )-48 \ln \left (2\right )+20 x \right )}{2 \ln \left (2\right )}-\frac {\left (60 \ln \left (2\right )^{2}+120 \ln \left (2\right )+100-\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \left (12 \ln \left (2\right )+20\right )}{2 \ln \left (2\right )}\right ) \operatorname {arctanh}\left (\frac {2 x \ln \left (2\right )+12 \ln \left (2\right )+20}{4 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}\right )}{2 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}}{12 \ln \left (2\right )^{2}}\right )\) | \(337\) |
| parts | \(\frac {\ln \left (\frac {-x^{2} \ln \left (2\right )-12 x \ln \left (2\right )+48 \ln \left (2\right )-20 x}{x}\right )}{x}-\ln \left (2\right ) \left (\frac {1}{x \ln \left (2\right )}+\frac {\left (-3 \ln \left (2\right )-5\right ) \ln \left (x \right )}{12 \ln \left (2\right )^{2}}+\frac {\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \ln \left (x^{2} \ln \left (2\right )+12 x \ln \left (2\right )-48 \ln \left (2\right )+20 x \right )}{2 \ln \left (2\right )}-\frac {\left (60 \ln \left (2\right )^{2}+120 \ln \left (2\right )+100-\frac {\left (3 \ln \left (2\right )^{2}+5 \ln \left (2\right )\right ) \left (12 \ln \left (2\right )+20\right )}{2 \ln \left (2\right )}\right ) \operatorname {arctanh}\left (\frac {2 x \ln \left (2\right )+12 \ln \left (2\right )+20}{4 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}\right )}{2 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}}{12 \ln \left (2\right )^{2}}\right )-\frac {2 \ln \left (2\right )}{x}-\frac {\ln \left (\ln \left (2\right )\right )}{x}+\frac {5}{x}-\frac {\left (3 \ln \left (2\right )+5\right ) \ln \left (x \right )}{12 \ln \left (2\right )}-\frac {\frac {\left (-3 \ln \left (2\right )^{2}-5 \ln \left (2\right )\right ) \ln \left (x^{2} \ln \left (2\right )+12 x \ln \left (2\right )-48 \ln \left (2\right )+20 x \right )}{2 \ln \left (2\right )}-\frac {\left (-60 \ln \left (2\right )^{2}-120 \ln \left (2\right )-100-\frac {\left (-3 \ln \left (2\right )^{2}-5 \ln \left (2\right )\right ) \left (12 \ln \left (2\right )+20\right )}{2 \ln \left (2\right )}\right ) \operatorname {arctanh}\left (\frac {2 x \ln \left (2\right )+12 \ln \left (2\right )+20}{4 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}\right )}{2 \sqrt {21 \ln \left (2\right )^{2}+30 \ln \left (2\right )+25}}}{12 \ln \left (2\right )}\) | \(338\) |
Input:
int((((-x^2-12*x+48)*ln(2)-20*x)*ln(1/4*((-x^2-12*x+48)*ln(2)-20*x)/x/ln(2 ))+(-3*x^2-48*x+240)*ln(2)-80*x)/((x^4+12*x^3-48*x^2)*ln(2)+20*x^3),x,meth od=_RETURNVERBOSE)
Output:
(4+ln(1/4*((-x^2-12*x+48)*ln(2)-20*x)/x/ln(2)))/x
Time = 0.07 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.94 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {\log \left (-\frac {{\left (x^{2} + 12 \, x - 48\right )} \log \left (2\right ) + 20 \, x}{4 \, x \log \left (2\right )}\right ) + 4}{x} \] Input:
integrate((((-x^2-12*x+48)*log(2)-20*x)*log(1/4*((-x^2-12*x+48)*log(2)-20* x)/x/log(2))+(-3*x^2-48*x+240)*log(2)-80*x)/((x^4+12*x^3-48*x^2)*log(2)+20 *x^3),x, algorithm="fricas")
Output:
(log(-1/4*((x^2 + 12*x - 48)*log(2) + 20*x)/(x*log(2))) + 4)/x
Time = 0.13 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.82 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {\log {\left (\frac {- 5 x + \frac {\left (- x^{2} - 12 x + 48\right ) \log {\left (2 \right )}}{4}}{x \log {\left (2 \right )}} \right )}}{x} + \frac {4}{x} \] Input:
integrate((((-x**2-12*x+48)*ln(2)-20*x)*ln(1/4*((-x**2-12*x+48)*ln(2)-20*x )/x/ln(2))+(-3*x**2-48*x+240)*ln(2)-80*x)/((x**4+12*x**3-48*x**2)*ln(2)+20 *x**3),x)
Output:
log((-5*x + (-x**2 - 12*x + 48)*log(2)/4)/(x*log(2)))/x + 4/x
Leaf count of result is larger than twice the leaf count of optimal. 317 vs. \(2 (23) = 46\).
Time = 0.17 (sec) , antiderivative size = 317, normalized size of antiderivative = 9.61 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {5}{24} \, {\left (\frac {{\left (3 \, \log \left (2\right ) + 5\right )} \log \left (x^{2} \log \left (2\right ) + 4 \, x {\left (3 \, \log \left (2\right ) + 5\right )} - 48 \, \log \left (2\right )\right )}{\log \left (2\right )^{2}} - \frac {2 \, {\left (3 \, \log \left (2\right ) + 5\right )} \log \left (x\right )}{\log \left (2\right )^{2}} + \frac {5 \, {\left (3 \, \log \left (2\right )^{2} + 6 \, \log \left (2\right ) + 5\right )} \log \left (\frac {x \log \left (2\right ) - 2 \, \sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} + 6 \, \log \left (2\right ) + 10}{x \log \left (2\right ) + 2 \, \sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} + 6 \, \log \left (2\right ) + 10}\right )}{\sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} \log \left (2\right )^{2}} + \frac {24}{x \log \left (2\right )}\right )} \log \left (2\right ) - \frac {25 \, {\left (3 \, \log \left (2\right )^{2} + 6 \, \log \left (2\right ) + 5\right )} \log \left (\frac {x \log \left (2\right ) - 2 \, \sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} + 6 \, \log \left (2\right ) + 10}{x \log \left (2\right ) + 2 \, \sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} + 6 \, \log \left (2\right ) + 10}\right )}{24 \, \sqrt {21 \, \log \left (2\right )^{2} + 30 \, \log \left (2\right ) + 25} \log \left (2\right )} - \frac {24 \, {\left (\log \left (\log \left (2\right )\right ) + 1\right )} \log \left (2\right ) + 48 \, \log \left (2\right )^{2} + {\left (5 \, x {\left (3 \, \log \left (2\right ) + 5\right )} - 24 \, \log \left (2\right )\right )} \log \left (-x^{2} \log \left (2\right ) - 4 \, x {\left (3 \, \log \left (2\right ) + 5\right )} + 48 \, \log \left (2\right )\right ) - 2 \, {\left (5 \, x {\left (3 \, \log \left (2\right ) + 5\right )} - 12 \, \log \left (2\right )\right )} \log \left (x\right )}{24 \, x \log \left (2\right )} \] Input:
integrate((((-x^2-12*x+48)*log(2)-20*x)*log(1/4*((-x^2-12*x+48)*log(2)-20* x)/x/log(2))+(-3*x^2-48*x+240)*log(2)-80*x)/((x^4+12*x^3-48*x^2)*log(2)+20 *x^3),x, algorithm="maxima")
Output:
5/24*((3*log(2) + 5)*log(x^2*log(2) + 4*x*(3*log(2) + 5) - 48*log(2))/log( 2)^2 - 2*(3*log(2) + 5)*log(x)/log(2)^2 + 5*(3*log(2)^2 + 6*log(2) + 5)*lo g((x*log(2) - 2*sqrt(21*log(2)^2 + 30*log(2) + 25) + 6*log(2) + 10)/(x*log (2) + 2*sqrt(21*log(2)^2 + 30*log(2) + 25) + 6*log(2) + 10))/(sqrt(21*log( 2)^2 + 30*log(2) + 25)*log(2)^2) + 24/(x*log(2)))*log(2) - 25/24*(3*log(2) ^2 + 6*log(2) + 5)*log((x*log(2) - 2*sqrt(21*log(2)^2 + 30*log(2) + 25) + 6*log(2) + 10)/(x*log(2) + 2*sqrt(21*log(2)^2 + 30*log(2) + 25) + 6*log(2) + 10))/(sqrt(21*log(2)^2 + 30*log(2) + 25)*log(2)) - 1/24*(24*(log(log(2) ) + 1)*log(2) + 48*log(2)^2 + (5*x*(3*log(2) + 5) - 24*log(2))*log(-x^2*lo g(2) - 4*x*(3*log(2) + 5) + 48*log(2)) - 2*(5*x*(3*log(2) + 5) - 12*log(2) )*log(x))/(x*log(2))
Time = 0.19 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.36 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=-\frac {2 \, {\left (\log \left (2\right ) - 2\right )}}{x} + \frac {\log \left (-x^{2} \log \left (2\right ) - 12 \, x \log \left (2\right ) - 20 \, x + 48 \, \log \left (2\right )\right )}{x} - \frac {\log \left (x \log \left (2\right )\right )}{x} \] Input:
integrate((((-x^2-12*x+48)*log(2)-20*x)*log(1/4*((-x^2-12*x+48)*log(2)-20* x)/x/log(2))+(-3*x^2-48*x+240)*log(2)-80*x)/((x^4+12*x^3-48*x^2)*log(2)+20 *x^3),x, algorithm="giac")
Output:
-2*(log(2) - 2)/x + log(-x^2*log(2) - 12*x*log(2) - 20*x + 48*log(2))/x - log(x*log(2))/x
Time = 2.58 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {\ln \left (-\frac {5\,x+\frac {\ln \left (2\right )\,\left (x^2+12\,x-48\right )}{4}}{x\,\ln \left (2\right )}\right )+4}{x} \] Input:
int(-(80*x + log(2)*(48*x + 3*x^2 - 240) + log(-(5*x + (log(2)*(12*x + x^2 - 48))/4)/(x*log(2)))*(20*x + log(2)*(12*x + x^2 - 48)))/(log(2)*(12*x^3 - 48*x^2 + x^4) + 20*x^3),x)
Output:
(log(-(5*x + (log(2)*(12*x + x^2 - 48))/4)/(x*log(2))) + 4)/x
Time = 0.20 (sec) , antiderivative size = 176, normalized size of antiderivative = 5.33 \[ \int \frac {-80 x+\left (240-48 x-3 x^2\right ) \log (2)+\left (-20 x+\left (48-12 x-x^2\right ) \log (2)\right ) \log \left (\frac {-20 x+\left (48-12 x-x^2\right ) \log (2)}{4 x \log (2)}\right )}{20 x^3+\left (-48 x^2+12 x^3+x^4\right ) \log (2)} \, dx=\frac {3 \,\mathrm {log}\left (\mathrm {log}\left (2\right ) x^{2}+12 \,\mathrm {log}\left (2\right ) x -48 \,\mathrm {log}\left (2\right )+20 x \right ) \mathrm {log}\left (2\right ) x +5 \,\mathrm {log}\left (\mathrm {log}\left (2\right ) x^{2}+12 \,\mathrm {log}\left (2\right ) x -48 \,\mathrm {log}\left (2\right )+20 x \right ) x -3 \,\mathrm {log}\left (\frac {-\mathrm {log}\left (2\right ) x^{2}-12 \,\mathrm {log}\left (2\right ) x +48 \,\mathrm {log}\left (2\right )-20 x}{4 \,\mathrm {log}\left (2\right ) x}\right ) \mathrm {log}\left (2\right ) x +24 \,\mathrm {log}\left (\frac {-\mathrm {log}\left (2\right ) x^{2}-12 \,\mathrm {log}\left (2\right ) x +48 \,\mathrm {log}\left (2\right )-20 x}{4 \,\mathrm {log}\left (2\right ) x}\right ) \mathrm {log}\left (2\right )-5 \,\mathrm {log}\left (\frac {-\mathrm {log}\left (2\right ) x^{2}-12 \,\mathrm {log}\left (2\right ) x +48 \,\mathrm {log}\left (2\right )-20 x}{4 \,\mathrm {log}\left (2\right ) x}\right ) x -3 \,\mathrm {log}\left (x \right ) \mathrm {log}\left (2\right ) x -5 \,\mathrm {log}\left (x \right ) x +96 \,\mathrm {log}\left (2\right )}{24 \,\mathrm {log}\left (2\right ) x} \] Input:
int((((-x^2-12*x+48)*log(2)-20*x)*log(1/4*((-x^2-12*x+48)*log(2)-20*x)/x/l og(2))+(-3*x^2-48*x+240)*log(2)-80*x)/((x^4+12*x^3-48*x^2)*log(2)+20*x^3), x)
Output:
(3*log(log(2)*x**2 + 12*log(2)*x - 48*log(2) + 20*x)*log(2)*x + 5*log(log( 2)*x**2 + 12*log(2)*x - 48*log(2) + 20*x)*x - 3*log(( - log(2)*x**2 - 12*l og(2)*x + 48*log(2) - 20*x)/(4*log(2)*x))*log(2)*x + 24*log(( - log(2)*x** 2 - 12*log(2)*x + 48*log(2) - 20*x)/(4*log(2)*x))*log(2) - 5*log(( - log(2 )*x**2 - 12*log(2)*x + 48*log(2) - 20*x)/(4*log(2)*x))*x - 3*log(x)*log(2) *x - 5*log(x)*x + 96*log(2))/(24*log(2)*x)