Integrand size = 177, antiderivative size = 38 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=1-\frac {x}{2-\log (2)}+\frac {\log \left (\frac {-4+x}{-x+x (x-2 (2+\log (x)))}\right )}{x} \] Output:
1+ln((-4+x)/(x*(x-2*ln(x)-4)-x))/x-x/(2-ln(2))
Time = 0.08 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.89 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x+\frac {(-2+\log (2)) \log \left (\frac {-4+x}{x (-5+x-2 \log (x))}\right )}{x}}{-2+\log (2)} \] Input:
Integrate[(-56 + 20*x - 22*x^2 + 9*x^3 - x^4 + (28 - 10*x + x^2)*Log[2] + (-16 - 8*x^2 + 2*x^3 + 8*Log[2])*Log[x] + (-40 + 18*x - 2*x^2 + (20 - 9*x + x^2)*Log[2] + (-16 + 4*x + (8 - 2*x)*Log[2])*Log[x])*Log[(4 - x)/(5*x - x^2 + 2*x*Log[x])])/(40*x^2 - 18*x^3 + 2*x^4 + (-20*x^2 + 9*x^3 - x^4)*Log [2] + (16*x^2 - 4*x^3 + (-8*x^2 + 2*x^3)*Log[2])*Log[x]),x]
Output:
(x + ((-2 + Log[2])*Log[(-4 + x)/(x*(-5 + x - 2*Log[x]))])/x)/(-2 + Log[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.
| \(\displaystyle \int \frac {-x^4+9 x^3-22 x^2+\left (-2 x^2+\left (x^2-9 x+20\right ) \log (2)+18 x+(4 x+(8-2 x) \log (2)-16) \log (x)-40\right ) \log \left (\frac {4-x}{-x^2+5 x+2 x \log (x)}\right )+\left (x^2-10 x+28\right ) \log (2)+\left (2 x^3-8 x^2-16+8 \log (2)\right ) \log (x)+20 x-56}{2 x^4-18 x^3+40 x^2+\left (-4 x^3+16 x^2+\left (2 x^3-8 x^2\right ) \log (2)\right ) \log (x)+\left (-x^4+9 x^3-20 x^2\right ) \log (2)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-x^4+9 x^3-22 x^2+\left (-2 x^2+\left (x^2-9 x+20\right ) \log (2)+18 x+(4 x+(8-2 x) \log (2)-16) \log (x)-40\right ) \log \left (\frac {4-x}{-x^2+5 x+2 x \log (x)}\right )+\left (x^2-10 x+28\right ) \log (2)+\left (2 x^3-8 x^2-16+8 \log (2)\right ) \log (x)+20 x-56}{(4-x) x^2 (2-\log (2)) (-x+2 \log (x)+5)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {x^4-9 x^3+22 x^2-20 x+2 \left (-x^3+4 x^2+4 (2-\log (2))\right ) \log (x)+\left (2 x^2-18 x+2 (-\log (2) (4-x)-2 x+8) \log (x)-\left (x^2-9 x+20\right ) \log (2)+40\right ) \log \left (\frac {4-x}{-x^2+2 \log (x) x+5 x}\right )-\left (x^2-10 x+28\right ) \log (2)+56}{(4-x) x^2 (-x+2 \log (x)+5)}dx}{2-\log (2)}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {x^4-9 x^3+22 x^2-20 x+2 \left (-x^3+4 x^2+4 (2-\log (2))\right ) \log (x)+\left (2 x^2-18 x+2 (-\log (2) (4-x)-2 x+8) \log (x)-\left (x^2-9 x+20\right ) \log (2)+40\right ) \log \left (\frac {4-x}{-x^2+2 \log (x) x+5 x}\right )-\left (x^2-10 x+28\right ) \log (2)+56}{(4-x) x^2 (-x+2 \log (x)+5)}dx}{2-\log (2)}\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {\int \left (\frac {x^2}{(x-4) (x-2 \log (x)-5)}-\frac {9 x}{(x-4) (x-2 \log (x)-5)}+\frac {22}{(x-4) (x-2 \log (x)-5)}-\frac {20}{(x-4) (x-2 \log (x)-5) x}-\frac {2 \left (x^3-4 x^2+\log (16)-8\right ) \log (x)}{(x-4) (x-2 \log (x)-5) x^2}-\frac {(-2+\log (2)) \log \left (\frac {x-4}{x (x-2 \log (x)-5)}\right )}{x^2}+\frac {56}{(x-4) (x-2 \log (x)-5) x^2}-\frac {\left (x^2-10 x+28\right ) \log (2)}{(x-4) (x-2 \log (x)-5) x^2}\right )dx}{2-\log (2)}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {\frac {5}{4} (8-\log (16)) \int \frac {1}{x^2 (x-2 \log (x)-5)}dx+7 \log (2) \int \frac {1}{x^2 (x-2 \log (x)-5)}dx+2 (2-\log (2)) \int \frac {1}{x^2 (x-2 \log (x)-5)}dx-14 \int \frac {1}{x^2 (x-2 \log (x)-5)}dx-\frac {1}{16} (8-\log (16)) \int \frac {1}{(x-4) (x-2 \log (x)-5)}dx-\frac {1}{4} \log (2) \int \frac {1}{(x-4) (x-2 \log (x)-5)}dx+\frac {1}{2} \int \frac {1}{(x-4) (x-2 \log (x)-5)}dx+\frac {1}{16} (8-\log (16)) \int \frac {1}{x (x-2 \log (x)-5)}dx-\frac {3}{4} \log (2) \int \frac {1}{x (x-2 \log (x)-5)}dx-(2-\log (2)) \int \frac {1}{x (x-2 \log (x)-5)}dx+\frac {3}{2} \int \frac {1}{x (x-2 \log (x)-5)}dx+x-\frac {1}{16} (8-\log (16)) \log (4-x)+\frac {1}{4} (2-\log (2)) \log (4-x)+\frac {1}{16} (8-\log (16)) \log (x)-\frac {1}{4} (2-\log (2)) \log (x)-\frac {(2-\log (2)) \log \left (\frac {4-x}{x (-x+2 \log (x)+5)}\right )}{x}-\frac {8-\log (16)}{4 x}+\frac {2-\log (2)}{x}}{2-\log (2)}\) |
Input:
Int[(-56 + 20*x - 22*x^2 + 9*x^3 - x^4 + (28 - 10*x + x^2)*Log[2] + (-16 - 8*x^2 + 2*x^3 + 8*Log[2])*Log[x] + (-40 + 18*x - 2*x^2 + (20 - 9*x + x^2) *Log[2] + (-16 + 4*x + (8 - 2*x)*Log[2])*Log[x])*Log[(4 - x)/(5*x - x^2 + 2*x*Log[x])])/(40*x^2 - 18*x^3 + 2*x^4 + (-20*x^2 + 9*x^3 - x^4)*Log[2] + (16*x^2 - 4*x^3 + (-8*x^2 + 2*x^3)*Log[2])*Log[x]),x]
Output:
$Aborted
Time = 2.57 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.76
| method | result | size |
| parallelrisch | \(\frac {4 \ln \left (2\right ) \ln \left (-\frac {x -4}{x \left (2 \ln \left (x \right )-x +5\right )}\right )+4 x^{2}+32 x -8 \ln \left (-\frac {x -4}{x \left (2 \ln \left (x \right )-x +5\right )}\right )}{4 x \left (\ln \left (2\right )-2\right )}\) | \(67\) |
| risch | \(-\frac {\ln \left (-2 \ln \left (x \right )+x -5\right )}{x}+\frac {2 i \pi \,\operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{2}-2 i \pi \,\operatorname {csgn}\left (i \left (x -4\right )\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{2}+i \ln \left (2\right ) \pi \,\operatorname {csgn}\left (i \left (x -4\right )\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{2}+2 i \pi \,\operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right ) \operatorname {csgn}\left (\frac {i}{x}\right )-i \ln \left (2\right ) \pi \,\operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{2}-i \ln \left (2\right ) \pi \,\operatorname {csgn}\left (\frac {i}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{2}-i \ln \left (2\right ) \pi \,\operatorname {csgn}\left (i \left (x -4\right )\right ) \operatorname {csgn}\left (\frac {i}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )-2 i \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{2} \operatorname {csgn}\left (\frac {i}{x}\right )+2 i \pi \,\operatorname {csgn}\left (i \left (x -4\right )\right ) \operatorname {csgn}\left (\frac {i}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )+i \ln \left (2\right ) \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{2} \operatorname {csgn}\left (\frac {i}{x}\right )+i \ln \left (2\right ) \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{3}-2 i \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{3}-2 i \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right )^{3}-i \ln \left (2\right ) \pi \,\operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{x \left (2 \ln \left (x \right )-x +5\right )}\right ) \operatorname {csgn}\left (\frac {i}{x}\right )+i \ln \left (2\right ) \pi \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{3}+2 i \pi \,\operatorname {csgn}\left (\frac {i}{2 \ln \left (x \right )-x +5}\right ) \operatorname {csgn}\left (\frac {i \left (x -4\right )}{2 \ln \left (x \right )-x +5}\right )^{2}-2 \ln \left (2\right ) \ln \left (x \right )+2 \ln \left (2\right ) \ln \left (x -4\right )+2 x^{2}+4 \ln \left (x \right )-4 \ln \left (x -4\right )}{2 \left (\ln \left (2\right )-2\right ) x}\) | \(660\) |
Input:
int(((((-2*x+8)*ln(2)+4*x-16)*ln(x)+(x^2-9*x+20)*ln(2)-2*x^2+18*x-40)*ln(( -x+4)/(2*x*ln(x)-x^2+5*x))+(8*ln(2)+2*x^3-8*x^2-16)*ln(x)+(x^2-10*x+28)*ln (2)-x^4+9*x^3-22*x^2+20*x-56)/(((2*x^3-8*x^2)*ln(2)-4*x^3+16*x^2)*ln(x)+(- x^4+9*x^3-20*x^2)*ln(2)+2*x^4-18*x^3+40*x^2),x,method=_RETURNVERBOSE)
Output:
1/4/x*(4*ln(2)*ln(-(x-4)/x/(2*ln(x)-x+5))+4*x^2+32*x-8*ln(-(x-4)/x/(2*ln(x )-x+5)))/(ln(2)-2)
Time = 0.07 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.03 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x^{2} + {\left (\log \left (2\right ) - 2\right )} \log \left (\frac {x - 4}{x^{2} - 2 \, x \log \left (x\right ) - 5 \, x}\right )}{x \log \left (2\right ) - 2 \, x} \] Input:
integrate(((((-2*x+8)*log(2)+4*x-16)*log(x)+(x^2-9*x+20)*log(2)-2*x^2+18*x -40)*log((-x+4)/(2*x*log(x)-x^2+5*x))+(8*log(2)+2*x^3-8*x^2-16)*log(x)+(x^ 2-10*x+28)*log(2)-x^4+9*x^3-22*x^2+20*x-56)/(((2*x^3-8*x^2)*log(2)-4*x^3+1 6*x^2)*log(x)+(-x^4+9*x^3-20*x^2)*log(2)+2*x^4-18*x^3+40*x^2),x, algorithm ="fricas")
Output:
(x^2 + (log(2) - 2)*log((x - 4)/(x^2 - 2*x*log(x) - 5*x)))/(x*log(2) - 2*x )
Time = 0.33 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.68 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x}{-2 + \log {\left (2 \right )}} + \frac {\log {\left (\frac {4 - x}{- x^{2} + 2 x \log {\left (x \right )} + 5 x} \right )}}{x} \] Input:
integrate(((((-2*x+8)*ln(2)+4*x-16)*ln(x)+(x**2-9*x+20)*ln(2)-2*x**2+18*x- 40)*ln((-x+4)/(2*x*ln(x)-x**2+5*x))+(8*ln(2)+2*x**3-8*x**2-16)*ln(x)+(x**2 -10*x+28)*ln(2)-x**4+9*x**3-22*x**2+20*x-56)/(((2*x**3-8*x**2)*ln(2)-4*x** 3+16*x**2)*ln(x)+(-x**4+9*x**3-20*x**2)*ln(2)+2*x**4-18*x**3+40*x**2),x)
Output:
x/(-2 + log(2)) + log((4 - x)/(-x**2 + 2*x*log(x) + 5*x))/x
Time = 0.17 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.18 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x^{2} - {\left (\log \left (2\right ) - 2\right )} \log \left (x - 2 \, \log \left (x\right ) - 5\right ) + {\left (\log \left (2\right ) - 2\right )} \log \left (x - 4\right ) - {\left (\log \left (2\right ) - 2\right )} \log \left (x\right )}{x {\left (\log \left (2\right ) - 2\right )}} \] Input:
integrate(((((-2*x+8)*log(2)+4*x-16)*log(x)+(x^2-9*x+20)*log(2)-2*x^2+18*x -40)*log((-x+4)/(2*x*log(x)-x^2+5*x))+(8*log(2)+2*x^3-8*x^2-16)*log(x)+(x^ 2-10*x+28)*log(2)-x^4+9*x^3-22*x^2+20*x-56)/(((2*x^3-8*x^2)*log(2)-4*x^3+1 6*x^2)*log(x)+(-x^4+9*x^3-20*x^2)*log(2)+2*x^4-18*x^3+40*x^2),x, algorithm ="maxima")
Output:
(x^2 - (log(2) - 2)*log(x - 2*log(x) - 5) + (log(2) - 2)*log(x - 4) - (log (2) - 2)*log(x))/(x*(log(2) - 2))
Time = 0.21 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.97 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x}{\log \left (2\right ) - 2} - \frac {\log \left (x - 2 \, \log \left (x\right ) - 5\right )}{x} + \frac {\log \left (x - 4\right )}{x} - \frac {\log \left (x\right )}{x} \] Input:
integrate(((((-2*x+8)*log(2)+4*x-16)*log(x)+(x^2-9*x+20)*log(2)-2*x^2+18*x -40)*log((-x+4)/(2*x*log(x)-x^2+5*x))+(8*log(2)+2*x^3-8*x^2-16)*log(x)+(x^ 2-10*x+28)*log(2)-x^4+9*x^3-22*x^2+20*x-56)/(((2*x^3-8*x^2)*log(2)-4*x^3+1 6*x^2)*log(x)+(-x^4+9*x^3-20*x^2)*log(2)+2*x^4-18*x^3+40*x^2),x, algorithm ="giac")
Output:
x/(log(2) - 2) - log(x - 2*log(x) - 5)/x + log(x - 4)/x - log(x)/x
Time = 2.53 (sec) , antiderivative size = 35, normalized size of antiderivative = 0.92 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {x}{\ln \left (2\right )-2}+\frac {\ln \left (-\frac {x-4}{5\,x+2\,x\,\ln \left (x\right )-x^2}\right )}{x} \] Input:
int(-(20*x - log(-(x - 4)/(5*x + 2*x*log(x) - x^2))*(log(x)*(log(2)*(2*x - 8) - 4*x + 16) - 18*x + 2*x^2 - log(2)*(x^2 - 9*x + 20) + 40) - 22*x^2 + 9*x^3 - x^4 + log(2)*(x^2 - 10*x + 28) + log(x)*(8*log(2) - 8*x^2 + 2*x^3 - 16) - 56)/(log(2)*(20*x^2 - 9*x^3 + x^4) + log(x)*(log(2)*(8*x^2 - 2*x^3 ) - 16*x^2 + 4*x^3) - 40*x^2 + 18*x^3 - 2*x^4),x)
Output:
x/(log(2) - 2) + log(-(x - 4)/(5*x + 2*x*log(x) - x^2))/x
Time = 0.19 (sec) , antiderivative size = 65, normalized size of antiderivative = 1.71 \[ \int \frac {-56+20 x-22 x^2+9 x^3-x^4+\left (28-10 x+x^2\right ) \log (2)+\left (-16-8 x^2+2 x^3+8 \log (2)\right ) \log (x)+\left (-40+18 x-2 x^2+\left (20-9 x+x^2\right ) \log (2)+(-16+4 x+(8-2 x) \log (2)) \log (x)\right ) \log \left (\frac {4-x}{5 x-x^2+2 x \log (x)}\right )}{40 x^2-18 x^3+2 x^4+\left (-20 x^2+9 x^3-x^4\right ) \log (2)+\left (16 x^2-4 x^3+\left (-8 x^2+2 x^3\right ) \log (2)\right ) \log (x)} \, dx=\frac {\mathrm {log}\left (\frac {-x +4}{2 \,\mathrm {log}\left (x \right ) x -x^{2}+5 x}\right ) \mathrm {log}\left (2\right )-2 \,\mathrm {log}\left (\frac {-x +4}{2 \,\mathrm {log}\left (x \right ) x -x^{2}+5 x}\right )+x^{2}}{x \left (\mathrm {log}\left (2\right )-2\right )} \] Input:
int(((((-2*x+8)*log(2)+4*x-16)*log(x)+(x^2-9*x+20)*log(2)-2*x^2+18*x-40)*l og((-x+4)/(2*x*log(x)-x^2+5*x))+(8*log(2)+2*x^3-8*x^2-16)*log(x)+(x^2-10*x +28)*log(2)-x^4+9*x^3-22*x^2+20*x-56)/(((2*x^3-8*x^2)*log(2)-4*x^3+16*x^2) *log(x)+(-x^4+9*x^3-20*x^2)*log(2)+2*x^4-18*x^3+40*x^2),x)
Output:
(log(( - x + 4)/(2*log(x)*x - x**2 + 5*x))*log(2) - 2*log(( - x + 4)/(2*lo g(x)*x - x**2 + 5*x)) + x**2)/(x*(log(2) - 2))