Integrand size = 237, antiderivative size = 33 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\frac {1}{3} x \log \left (\frac {4+e^9+x \left (-x+x^2\right )}{x+\log \left (\frac {x}{-2+x}\right )}\right ) \]
Time = 0.19 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.97 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\frac {1}{3} x \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right ) \]
Integrate[(8 + 8*x - 6*x^2 + 4*x^3 - 5*x^4 + 2*x^5 + E^9*(2 + 2*x - x^2) + (4*x^2 - 8*x^3 + 3*x^4)*Log[x/(-2 + x)] + (-8*x + 4*x^2 + 2*x^3 - 3*x^4 + x^5 + E^9*(-2*x + x^2) + (-8 + E^9*(-2 + x) + 4*x + 2*x^2 - 3*x^3 + x^4)* Log[x/(-2 + x)])*Log[(4 + E^9 - x^2 + x^3)/(x + Log[x/(-2 + x)])])/(-24*x + 12*x^2 + 6*x^3 - 9*x^4 + 3*x^5 + E^9*(-6*x + 3*x^2) + (-24 + 12*x + 6*x^ 2 - 9*x^3 + 3*x^4 + E^9*(-6 + 3*x))*Log[x/(-2 + x)]),x]
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.
| \(\displaystyle \int \frac {2 x^5-5 x^4+4 x^3-6 x^2+e^9 \left (-x^2+2 x+2\right )+\left (3 x^4-8 x^3+4 x^2\right ) \log \left (\frac {x}{x-2}\right )+\left (x^5-3 x^4+2 x^3+4 x^2+e^9 \left (x^2-2 x\right )+\left (x^4-3 x^3+2 x^2+4 x+e^9 (x-2)-8\right ) \log \left (\frac {x}{x-2}\right )-8 x\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )+8 x+8}{3 x^5-9 x^4+6 x^3+12 x^2+e^9 \left (3 x^2-6 x\right )+\left (3 x^4-9 x^3+6 x^2+12 x+e^9 (3 x-6)-24\right ) \log \left (\frac {x}{x-2}\right )-24 x} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-2 x^5+5 x^4-4 x^3+6 x^2-e^9 \left (-x^2+2 x+2\right )-\left (3 x^4-8 x^3+4 x^2\right ) \log \left (\frac {x}{x-2}\right )-\left (x^5-3 x^4+2 x^3+4 x^2+e^9 \left (x^2-2 x\right )+\left (x^4-3 x^3+2 x^2+4 x+e^9 (x-2)-8\right ) \log \left (\frac {x}{x-2}\right )-8 x\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )-8 x-8}{3 (2-x) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{3} \int -\frac {2 x^5-5 x^4+4 x^3-6 x^2+8 x+e^9 \left (-x^2+2 x+2\right )+\left (3 x^4-8 x^3+4 x^2\right ) \log \left (-\frac {x}{2-x}\right )-\left (-x^5+3 x^4-2 x^3-4 x^2+8 x+e^9 \left (2 x-x^2\right )+\left (-x^4+3 x^3-2 x^2-4 x+e^9 (2-x)+8\right ) \log \left (-\frac {x}{2-x}\right )\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (-\frac {x}{2-x}\right )}\right )+8}{(2-x) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (-\frac {x}{2-x}\right )\right )}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {1}{3} \int \frac {2 x^5-5 x^4+4 x^3-6 x^2+8 x+e^9 \left (-x^2+2 x+2\right )+\left (3 x^4-8 x^3+4 x^2\right ) \log \left (-\frac {x}{2-x}\right )-\left (-x^5+3 x^4-2 x^3-4 x^2+8 x+e^9 \left (2 x-x^2\right )+\left (-x^4+3 x^3-2 x^2-4 x+e^9 (2-x)+8\right ) \log \left (-\frac {x}{2-x}\right )\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (-\frac {x}{2-x}\right )}\right )+8}{(2-x) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (-\frac {x}{2-x}\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {2 x^5}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {5 x^4}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {4 x^3}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {(3 x-2) \log \left (\frac {x}{x-2}\right ) x^2}{\left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {6 x^2}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {8 x}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )+\frac {e^9 \left (x^2-2 x-2\right )}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {8}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -\frac {1}{3} \int \frac {2 x^5-5 x^4+4 x^3-6 \left (1+\frac {e^9}{6}\right ) x^2+(x-2) \left (x^3-x^2+e^9+4\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right ) x+8 \left (1+\frac {e^9}{4}\right ) x+(x-2) \log \left (\frac {x}{x-2}\right ) \left ((3 x-2) x^2+\left (x^3-x^2+e^9+4\right ) \log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )\right )+8 \left (1+\frac {e^9}{4}\right )}{(2-x) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {2 x^5}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {5 x^4}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {4 x^3}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {(3 x-2) \log \left (\frac {x}{x-2}\right ) x^2}{\left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {\left (6+e^9\right ) x^2}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {2 \left (4+e^9\right ) x}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )-\frac {2 \left (4+e^9\right )}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -\frac {1}{3} \int \left (-\frac {2 x^5}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {5 x^4}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {4 x^3}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {(3 x-2) \log \left (\frac {x}{x-2}\right ) x^2}{\left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}+\frac {\left (6+e^9\right ) x^2}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\frac {2 \left (4+e^9\right ) x}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}-\log \left (\frac {x^3-x^2+e^9+4}{x+\log \left (\frac {x}{x-2}\right )}\right )-\frac {2 \left (4+e^9\right )}{(x-2) \left (x^3-x^2+e^9+4\right ) \left (x+\log \left (\frac {x}{x-2}\right )\right )}\right )dx\) |
Int[(8 + 8*x - 6*x^2 + 4*x^3 - 5*x^4 + 2*x^5 + E^9*(2 + 2*x - x^2) + (4*x^ 2 - 8*x^3 + 3*x^4)*Log[x/(-2 + x)] + (-8*x + 4*x^2 + 2*x^3 - 3*x^4 + x^5 + E^9*(-2*x + x^2) + (-8 + E^9*(-2 + x) + 4*x + 2*x^2 - 3*x^3 + x^4)*Log[x/ (-2 + x)])*Log[(4 + E^9 - x^2 + x^3)/(x + Log[x/(-2 + x)])])/(-24*x + 12*x ^2 + 6*x^3 - 9*x^4 + 3*x^5 + E^9*(-6*x + 3*x^2) + (-24 + 12*x + 6*x^2 - 9* x^3 + 3*x^4 + E^9*(-6 + 3*x))*Log[x/(-2 + x)]),x]
3.28.23.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 24.94 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.91
| method | result | size |
| parallelrisch | \(\frac {\ln \left (\frac {{\mathrm e}^{9}+x^{3}-x^{2}+4}{\ln \left (\frac {x}{-2+x}\right )+x}\right ) x}{3}\) | \(30\) |
int(((((-2+x)*exp(9)+x^4-3*x^3+2*x^2+4*x-8)*ln(x/(-2+x))+(x^2-2*x)*exp(9)+ x^5-3*x^4+2*x^3+4*x^2-8*x)*ln((exp(9)+x^3-x^2+4)/(ln(x/(-2+x))+x))+(3*x^4- 8*x^3+4*x^2)*ln(x/(-2+x))+(-x^2+2*x+2)*exp(9)+2*x^5-5*x^4+4*x^3-6*x^2+8*x+ 8)/(((-6+3*x)*exp(9)+3*x^4-9*x^3+6*x^2+12*x-24)*ln(x/(-2+x))+(3*x^2-6*x)*e xp(9)+3*x^5-9*x^4+6*x^3+12*x^2-24*x),x,method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.88 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\frac {1}{3} \, x \log \left (\frac {x^{3} - x^{2} + e^{9} + 4}{x + \log \left (\frac {x}{x - 2}\right )}\right ) \]
integrate(((((-2+x)*exp(9)+x^4-3*x^3+2*x^2+4*x-8)*log(x/(-2+x))+(x^2-2*x)* exp(9)+x^5-3*x^4+2*x^3+4*x^2-8*x)*log((exp(9)+x^3-x^2+4)/(log(x/(-2+x))+x) )+(3*x^4-8*x^3+4*x^2)*log(x/(-2+x))+(-x^2+2*x+2)*exp(9)+2*x^5-5*x^4+4*x^3- 6*x^2+8*x+8)/(((-6+3*x)*exp(9)+3*x^4-9*x^3+6*x^2+12*x-24)*log(x/(-2+x))+(3 *x^2-6*x)*exp(9)+3*x^5-9*x^4+6*x^3+12*x^2-24*x),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (24) = 48\).
Time = 1.43 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.64 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\left (\frac {x}{3} - \frac {1}{30}\right ) \log {\left (\frac {x^{3} - x^{2} + 4 + e^{9}}{x + \log {\left (\frac {x}{x - 2} \right )}} \right )} - \frac {\log {\left (x + \log {\left (\frac {x}{x - 2} \right )} \right )}}{30} + \frac {\log {\left (x^{3} - x^{2} + 4 + e^{9} \right )}}{30} \]
integrate(((((-2+x)*exp(9)+x**4-3*x**3+2*x**2+4*x-8)*ln(x/(-2+x))+(x**2-2* x)*exp(9)+x**5-3*x**4+2*x**3+4*x**2-8*x)*ln((exp(9)+x**3-x**2+4)/(ln(x/(-2 +x))+x))+(3*x**4-8*x**3+4*x**2)*ln(x/(-2+x))+(-x**2+2*x+2)*exp(9)+2*x**5-5 *x**4+4*x**3-6*x**2+8*x+8)/(((-6+3*x)*exp(9)+3*x**4-9*x**3+6*x**2+12*x-24) *ln(x/(-2+x))+(3*x**2-6*x)*exp(9)+3*x**5-9*x**4+6*x**3+12*x**2-24*x),x)
(x/3 - 1/30)*log((x**3 - x**2 + 4 + exp(9))/(x + log(x/(x - 2)))) - log(x + log(x/(x - 2)))/30 + log(x**3 - x**2 + 4 + exp(9))/30
Time = 0.23 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.94 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\frac {1}{3} \, x \log \left (x^{3} - x^{2} + e^{9} + 4\right ) - \frac {1}{3} \, x \log \left (x - \log \left (x - 2\right ) + \log \left (x\right )\right ) \]
integrate(((((-2+x)*exp(9)+x^4-3*x^3+2*x^2+4*x-8)*log(x/(-2+x))+(x^2-2*x)* exp(9)+x^5-3*x^4+2*x^3+4*x^2-8*x)*log((exp(9)+x^3-x^2+4)/(log(x/(-2+x))+x) )+(3*x^4-8*x^3+4*x^2)*log(x/(-2+x))+(-x^2+2*x+2)*exp(9)+2*x^5-5*x^4+4*x^3- 6*x^2+8*x+8)/(((-6+3*x)*exp(9)+3*x^4-9*x^3+6*x^2+12*x-24)*log(x/(-2+x))+(3 *x^2-6*x)*exp(9)+3*x^5-9*x^4+6*x^3+12*x^2-24*x),x, algorithm=\
\[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\int { \frac {2 \, x^{5} - 5 \, x^{4} + 4 \, x^{3} - 6 \, x^{2} - {\left (x^{2} - 2 \, x - 2\right )} e^{9} + {\left (x^{5} - 3 \, x^{4} + 2 \, x^{3} + 4 \, x^{2} + {\left (x^{2} - 2 \, x\right )} e^{9} + {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2} + {\left (x - 2\right )} e^{9} + 4 \, x - 8\right )} \log \left (\frac {x}{x - 2}\right ) - 8 \, x\right )} \log \left (\frac {x^{3} - x^{2} + e^{9} + 4}{x + \log \left (\frac {x}{x - 2}\right )}\right ) + {\left (3 \, x^{4} - 8 \, x^{3} + 4 \, x^{2}\right )} \log \left (\frac {x}{x - 2}\right ) + 8 \, x + 8}{3 \, {\left (x^{5} - 3 \, x^{4} + 2 \, x^{3} + 4 \, x^{2} + {\left (x^{2} - 2 \, x\right )} e^{9} + {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2} + {\left (x - 2\right )} e^{9} + 4 \, x - 8\right )} \log \left (\frac {x}{x - 2}\right ) - 8 \, x\right )}} \,d x } \]
integrate(((((-2+x)*exp(9)+x^4-3*x^3+2*x^2+4*x-8)*log(x/(-2+x))+(x^2-2*x)* exp(9)+x^5-3*x^4+2*x^3+4*x^2-8*x)*log((exp(9)+x^3-x^2+4)/(log(x/(-2+x))+x) )+(3*x^4-8*x^3+4*x^2)*log(x/(-2+x))+(-x^2+2*x+2)*exp(9)+2*x^5-5*x^4+4*x^3- 6*x^2+8*x+8)/(((-6+3*x)*exp(9)+3*x^4-9*x^3+6*x^2+12*x-24)*log(x/(-2+x))+(3 *x^2-6*x)*exp(9)+3*x^5-9*x^4+6*x^3+12*x^2-24*x),x, algorithm=\
integrate(1/3*(2*x^5 - 5*x^4 + 4*x^3 - 6*x^2 - (x^2 - 2*x - 2)*e^9 + (x^5 - 3*x^4 + 2*x^3 + 4*x^2 + (x^2 - 2*x)*e^9 + (x^4 - 3*x^3 + 2*x^2 + (x - 2) *e^9 + 4*x - 8)*log(x/(x - 2)) - 8*x)*log((x^3 - x^2 + e^9 + 4)/(x + log(x /(x - 2)))) + (3*x^4 - 8*x^3 + 4*x^2)*log(x/(x - 2)) + 8*x + 8)/(x^5 - 3*x ^4 + 2*x^3 + 4*x^2 + (x^2 - 2*x)*e^9 + (x^4 - 3*x^3 + 2*x^2 + (x - 2)*e^9 + 4*x - 8)*log(x/(x - 2)) - 8*x), x)
Time = 11.96 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.88 \[ \int \frac {8+8 x-6 x^2+4 x^3-5 x^4+2 x^5+e^9 \left (2+2 x-x^2\right )+\left (4 x^2-8 x^3+3 x^4\right ) \log \left (\frac {x}{-2+x}\right )+\left (-8 x+4 x^2+2 x^3-3 x^4+x^5+e^9 \left (-2 x+x^2\right )+\left (-8+e^9 (-2+x)+4 x+2 x^2-3 x^3+x^4\right ) \log \left (\frac {x}{-2+x}\right )\right ) \log \left (\frac {4+e^9-x^2+x^3}{x+\log \left (\frac {x}{-2+x}\right )}\right )}{-24 x+12 x^2+6 x^3-9 x^4+3 x^5+e^9 \left (-6 x+3 x^2\right )+\left (-24+12 x+6 x^2-9 x^3+3 x^4+e^9 (-6+3 x)\right ) \log \left (\frac {x}{-2+x}\right )} \, dx=\frac {x\,\ln \left (\frac {x^3-x^2+{\mathrm {e}}^9+4}{x+\ln \left (\frac {x}{x-2}\right )}\right )}{3} \]
int((8*x + exp(9)*(2*x - x^2 + 2) + log((exp(9) - x^2 + x^3 + 4)/(x + log( x/(x - 2))))*(4*x^2 - exp(9)*(2*x - x^2) - 8*x + 2*x^3 - 3*x^4 + x^5 + log (x/(x - 2))*(4*x + exp(9)*(x - 2) + 2*x^2 - 3*x^3 + x^4 - 8)) - 6*x^2 + 4* x^3 - 5*x^4 + 2*x^5 + log(x/(x - 2))*(4*x^2 - 8*x^3 + 3*x^4) + 8)/(log(x/( x - 2))*(12*x + 6*x^2 - 9*x^3 + 3*x^4 + exp(9)*(3*x - 6) - 24) - exp(9)*(6 *x - 3*x^2) - 24*x + 12*x^2 + 6*x^3 - 9*x^4 + 3*x^5),x)