Integrand size = 214, antiderivative size = 26 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=4-\left (3-\frac {1}{x}\right ) \left (-5+x+\log ^2\left (x+\frac {x}{(-1+x)^4}\right )\right ) \]
Time = 0.09 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.81 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=-\frac {5}{x}-3 x-\frac {(-1+3 x) \log ^2\left (\frac {x \left (2-4 x+6 x^2-4 x^3+x^4\right )}{(-1+x)^4}\right )}{x} \]
Integrate[(-10 + 30*x - 44*x^2 + 32*x^3 + 5*x^4 - 25*x^5 + 15*x^6 - 3*x^7 + (-4 + 16*x - 32*x^2 + 80*x^3 - 70*x^4 + 32*x^5 - 6*x^6)*Log[(2*x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)/(1 - 4*x + 6*x^2 - 4*x^3 + x^4)] + (2 - 6*x + 10*x ^2 - 10*x^3 + 5*x^4 - x^5)*Log[(2*x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)/(1 - 4* x + 6*x^2 - 4*x^3 + x^4)]^2)/(-2*x^2 + 6*x^3 - 10*x^4 + 10*x^5 - 5*x^6 + x ^7),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.
| \(\displaystyle \int \frac {-3 x^7+15 x^6-25 x^5+5 x^4+32 x^3-44 x^2+\left (-x^5+5 x^4-10 x^3+10 x^2-6 x+2\right ) \log ^2\left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+\left (-6 x^6+32 x^5-70 x^4+80 x^3-32 x^2+16 x-4\right ) \log \left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+30 x-10}{x^7-5 x^6+10 x^5-10 x^4+6 x^3-2 x^2} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-3 x^7+15 x^6-25 x^5+5 x^4+32 x^3-44 x^2+\left (-x^5+5 x^4-10 x^3+10 x^2-6 x+2\right ) \log ^2\left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+\left (-6 x^6+32 x^5-70 x^4+80 x^3-32 x^2+16 x-4\right ) \log \left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+30 x-10}{x^2 \left (x^5-5 x^4+10 x^3-10 x^2+6 x-2\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {-3 x^7+15 x^6-25 x^5+5 x^4+32 x^3-44 x^2+\left (-x^5+5 x^4-10 x^3+10 x^2-6 x+2\right ) \log ^2\left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+\left (-6 x^6+32 x^5-70 x^4+80 x^3-32 x^2+16 x-4\right ) \log \left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+30 x-10}{(x-1) x^2}-\frac {(x-1)^3 \left (-3 x^7+15 x^6-25 x^5+5 x^4+32 x^3-44 x^2+\left (-x^5+5 x^4-10 x^3+10 x^2-6 x+2\right ) \log ^2\left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+\left (-6 x^6+32 x^5-70 x^4+80 x^3-32 x^2+16 x-4\right ) \log \left (\frac {x^5-4 x^4+6 x^3-4 x^2+2 x}{x^4-4 x^3+6 x^2-4 x+1}\right )+30 x-10\right )}{x^2 \left (x^4-4 x^3+6 x^2-4 x+2\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {3 x^7-15 x^6+25 x^5-5 x^4-32 x^3+44 x^2+\left (x^5-5 x^4+10 x^3-10 x^2+6 x-2\right ) \log ^2\left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )+2 \left (3 x^6-16 x^5+35 x^4-40 x^3+16 x^2-8 x+2\right ) \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )-30 x+10}{(1-x) x^2 \left (x^4-4 x^3+6 x^2-4 x+2\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {15 x^4}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}-\frac {25 x^3}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}+\frac {5 x^2}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}+\frac {32 x}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}-\frac {44}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}+\frac {30}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right ) x}-\frac {10}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right ) x^2}-\frac {\log ^2\left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{x^2}-\frac {3 x^5}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right )}-\frac {2 (3 x-1) \left (x^5-5 x^4+10 x^3-10 x^2+2 x-2\right ) \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{(x-1) \left (x^4-4 x^3+6 x^2-4 x+2\right ) x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -96 \int \frac {\log (x-1)}{-x^4+4 x^3-6 x^2+4 x-2}dx-288 \int \frac {x \log (x-1)}{x^4-4 x^3+6 x^2-4 x+2}dx+288 \int \frac {x^2 \log (x-1)}{x^4-4 x^3+6 x^2-4 x+2}dx-96 \int \frac {x^3 \log (x-1)}{x^4-4 x^3+6 x^2-4 x+2}dx+24 \int \frac {\log (x)}{-x^4+4 x^3-6 x^2+4 x-2}dx+72 \int \frac {x \log (x)}{x^4-4 x^3+6 x^2-4 x+2}dx-72 \int \frac {x^2 \log (x)}{x^4-4 x^3+6 x^2-4 x+2}dx+24 \int \frac {x^3 \log (x)}{x^4-4 x^3+6 x^2-4 x+2}dx+24 \int \frac {\log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{x^4-4 x^3+6 x^2-4 x+2}dx-72 \int \frac {x \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{x^4-4 x^3+6 x^2-4 x+2}dx+72 \int \frac {x^2 \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{x^4-4 x^3+6 x^2-4 x+2}dx-24 \int \frac {x^3 \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(x-1)^4}\right )}{x^4-4 x^3+6 x^2-4 x+2}dx+\frac {\log ^2\left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(1-x)^4}\right )}{x}+24 \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(1-x)^4}\right ) \log (x-1)-6 \log (x) \log \left (\frac {x \left (x^4-4 x^3+6 x^2-4 x+2\right )}{(1-x)^4}\right )-3 x-\frac {5}{x}+48 \log ^2(x-1)+3 \log ^2(x)-24 \log (x) \log (x-1)\) |
Int[(-10 + 30*x - 44*x^2 + 32*x^3 + 5*x^4 - 25*x^5 + 15*x^6 - 3*x^7 + (-4 + 16*x - 32*x^2 + 80*x^3 - 70*x^4 + 32*x^5 - 6*x^6)*Log[(2*x - 4*x^2 + 6*x ^3 - 4*x^4 + x^5)/(1 - 4*x + 6*x^2 - 4*x^3 + x^4)] + (2 - 6*x + 10*x^2 - 1 0*x^3 + 5*x^4 - x^5)*Log[(2*x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)/(1 - 4*x + 6* x^2 - 4*x^3 + x^4)]^2)/(-2*x^2 + 6*x^3 - 10*x^4 + 10*x^5 - 5*x^6 + x^7),x]
3.7.1.3.1 Defintions of rubi rules used
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_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(106\) vs. \(2(26)=52\).
Time = 0.89 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.12
| method | result | size |
| norman | \(\frac {-5+\ln \left (\frac {x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x}{x^{4}-4 x^{3}+6 x^{2}-4 x +1}\right )^{2}-3 x^{2}-3 x \ln \left (\frac {x^{5}-4 x^{4}+6 x^{3}-4 x^{2}+2 x}{x^{4}-4 x^{3}+6 x^{2}-4 x +1}\right )^{2}}{x}\) | \(107\) |
int(((-x^5+5*x^4-10*x^3+10*x^2-6*x+2)*ln((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4- 4*x^3+6*x^2-4*x+1))^2+(-6*x^6+32*x^5-70*x^4+80*x^3-32*x^2+16*x-4)*ln((x^5- 4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))-3*x^7+15*x^6-25*x^5+5*x^4+ 32*x^3-44*x^2+30*x-10)/(x^7-5*x^6+10*x^5-10*x^4+6*x^3-2*x^2),x,method=_RET URNVERBOSE)
(-5+ln((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))^2-3*x^2-3*x*ln ((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))^2)/x
Leaf count of result is larger than twice the leaf count of optimal. 64 vs. \(2 (23) = 46\).
Time = 0.38 (sec) , antiderivative size = 64, normalized size of antiderivative = 2.46 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=-\frac {{\left (3 \, x - 1\right )} \log \left (\frac {x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x}{x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1}\right )^{2} + 3 \, x^{2} + 5}{x} \]
integrate(((-x^5+5*x^4-10*x^3+10*x^2-6*x+2)*log((x^5-4*x^4+6*x^3-4*x^2+2*x )/(x^4-4*x^3+6*x^2-4*x+1))^2+(-6*x^6+32*x^5-70*x^4+80*x^3-32*x^2+16*x-4)*l og((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))-3*x^7+15*x^6-25*x^ 5+5*x^4+32*x^3-44*x^2+30*x-10)/(x^7-5*x^6+10*x^5-10*x^4+6*x^3-2*x^2),x, al gorithm=\
-((3*x - 1)*log((x^5 - 4*x^4 + 6*x^3 - 4*x^2 + 2*x)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1))^2 + 3*x^2 + 5)/x
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (20) = 40\).
Time = 0.17 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.15 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=- 3 x + \frac {\left (1 - 3 x\right ) \log {\left (\frac {x^{5} - 4 x^{4} + 6 x^{3} - 4 x^{2} + 2 x}{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1} \right )}^{2}}{x} - \frac {5}{x} \]
integrate(((-x**5+5*x**4-10*x**3+10*x**2-6*x+2)*ln((x**5-4*x**4+6*x**3-4*x **2+2*x)/(x**4-4*x**3+6*x**2-4*x+1))**2+(-6*x**6+32*x**5-70*x**4+80*x**3-3 2*x**2+16*x-4)*ln((x**5-4*x**4+6*x**3-4*x**2+2*x)/(x**4-4*x**3+6*x**2-4*x+ 1))-3*x**7+15*x**6-25*x**5+5*x**4+32*x**3-44*x**2+30*x-10)/(x**7-5*x**6+10 *x**5-10*x**4+6*x**3-2*x**2),x)
-3*x + (1 - 3*x)*log((x**5 - 4*x**4 + 6*x**3 - 4*x**2 + 2*x)/(x**4 - 4*x** 3 + 6*x**2 - 4*x + 1))**2/x - 5/x
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (23) = 46\).
Time = 0.29 (sec) , antiderivative size = 117, normalized size of antiderivative = 4.50 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=-\frac {{\left (3 \, x - 1\right )} \log \left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 2\right )^{2} + 16 \, {\left (3 \, x - 1\right )} \log \left (x - 1\right )^{2} - 8 \, {\left (3 \, x - 1\right )} \log \left (x - 1\right ) \log \left (x\right ) + {\left (3 \, x - 1\right )} \log \left (x\right )^{2} + 3 \, x^{2} - 2 \, {\left (4 \, {\left (3 \, x - 1\right )} \log \left (x - 1\right ) - {\left (3 \, x - 1\right )} \log \left (x\right )\right )} \log \left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 2\right ) + 5}{x} \]
integrate(((-x^5+5*x^4-10*x^3+10*x^2-6*x+2)*log((x^5-4*x^4+6*x^3-4*x^2+2*x )/(x^4-4*x^3+6*x^2-4*x+1))^2+(-6*x^6+32*x^5-70*x^4+80*x^3-32*x^2+16*x-4)*l og((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))-3*x^7+15*x^6-25*x^ 5+5*x^4+32*x^3-44*x^2+30*x-10)/(x^7-5*x^6+10*x^5-10*x^4+6*x^3-2*x^2),x, al gorithm=\
-((3*x - 1)*log(x^4 - 4*x^3 + 6*x^2 - 4*x + 2)^2 + 16*(3*x - 1)*log(x - 1) ^2 - 8*(3*x - 1)*log(x - 1)*log(x) + (3*x - 1)*log(x)^2 + 3*x^2 - 2*(4*(3* x - 1)*log(x - 1) - (3*x - 1)*log(x))*log(x^4 - 4*x^3 + 6*x^2 - 4*x + 2) + 5)/x
\[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx=\int { -\frac {3 \, x^{7} - 15 \, x^{6} + 25 \, x^{5} - 5 \, x^{4} - 32 \, x^{3} + {\left (x^{5} - 5 \, x^{4} + 10 \, x^{3} - 10 \, x^{2} + 6 \, x - 2\right )} \log \left (\frac {x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x}{x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1}\right )^{2} + 44 \, x^{2} + 2 \, {\left (3 \, x^{6} - 16 \, x^{5} + 35 \, x^{4} - 40 \, x^{3} + 16 \, x^{2} - 8 \, x + 2\right )} \log \left (\frac {x^{5} - 4 \, x^{4} + 6 \, x^{3} - 4 \, x^{2} + 2 \, x}{x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1}\right ) - 30 \, x + 10}{x^{7} - 5 \, x^{6} + 10 \, x^{5} - 10 \, x^{4} + 6 \, x^{3} - 2 \, x^{2}} \,d x } \]
integrate(((-x^5+5*x^4-10*x^3+10*x^2-6*x+2)*log((x^5-4*x^4+6*x^3-4*x^2+2*x )/(x^4-4*x^3+6*x^2-4*x+1))^2+(-6*x^6+32*x^5-70*x^4+80*x^3-32*x^2+16*x-4)*l og((x^5-4*x^4+6*x^3-4*x^2+2*x)/(x^4-4*x^3+6*x^2-4*x+1))-3*x^7+15*x^6-25*x^ 5+5*x^4+32*x^3-44*x^2+30*x-10)/(x^7-5*x^6+10*x^5-10*x^4+6*x^3-2*x^2),x, al gorithm=\
integrate(-(3*x^7 - 15*x^6 + 25*x^5 - 5*x^4 - 32*x^3 + (x^5 - 5*x^4 + 10*x ^3 - 10*x^2 + 6*x - 2)*log((x^5 - 4*x^4 + 6*x^3 - 4*x^2 + 2*x)/(x^4 - 4*x^ 3 + 6*x^2 - 4*x + 1))^2 + 44*x^2 + 2*(3*x^6 - 16*x^5 + 35*x^4 - 40*x^3 + 1 6*x^2 - 8*x + 2)*log((x^5 - 4*x^4 + 6*x^3 - 4*x^2 + 2*x)/(x^4 - 4*x^3 + 6* x^2 - 4*x + 1)) - 30*x + 10)/(x^7 - 5*x^6 + 10*x^5 - 10*x^4 + 6*x^3 - 2*x^ 2), x)
Time = 12.14 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {-10+30 x-44 x^2+32 x^3+5 x^4-25 x^5+15 x^6-3 x^7+\left (-4+16 x-32 x^2+80 x^3-70 x^4+32 x^5-6 x^6\right ) \log \left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )+\left (2-6 x+10 x^2-10 x^3+5 x^4-x^5\right ) \log ^2\left (\frac {2 x-4 x^2+6 x^3-4 x^4+x^5}{1-4 x+6 x^2-4 x^3+x^4}\right )}{-2 x^2+6 x^3-10 x^4+10 x^5-5 x^6+x^7} \, dx={\ln \left (\frac {x^5-4\,x^4+6\,x^3-4\,x^2+2\,x}{x^4-4\,x^3+6\,x^2-4\,x+1}\right )}^2\,\left (\frac {1}{x}-3\right )-3\,x-\frac {5}{x} \]
int((log((2*x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)/(6*x^2 - 4*x - 4*x^3 + x^4 + 1))*(32*x^2 - 16*x - 80*x^3 + 70*x^4 - 32*x^5 + 6*x^6 + 4) - 30*x + log((2 *x - 4*x^2 + 6*x^3 - 4*x^4 + x^5)/(6*x^2 - 4*x - 4*x^3 + x^4 + 1))^2*(6*x - 10*x^2 + 10*x^3 - 5*x^4 + x^5 - 2) + 44*x^2 - 32*x^3 - 5*x^4 + 25*x^5 - 15*x^6 + 3*x^7 + 10)/(2*x^2 - 6*x^3 + 10*x^4 - 10*x^5 + 5*x^6 - x^7),x)