3.42.0 ∫ −80x2+80x3−23x4+2x5+(50−20x+2x2) log(x)+(−25+10x−x2) log2(x) −80x3+56x4−13x5+x6+(25x−10x2+x3) log2(x) dx [4146]

Integrand size = 88, antiderivative size = 25 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=\log \left (-\frac {x}{5-x}+(-3+x) x+\frac {\log ^2(x)}{x}\right ) \]

Rubi [F]

\[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=\int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx \]

Rubi steps \begin{align*} \text {integral}& = \int \frac {80 x^2-80 x^3+23 x^4-2 x^5-\left (50-20 x+2 x^2\right ) \log (x)-\left (-25+10 x-x^2\right ) \log ^2(x)}{(5-x) x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx \\ & = \int \left (-\frac {1}{x}+\frac {-160 x^2+136 x^3-36 x^4+3 x^5+50 \log (x)-20 x \log (x)+2 x^2 \log (x)}{(-5+x) x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}\right ) \, dx \\ & = -\log (x)+\int \frac {-160 x^2+136 x^3-36 x^4+3 x^5+50 \log (x)-20 x \log (x)+2 x^2 \log (x)}{(-5+x) x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx \\ & = -\log (x)+\int \left (\frac {160 x^2-136 x^3+36 x^4-3 x^5-50 \log (x)+20 x \log (x)-2 x^2 \log (x)}{5 x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {-160 x^2+136 x^3-36 x^4+3 x^5+50 \log (x)-20 x \log (x)+2 x^2 \log (x)}{5 (-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}\right ) \, dx \\ & = -\log (x)+\frac {1}{5} \int \frac {160 x^2-136 x^3+36 x^4-3 x^5-50 \log (x)+20 x \log (x)-2 x^2 \log (x)}{x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+\frac {1}{5} \int \frac {-160 x^2+136 x^3-36 x^4+3 x^5+50 \log (x)-20 x \log (x)+2 x^2 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx \\ & = -\log (x)+\frac {1}{5} \int \frac {x^2 \left (160-136 x+36 x^2-3 x^3\right )-2 (-5+x)^2 \log (x)}{(-4+x)^2 x^3+(-5+x) x \log ^2(x)} \, dx+\frac {1}{5} \int \left (-\frac {160 x^2}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {136 x^3}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}-\frac {36 x^4}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {3 x^5}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {50 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}-\frac {20 x \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {2 x^2 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}\right ) \, dx \\ & = -\log (x)+\frac {1}{5} \int \left (\frac {160 x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}-\frac {136 x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {36 x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}-\frac {3 x^4}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {20 \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}-\frac {50 \log (x)}{x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}-\frac {2 x \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx+\frac {2}{5} \int \frac {x^2 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+\frac {3}{5} \int \frac {x^5}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-4 \int \frac {x \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-\frac {36}{5} \int \frac {x^4}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+10 \int \frac {\log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+\frac {136}{5} \int \frac {x^3}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-32 \int \frac {x^2}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx \\ & = -\log (x)+\frac {2}{5} \int \frac {x^2 \log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-\frac {2}{5} \int \frac {x \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+\frac {3}{5} \int \frac {x^5}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-\frac {3}{5} \int \frac {x^4}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-4 \int \frac {x \log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx+4 \int \frac {\log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-\frac {36}{5} \int \frac {x^4}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx+\frac {36}{5} \int \frac {x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+10 \int \frac {\log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-10 \int \frac {\log (x)}{x \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+\frac {136}{5} \int \frac {x^3}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-\frac {136}{5} \int \frac {x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-32 \int \frac {x^2}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx+32 \int \frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx \\ & = -\log (x)-\frac {2}{5} \int \frac {x \log (x)}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {2}{5} \int \left (\frac {5 \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {25 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {x \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx-\frac {3}{5} \int \frac {x^4}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {3}{5} \int \left (\frac {625}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {3125}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {125 x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {25 x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {5 x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {x^4}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx+4 \int \frac {\log (x)}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-4 \int \left (\frac {\log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {5 \log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}\right ) \, dx+\frac {36}{5} \int \frac {x^3}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-\frac {36}{5} \int \left (\frac {125}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {625}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {25 x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {5 x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx+10 \int \frac {\log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-10 \int \frac {\log (x)}{(-4+x)^2 x^3+(-5+x) x \log ^2(x)} \, dx-\frac {136}{5} \int \frac {x^2}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {136}{5} \int \left (\frac {25}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {125}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {5 x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx+32 \int \frac {x}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-32 \int \left (\frac {5}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}+\frac {25}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )}+\frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)}\right ) \, dx \\ & = -\log (x)-\frac {2}{5} \int \frac {x \log (x)}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {2}{5} \int \frac {x \log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-\frac {3}{5} \int \frac {x^4}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {3}{5} \int \frac {x^4}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+2 \int \frac {\log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+3 \int \frac {x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+4 \int \frac {\log (x)}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-4 \int \frac {\log (x)}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+\frac {36}{5} \int \frac {x^3}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-\frac {36}{5} \int \frac {x^3}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+10 \int \frac {\log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx+10 \int \frac {\log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-10 \int \frac {\log (x)}{(-4+x)^2 x^3+(-5+x) x \log ^2(x)} \, dx+15 \int \frac {x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-20 \int \frac {\log (x)}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-\frac {136}{5} \int \frac {x^2}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+\frac {136}{5} \int \frac {x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+32 \int \frac {x}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-32 \int \frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-36 \int \frac {x^2}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+75 \int \frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+136 \int \frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-160 \int \frac {1}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-180 \int \frac {x}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+375 \int \frac {1}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+680 \int \frac {1}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx-800 \int \frac {1}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-900 \int \frac {1}{16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)} \, dx+1875 \int \frac {1}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx+3400 \int \frac {1}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx-4500 \int \frac {1}{(-5+x) \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right )} \, dx \\ & = -\log (x)+2 \int \frac {\log (x)}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+3 \int \frac {x^3}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+2 \left (10 \int \frac {\log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx\right )-10 \int \frac {\log (x)}{(-4+x)^2 x^3+(-5+x) x \log ^2(x)} \, dx+15 \int \frac {x^2}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-20 \int \frac {\log (x)}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-36 \int \frac {x^2}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+75 \int \frac {x}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+136 \int \frac {x}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-160 \int \frac {1}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-180 \int \frac {x}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+375 \int \frac {1}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+680 \int \frac {1}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx-800 \int \frac {1}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-900 \int \frac {1}{(-4+x)^2 x^2+(-5+x) \log ^2(x)} \, dx+1875 \int \frac {1}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx+3400 \int \frac {1}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx-4500 \int \frac {1}{(-5+x) \left ((-4+x)^2 x^2+(-5+x) \log ^2(x)\right )} \, dx \\ \end{align*}

Mathematica [A] (veriﬁed)

Time = 0.30 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.60 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=-\log (5-x)-\log (x)+\log \left (16 x^2-8 x^3+x^4-5 \log ^2(x)+x \log ^2(x)\right ) \]

Maple [A] (veriﬁed)

Time = 2.60 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16


method	result	size

risch	\(-\ln \left (x \right )+\ln \left (\ln \left (x \right )^{2}+\frac {x^{2} \left (x^{2}-8 x +16\right )}{-5+x}\right )\)	\(29\)
default	\(-\ln \left (x \right )+\ln \left (x^{4}+x \ln \left (x \right )^{2}-8 x^{3}-5 \ln \left (x \right )^{2}+16 x^{2}\right )-\ln \left (-5+x \right )\)	\(39\)
norman	\(-\ln \left (x \right )+\ln \left (x^{4}+x \ln \left (x \right )^{2}-8 x^{3}-5 \ln \left (x \right )^{2}+16 x^{2}\right )-\ln \left (-5+x \right )\)	\(39\)
parallelrisch	\(-\ln \left (x \right )+\ln \left (x^{4}+x \ln \left (x \right )^{2}-8 x^{3}-5 \ln \left (x \right )^{2}+16 x^{2}\right )-\ln \left (-5+x \right )\)	\(39\)

Fricas [A] (veriﬁcation not implemented)

Time = 0.24 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.36 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=-\log \left (x\right ) + \log \left (\frac {x^{4} - 8 \, x^{3} + {\left (x - 5\right )} \log \left (x\right )^{2} + 16 \, x^{2}}{x - 5}\right ) \]

Sympy [A] (veriﬁcation not implemented)

Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.04 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=- \log {\left (x \right )} + \log {\left (\log {\left (x \right )}^{2} + \frac {x^{4} - 8 x^{3} + 16 x^{2}}{x - 5} \right )} \]

Maxima [A] (veriﬁcation not implemented)

Time = 0.23 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.36 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=-\log \left (x\right ) + \log \left (\frac {x^{4} - 8 \, x^{3} + {\left (x - 5\right )} \log \left (x\right )^{2} + 16 \, x^{2}}{x - 5}\right ) \]

Giac [A] (veriﬁcation not implemented)

Time = 0.29 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.52 \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=\log \left (x^{4} - 8 \, x^{3} + x \log \left (x\right )^{2} + 16 \, x^{2} - 5 \, \log \left (x\right )^{2}\right ) - \log \left (x - 5\right ) - \log \left (x\right ) \]

Mupad [F(-1)]

Timed out. \[ \int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+\left (50-20 x+2 x^2\right ) \log (x)+\left (-25+10 x-x^2\right ) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+\left (25 x-10 x^2+x^3\right ) \log ^2(x)} \, dx=\int \frac {\ln \left (x\right )\,\left (2\,x^2-20\,x+50\right )-{\ln \left (x\right )}^2\,\left (x^2-10\,x+25\right )-80\,x^2+80\,x^3-23\,x^4+2\,x^5}{56\,x^4-80\,x^3-13\,x^5+x^6+{\ln \left (x\right )}^2\,\left (x^3-10\,x^2+25\,x\right )} \,d x \]

\(\int \frac {-80 x^2+80 x^3-23 x^4+2 x^5+(50-20 x+2 x^2) \log (x)+(-25+10 x-x^2) \log ^2(x)}{-80 x^3+56 x^4-13 x^5+x^6+(25 x-10 x^2+x^3) \log ^2(x)} \, dx\) [4146]

Optimal result