Integrand size = 504, antiderivative size = 33 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=x^2+\frac {4}{\log \left ((-1+x)^2\right )+\frac {-x+\log (x)}{\log (x)-\log (3+x)}} \]
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\[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=\int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (-x \left (6-6 x-3 x^3+2 x^4+x^5\right )-x (3+x) \left (-4-x+x^2+2 (-1+x) x \log \left ((-1+x)^2\right )+(-1+x) x \log ^2\left ((-1+x)^2\right )\right ) \log ^2(x)-2 \left (-3+2 x+x^2\right ) \left (1-x+x^3 \log \left ((-1+x)^2\right )\right ) \log (3+x)-x (3+x) \left (-4+(-1+x) x \log ^2\left ((-1+x)^2\right )\right ) \log ^2(3+x)+2 x \log (x) \left (2-x-4 x^2+2 x^3+x^4-12 \log (3+x)-4 x \log (3+x)+x \left (-3+2 x+x^2\right ) \log ^2\left ((-1+x)^2\right ) \log (3+x)+x \left (-3+2 x+x^2\right ) \log \left ((-1+x)^2\right ) (x+\log (3+x))\right )\right )}{x \left (3-2 x-x^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx \\ & = 2 \int \frac {-x \left (6-6 x-3 x^3+2 x^4+x^5\right )-x (3+x) \left (-4-x+x^2+2 (-1+x) x \log \left ((-1+x)^2\right )+(-1+x) x \log ^2\left ((-1+x)^2\right )\right ) \log ^2(x)-2 \left (-3+2 x+x^2\right ) \left (1-x+x^3 \log \left ((-1+x)^2\right )\right ) \log (3+x)-x (3+x) \left (-4+(-1+x) x \log ^2\left ((-1+x)^2\right )\right ) \log ^2(3+x)+2 x \log (x) \left (2-x-4 x^2+2 x^3+x^4-12 \log (3+x)-4 x \log (3+x)+x \left (-3+2 x+x^2\right ) \log ^2\left ((-1+x)^2\right ) \log (3+x)+x \left (-3+2 x+x^2\right ) \log \left ((-1+x)^2\right ) (x+\log (3+x))\right )}{x \left (3-2 x-x^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx \\ & = 2 \int \left (\frac {-4-x \log ^2\left ((-1+x)^2\right )+x^2 \log ^2\left ((-1+x)^2\right )}{(-1+x) \log ^2\left ((-1+x)^2\right )}+\frac {2 (x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{(-1+x) x (3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2}-\frac {2 \left (-4 x^2+\log \left ((-1+x)^2\right )-2 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+4 x \log (x)\right )}{(-1+x) x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}\right ) \, dx \\ & = 2 \int \frac {-4-x \log ^2\left ((-1+x)^2\right )+x^2 \log ^2\left ((-1+x)^2\right )}{(-1+x) \log ^2\left ((-1+x)^2\right )} \, dx+4 \int \frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{(-1+x) x (3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-4 \int \frac {-4 x^2+\log \left ((-1+x)^2\right )-2 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+4 x \log (x)}{(-1+x) x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx \\ & = 2 \int \left (x-\frac {4}{(-1+x) \log ^2\left ((-1+x)^2\right )}\right ) \, dx+4 \int \frac {\left ((-1+x)^2 (3+x) \log \left ((-1+x)^2\right )-3 (-1+x) \log ^2\left ((-1+x)^2\right )-2 x (3+x) (x-\log (x))\right ) (-x+\log (x))}{(1-x) x (3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-4 \int \left (\frac {4 x^2-\log \left ((-1+x)^2\right )+2 x \log \left ((-1+x)^2\right )-x^2 \log \left ((-1+x)^2\right )-4 x \log (x)}{x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {-4 x^2+\log \left ((-1+x)^2\right )-2 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+4 x \log (x)}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}\right ) \, dx \\ & = x^2-4 \int \frac {4 x^2-\log \left ((-1+x)^2\right )+2 x \log \left ((-1+x)^2\right )-x^2 \log \left ((-1+x)^2\right )-4 x \log (x)}{x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx-4 \int \frac {-4 x^2+\log \left ((-1+x)^2\right )-2 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+4 x \log (x)}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx+4 \int \left (\frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{4 (-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2}-\frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{3 x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2}+\frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{12 (3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2}\right ) \, dx-8 \int \frac {1}{(-1+x) \log ^2\left ((-1+x)^2\right )} \, dx \\ & = x^2+\frac {1}{3} \int \frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{(3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-\frac {4}{3} \int \frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{x \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-4 \int \frac {-(-1+x)^2 \log \left ((-1+x)^2\right )+4 x (x-\log (x))}{x \log ^2\left ((-1+x)^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx-4 \int \left (-\frac {4 x^2}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {1}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}-\frac {2 x}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {x^2}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {4 x \log (x)}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}\right ) \, dx-8 \text {Subst}\left (\int \frac {1}{x \log ^2\left (x^2\right )} \, dx,x,-1+x\right )+\int \frac {(x-\log (x)) \left (-6 x^2-2 x^3+3 \log \left ((-1+x)^2\right )-5 x \log \left ((-1+x)^2\right )+x^2 \log \left ((-1+x)^2\right )+x^3 \log \left ((-1+x)^2\right )+3 \log ^2\left ((-1+x)^2\right )-3 x \log ^2\left ((-1+x)^2\right )+6 x \log (x)+2 x^2 \log (x)\right )}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx \\ & = x^2+\frac {1}{3} \int \frac {\left ((-1+x)^2 (3+x) \log \left ((-1+x)^2\right )-3 (-1+x) \log ^2\left ((-1+x)^2\right )-2 x (3+x) (x-\log (x))\right ) (x-\log (x))}{(3+x) \log ^2\left ((-1+x)^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-\frac {4}{3} \int \frac {\left ((-1+x)^2 (3+x) \log \left ((-1+x)^2\right )-3 (-1+x) \log ^2\left ((-1+x)^2\right )-2 x (3+x) (x-\log (x))\right ) (x-\log (x))}{x \log ^2\left ((-1+x)^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx-4 \int \frac {1}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx-4 \int \frac {x^2}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx-4 \int \left (-\frac {4 x}{\log ^2\left ((-1+x)^2\right ) \left (-x+\log (x)+\log \left ((-1+x)^2\right ) \log (x)-\log \left ((-1+x)^2\right ) \log (3+x)\right )}-\frac {2}{\log \left ((-1+x)^2\right ) \left (-x+\log (x)+\log \left ((-1+x)^2\right ) \log (x)-\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {x}{\log \left ((-1+x)^2\right ) \left (-x+\log (x)+\log \left ((-1+x)^2\right ) \log (x)-\log \left ((-1+x)^2\right ) \log (3+x)\right )}+\frac {4 \log (x)}{\log ^2\left ((-1+x)^2\right ) \left (-x+\log (x)+\log \left ((-1+x)^2\right ) \log (x)-\log \left ((-1+x)^2\right ) \log (3+x)\right )}-\frac {1}{x \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )}\right ) \, dx-4 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left ((-1+x)^2\right )\right )+8 \int \frac {x}{(-1+x) \log \left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx+16 \int \frac {x^2}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx-16 \int \frac {x \log (x)}{(-1+x) \log ^2\left ((-1+x)^2\right ) \left (x-\log (x)-\log \left ((-1+x)^2\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )} \, dx+\int \frac {\left ((-1+x)^2 (3+x) \log \left ((-1+x)^2\right )-3 (-1+x) \log ^2\left ((-1+x)^2\right )-2 x (3+x) (x-\log (x))\right ) (-x+\log (x))}{(1-x) \log ^2\left ((-1+x)^2\right ) \left (x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=2 \left (\frac {x^2}{2}+\frac {-2 \log (x)+2 \log (3+x)}{x-\left (1+\log \left ((-1+x)^2\right )\right ) \log (x)+\log \left ((-1+x)^2\right ) \log (3+x)}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(125\) vs. \(2(33)=66\).
Time = 255.88 (sec) , antiderivative size = 126, normalized size of antiderivative = 3.82
method | result | size |
parallelrisch | \(\frac {36 x +48 \ln \left (3+x \right )+12 x^{3}-84 \ln \left (x \right )-12 x^{2} \ln \left (x \right )-12 \ln \left (x \right ) \ln \left (x^{2}-2 x +1\right ) x^{2}+12 \ln \left (3+x \right ) \ln \left (x^{2}-2 x +1\right ) x^{2}+36 \ln \left (3+x \right ) \ln \left (x^{2}-2 x +1\right )-36 \ln \left (x \right ) \ln \left (x^{2}-2 x +1\right )}{-12 \ln \left (x \right ) \ln \left (x^{2}-2 x +1\right )+12 \ln \left (3+x \right ) \ln \left (x^{2}-2 x +1\right )+12 x -12 \ln \left (x \right )}\) | \(126\) |
default | \(x^{2}+\frac {8 i \left (\ln \left (x \right )-\ln \left (3+x \right )\right )}{\pi \ln \left (x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \ln \left (x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \ln \left (x \right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}-\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right ) \ln \left (3+x \right )+2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2} \ln \left (3+x \right )-\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3} \ln \left (3+x \right )+4 i \ln \left (x \right ) \ln \left (-1+x \right )-4 i \ln \left (3+x \right ) \ln \left (-1+x \right )+2 i \ln \left (x \right )-2 i x}\) | \(177\) |
risch | \(\frac {\pi \,x^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \,x^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \,x^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}+4 i x^{2} \ln \left (-1+x \right )+8 i}{\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}+4 i \ln \left (-1+x \right )}-\frac {16 i \left (x -\ln \left (x \right )\right )}{\left (\pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )-2 \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2}+\pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3}+4 i \ln \left (-1+x \right )\right ) \left (i \pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right ) \ln \left (x \right )-i \pi \operatorname {csgn}\left (i \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right ) \ln \left (3+x \right )-2 i \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2} \ln \left (x \right )+2 i \pi \,\operatorname {csgn}\left (i \left (-1+x \right )\right ) \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{2} \ln \left (3+x \right )+i \pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3} \ln \left (x \right )-i \pi \operatorname {csgn}\left (i \left (-1+x \right )^{2}\right )^{3} \ln \left (3+x \right )-4 \ln \left (x \right ) \ln \left (-1+x \right )+4 \ln \left (3+x \right ) \ln \left (-1+x \right )+2 x -2 \ln \left (x \right )\right )}\) | \(380\) |
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (33) = 66\).
Time = 0.28 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.21 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=\frac {x^{3} + {\left (x^{2} \log \left (x + 3\right ) - x^{2} \log \left (x\right )\right )} \log \left (x^{2} - 2 \, x + 1\right ) - {\left (x^{2} + 4\right )} \log \left (x\right ) + 4 \, \log \left (x + 3\right )}{{\left (\log \left (x + 3\right ) - \log \left (x\right )\right )} \log \left (x^{2} - 2 \, x + 1\right ) + x - \log \left (x\right )} \]
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Time = 0.37 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.12 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=x^{2} + \frac {4 \log {\left (x \right )} - 4 \log {\left (x + 3 \right )}}{- x + \left (\log {\left (x \right )} - \log {\left (x + 3 \right )}\right ) \log {\left (x^{2} - 2 x + 1 \right )} + \log {\left (x \right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (33) = 66\).
Time = 0.33 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.09 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=-\frac {2 \, x^{2} \log \left (x - 1\right ) \log \left (x\right ) - x^{3} - 2 \, {\left (x^{2} \log \left (x - 1\right ) + 2\right )} \log \left (x + 3\right ) + {\left (x^{2} + 4\right )} \log \left (x\right )}{2 \, \log \left (x + 3\right ) \log \left (x - 1\right ) - 2 \, \log \left (x - 1\right ) \log \left (x\right ) + x - \log \left (x\right )} \]
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Time = 2.35 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.52 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=x^{2} + \frac {4 \, {\left (\log \left (x + 3\right ) - \log \left (x\right )\right )}}{\log \left (x^{2} - 2 \, x + 1\right ) \log \left (x + 3\right ) - \log \left (x^{2} - 2 \, x + 1\right ) \log \left (x\right ) + x - \log \left (x\right )} \]
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Time = 9.99 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.55 \[ \int \frac {12 x-12 x^2-6 x^4+4 x^5+2 x^6+\left (-8 x+4 x^2+16 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-24 x-14 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (-12+20 x-4 x^2-4 x^3+\left (48 x+16 x^2\right ) \log (x)\right ) \log (3+x)+\left (-24 x-8 x^2\right ) \log ^2(3+x)+\left (\left (12 x^3-8 x^4-4 x^5\right ) \log (x)+\left (-12 x^2+8 x^3+4 x^4\right ) \log ^2(x)+\left (-12 x^3+8 x^4+4 x^5+\left (12 x^2-8 x^3-4 x^4\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(x)+\left (12 x^2-8 x^3-4 x^4\right ) \log (x) \log (3+x)+\left (-6 x^2+4 x^3+2 x^4\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )}{-3 x^3+2 x^4+x^5+\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (\left (6 x^2-4 x^3-2 x^4\right ) \log (x)+\left (-6 x+4 x^2+2 x^3\right ) \log ^2(x)+\left (-6 x^2+4 x^3+2 x^4+\left (6 x-4 x^2-2 x^3\right ) \log (x)\right ) \log (3+x)\right ) \log \left (1-2 x+x^2\right )+\left (\left (-3 x+2 x^2+x^3\right ) \log ^2(x)+\left (6 x-4 x^2-2 x^3\right ) \log (x) \log (3+x)+\left (-3 x+2 x^2+x^3\right ) \log ^2(3+x)\right ) \log ^2\left (1-2 x+x^2\right )} \, dx=x^2+\frac {4\,\ln \left (x+3\right )-4\,\ln \left (x\right )}{x-\ln \left (x\right )+\ln \left (x+3\right )\,\ln \left (x^2-2\,x+1\right )-\ln \left (x^2-2\,x+1\right )\,\ln \left (x\right )} \]
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