Integrand size = 132, antiderivative size = 25 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=x \left (-x+\log (2)+\log ^2\left (x^3\right )\right )^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(333\) vs. \(2(25)=50\).
Time = 0.36 (sec) , antiderivative size = 333, normalized size of antiderivative = 13.32, number of steps used = 55, number of rules used = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.098, Rules used = {2403, 2341, 2332, 2350, 2637, 12, 2333, 2408, 6874, 2367, 2342, 2413, 14} \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=-2 x \log ^4\left (x^3\right )+24 x \log ^3\left (x^3\right )-216 x \log ^2\left (x^3\right )+1296 x \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^4\left (x^3\right )+648 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log \left (x^3\right )-648 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log \left (x^3\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^3\left (x^3\right )-12 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^3\left (x^3\right )-2 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )-108 x \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )+2 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right ) \log ^2\left (x^3\right )+108 x \left (\log \left (\frac {x^2}{\log ^4(3)}\right )+2\right ) \log ^2\left (x^3\right )-3888 x+72 x \log (4)-144 x \log (2) \]
[In]
[Out]
Rule 12
Rule 14
Rule 2332
Rule 2333
Rule 2341
Rule 2342
Rule 2350
Rule 2367
Rule 2403
Rule 2408
Rule 2413
Rule 2637
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)+12 \int \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int (-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx+\int \log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx \\ & = \frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \left (1944-648 \log \left (x^3\right )+108 \log ^2\left (x^3\right )-12 \log ^3\left (x^3\right )+\log ^4\left (x^3\right )\right ) \, dx-24 \int \left (-162+54 \log \left (x^3\right )-9 \log ^2\left (x^3\right )+\log ^3\left (x^3\right )\right ) \, dx-\int 12 (-x+\log (4)) \log \left (x^3\right ) \, dx-\int 18 (-x+\log (4)) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\int \left (3 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )-4 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx+\int \left (-4 (x-\log (2)) \log ^2\left (x^3\right )-2 (2 x-\log (2)) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx \\ & = \frac {2 x^3}{3}-2 x^2 \log (2)+2 x \log ^2(2)-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \log ^4\left (x^3\right ) \, dx-2 \int (2 x-\log (2)) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+3 \int x^2 \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-4 \int (x-\log (2)) \log ^2\left (x^3\right ) \, dx-12 \int (-x+\log (4)) \log \left (x^3\right ) \, dx-18 \int (-x+\log (4)) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-(4 \log (2)) \int x \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+\log ^2(2) \int \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx \\ & = 6 x^2 \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-2 \int \left (2 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-\log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \, dx-4 \int \left (x \log ^2\left (x^3\right )-\log (2) \log ^2\left (x^3\right )\right ) \, dx+24 \int \log ^3\left (x^3\right ) \, dx+2 \left (36 \int \left (-\frac {x}{2}+\log (4)\right ) \, dx\right ) \\ & = 2 \left (-9 x^2+36 x \log (4)\right )+6 x^2 \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+9 x^2 \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-6 x^2 \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log (2) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-4 \int x \log ^2\left (x^3\right ) \, dx-4 \int x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx-216 \int \log ^2\left (x^3\right ) \, dx+(2 \log (2)) \int \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right ) \, dx+(4 \log (2)) \int \log ^2\left (x^3\right ) \, dx \\ & = 2 \left (-9 x^2+36 x \log (4)\right )+6 x^2 \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+4 x \log (2) \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+8 \int \frac {1}{4} x \left (9-6 \log \left (x^3\right )+2 \log ^2\left (x^3\right )\right ) \, dx+12 \int x \log \left (x^3\right ) \, dx+1296 \int \log \left (x^3\right ) \, dx-(4 \log (2)) \int \left (18-6 \log \left (x^3\right )+\log ^2\left (x^3\right )\right ) \, dx-(24 \log (2)) \int \log \left (x^3\right ) \, dx \\ & = -3888 x-9 x^2+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+12 x^2 \log \left (x^3\right )-24 x \log (2) \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+4 x \log (2) \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+2 \int x \left (9-6 \log \left (x^3\right )+2 \log ^2\left (x^3\right )\right ) \, dx-(4 \log (2)) \int \log ^2\left (x^3\right ) \, dx+(24 \log (2)) \int \log \left (x^3\right ) \, dx \\ & = -3888 x-9 x^2-72 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+12 x^2 \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+2 \int \left (9 x-6 x \log \left (x^3\right )+2 x \log ^2\left (x^3\right )\right ) \, dx+(24 \log (2)) \int \log \left (x^3\right ) \, dx \\ & = -3888 x-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+12 x^2 \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )-2 x^2 \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+4 \int x \log ^2\left (x^3\right ) \, dx-12 \int x \log \left (x^3\right ) \, dx \\ & = -3888 x+9 x^2-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+6 x^2 \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 \int x \log \left (x^3\right ) \, dx \\ & = -3888 x+18 x^2-144 x \log (2)+2 \left (-9 x^2+36 x \log (4)\right )+1296 x \log \left (x^3\right )+24 x \log (2) \log \left (x^3\right )-12 x \log (4) \log \left (x^3\right )-216 x \log ^2\left (x^3\right )+24 x \log ^3\left (x^3\right )-2 x \log ^4\left (x^3\right )-1944 x \log \left (\frac {x^2}{\log ^4(3)}\right )+x^3 \log \left (\frac {x^2}{\log ^4(3)}\right )+36 x \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log (2) \log \left (\frac {x^2}{\log ^4(3)}\right )+x \log ^2(2) \log \left (\frac {x^2}{\log ^4(3)}\right )-18 x \log (4) \log \left (\frac {x^2}{\log ^4(3)}\right )+648 x \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-108 x \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )-2 x^2 \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+2 x \log (2) \log ^2\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 x \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+1944 x \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-648 x \log \left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+108 x \log ^2\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )-12 x \log ^3\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+x \log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right ) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(112\) vs. \(2(25)=50\).
Time = 0.28 (sec) , antiderivative size = 112, normalized size of antiderivative = 4.48 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=\frac {1}{2} x \left (-4 \log ^2(2)+\log ^2(4)+\log \left (x^2\right ) \left (2 x^2+2 \log ^2(2)-x \log (16)+(-4 x+\log (16)) \log ^2\left (x^3\right )+2 \log ^4\left (x^3\right )\right )-8 x^2 \log (\log (3))-8 \log ^2(2) \log (\log (3))+x \log (65536) \log (\log (3))+(16 x-\log (65536)) \log ^2\left (x^3\right ) \log (\log (3))-8 \log ^4\left (x^3\right ) \log (\log (3))\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(25)=50\).
Time = 4.83 (sec) , antiderivative size = 103, normalized size of antiderivative = 4.12
method | result | size |
parallelrisch | \(\ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right ) x^{3}-2 \ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right ) \ln \left (x^{3}\right )^{2} x^{2}+\ln \left (2\right )^{2} \ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right ) x -2 \ln \left (2\right ) \ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right ) x^{2}+\ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right ) \ln \left (x^{3}\right )^{4} x +2 \ln \left (2\right ) x \ln \left (x^{3}\right )^{2} \ln \left (\frac {x^{2}}{\ln \left (3\right )^{4}}\right )\) | \(103\) |
default | \(36 x^{2} \ln \left (\ln \left (3\right )\right )+x^{3} \ln \left (x^{2}\right )+2 x \ln \left (2\right )^{2}-4 x^{3} \ln \left (\ln \left (3\right )\right )+2 x \ln \left (2\right ) \ln \left (x^{2}\right ) \ln \left (x^{3}\right )^{2}+48 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )-8 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )^{2}+\ln \left (x^{3}\right )^{4} \ln \left (x^{2}\right ) x -4 \ln \left (2\right )^{2} \ln \left (\ln \left (3\right )\right ) x -2 \ln \left (2\right ) x^{2} \ln \left (x^{2}\right )+8 \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) x^{2}-4 \ln \left (\ln \left (3\right )\right ) x \ln \left (x^{3}\right )^{4}+\ln \left (2\right )^{2} \left (x \ln \left (x^{2}\right )-2 x \right )-48 \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \left (x \ln \left (x^{3}\right )-3 x \right )+48 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (x^{3}\right )}{2}-\frac {3 x^{2}}{4}\right )-2 \ln \left (x^{2}\right ) x^{2} \ln \left (x^{3}\right )^{2}-144 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right )-24 x^{2} \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )+8 x^{2} \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )^{2}\) | \(230\) |
parts | \(36 x^{2} \ln \left (\ln \left (3\right )\right )+x^{3} \ln \left (x^{2}\right )+2 x \ln \left (2\right )^{2}-4 x^{3} \ln \left (\ln \left (3\right )\right )+2 x \ln \left (2\right ) \ln \left (x^{2}\right ) \ln \left (x^{3}\right )^{2}+48 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )-8 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )^{2}+\ln \left (x^{3}\right )^{4} \ln \left (x^{2}\right ) x -4 \ln \left (2\right )^{2} \ln \left (\ln \left (3\right )\right ) x -2 \ln \left (2\right ) x^{2} \ln \left (x^{2}\right )+8 \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) x^{2}-4 \ln \left (\ln \left (3\right )\right ) x \ln \left (x^{3}\right )^{4}+\ln \left (2\right )^{2} \left (x \ln \left (x^{2}\right )-2 x \right )-48 \ln \left (2\right ) \ln \left (\ln \left (3\right )\right ) \left (x \ln \left (x^{3}\right )-3 x \right )+48 \ln \left (\ln \left (3\right )\right ) \left (\frac {x^{2} \ln \left (x^{3}\right )}{2}-\frac {3 x^{2}}{4}\right )-2 \ln \left (x^{2}\right ) x^{2} \ln \left (x^{3}\right )^{2}-144 x \ln \left (2\right ) \ln \left (\ln \left (3\right )\right )-24 x^{2} \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )+8 x^{2} \ln \left (\ln \left (3\right )\right ) \ln \left (x^{3}\right )^{2}\) | \(230\) |
risch | \(\text {Expression too large to display}\) | \(16210\) |
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Leaf count of result is larger than twice the leaf count of optimal. 192 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 192, normalized size of antiderivative = 7.68 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=\frac {1}{16} \, x \log \left (\log \left (3\right )^{12}\right )^{4} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) + \frac {3}{4} \, x \log \left (\log \left (3\right )^{12}\right )^{3} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{2} + \frac {81}{16} \, x \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{5} - \frac {9}{2} \, {\left (x^{2} - x \log \left (2\right )\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{3} + \frac {1}{8} \, {\left (27 \, x \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{3} - 4 \, {\left (x^{2} - x \log \left (2\right )\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )\right )} \log \left (\log \left (3\right )^{12}\right )^{2} + \frac {3}{4} \, {\left (9 \, x \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{4} - 4 \, {\left (x^{2} - x \log \left (2\right )\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right )^{2}\right )} \log \left (\log \left (3\right )^{12}\right ) + {\left (x^{3} - 2 \, x^{2} \log \left (2\right ) + x \log \left (2\right )^{2}\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 146 vs. \(2 (24) = 48\).
Time = 0.16 (sec) , antiderivative size = 146, normalized size of antiderivative = 5.84 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=- 4 x^{3} \log {\left (\log {\left (3 \right )} \right )} + 8 x^{2} \log {\left (2 \right )} \log {\left (\log {\left (3 \right )} \right )} + \frac {2 x \log {\left (x^{3} \right )}^{5}}{3} - 4 x \log {\left (x^{3} \right )}^{4} \log {\left (\log {\left (3 \right )} \right )} - 4 x \log {\left (2 \right )}^{2} \log {\left (\log {\left (3 \right )} \right )} + \left (- \frac {4 x^{2}}{3} + \frac {4 x \log {\left (2 \right )}}{3}\right ) \log {\left (x^{3} \right )}^{3} + \left (8 x^{2} \log {\left (\log {\left (3 \right )} \right )} - 8 x \log {\left (2 \right )} \log {\left (\log {\left (3 \right )} \right )}\right ) \log {\left (x^{3} \right )}^{2} + \left (\frac {2 x^{3}}{3} - \frac {4 x^{2} \log {\left (2 \right )}}{3} + \frac {2 x \log {\left (2 \right )}^{2}}{3}\right ) \log {\left (x^{3} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.84 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=x \log \left (x^{3}\right )^{4} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) - 2 \, {\left (x^{2} - x \log \left (2\right )\right )} \log \left (x^{3}\right )^{2} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) + {\left (x^{3} - 2 \, x^{2} \log \left (2\right ) + x \log \left (2\right )^{2}\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (25) = 50\).
Time = 0.29 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.56 \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=-324 \, x {\left (\log \left (\log \left (3\right )\right ) + 2\right )} \log \left (x\right )^{4} + 162 \, x \log \left (x\right )^{5} + 648 \, x \log \left (x\right )^{4} - 36 \, {\left (x^{2} - x \log \left (2\right )\right )} \log \left (x\right )^{3} + 36 \, {\left (x^{2} {\left (2 \, \log \left (\log \left (3\right )\right ) + 1\right )} - 2 \, {\left (\log \left (2\right ) \log \left (\log \left (3\right )\right ) + \log \left (2\right )\right )} x\right )} \log \left (x\right )^{2} - 36 \, {\left (x^{2} - 2 \, x \log \left (2\right )\right )} \log \left (x\right )^{2} + {\left (x^{3} - 2 \, x^{2} \log \left (2\right ) + x \log \left (2\right )^{2}\right )} \log \left (\frac {x^{2}}{\log \left (3\right )^{4}}\right ) \]
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Timed out. \[ \int \left (2 x^2-4 x \log (2)+2 \log ^2(2)+\left (3 x^2-4 x \log (2)+\log ^2(2)\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+(-12 x+12 \log (2)) \log \left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+12 \log ^3\left (x^3\right ) \log \left (\frac {x^2}{\log ^4(3)}\right )+\log ^4\left (x^3\right ) \left (2+\log \left (\frac {x^2}{\log ^4(3)}\right )\right )+\log ^2\left (x^3\right ) \left (-4 x+4 \log (2)+(-4 x+2 \log (2)) \log \left (\frac {x^2}{\log ^4(3)}\right )\right )\right ) \, dx=\int 12\,{\ln \left (x^3\right )}^3\,\ln \left (\frac {x^2}{{\ln \left (3\right )}^4}\right )-4\,x\,\ln \left (2\right )+\ln \left (\frac {x^2}{{\ln \left (3\right )}^4}\right )\,\left (3\,x^2-4\,\ln \left (2\right )\,x+{\ln \left (2\right )}^2\right )+2\,{\ln \left (2\right )}^2+{\ln \left (x^3\right )}^4\,\left (\ln \left (\frac {x^2}{{\ln \left (3\right )}^4}\right )+2\right )-{\ln \left (x^3\right )}^2\,\left (4\,x-4\,\ln \left (2\right )+\ln \left (\frac {x^2}{{\ln \left (3\right )}^4}\right )\,\left (4\,x-2\,\ln \left (2\right )\right )\right )+2\,x^2-\ln \left (x^3\right )\,\ln \left (\frac {x^2}{{\ln \left (3\right )}^4}\right )\,\left (12\,x-12\,\ln \left (2\right )\right ) \,d x \]
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