Integrand size = 237, antiderivative size = 33 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\frac {1}{9} \left (3+e^{e^x}-x\right )^2 x^2 \left (\frac {3}{4}+\log \left (\frac {4}{x}\right )\right ) \log ^2(x) \]
[Out]
\[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \frac {1}{18} \int \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx \\ & = \frac {1}{18} \int \left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int \left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx \\ & = \frac {1}{18} \int (3-x)^2 x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int (3-x) x \left (3-4 x-4 (-3+2 x) \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{e^x} x \log (x) \left (18-6 x-8 (-3+x) \log \left (\frac {4}{x}\right )+\left (6-5 x-3 e^x (-3+x) x-4 \left (-6-3 \left (-1+e^x\right ) x+e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)\right ) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+\log (x)+3 e^x x \log (x)+4 \log \left (\frac {4}{x}\right ) \left (1+\log (x)+e^x x \log (x)\right )\right ) \, dx \\ & = \frac {1}{18} \int \left (9 x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-6 x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)\right ) \, dx+\frac {1}{18} \int \left (-3 x \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+x^2 \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int \left (e^{2 e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} x \log (x) \left (3+4 \log \left (\frac {4}{x}\right )+\log (x)+4 \log \left (\frac {4}{x}\right ) \log (x)\right )\right ) \, dx+\frac {1}{18} \int \left (-e^{e^x+x} (-3+x) x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)-e^{e^x} x \log (x) \left (-18+6 x-24 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )-6 \log (x)+5 x \log (x)-24 \log \left (\frac {4}{x}\right ) \log (x)+12 x \log \left (\frac {4}{x}\right ) \log (x)\right )\right ) \, dx \\ & = \frac {1}{18} \int x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int e^{2 e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{18} \int e^{e^x+x} (-3+x) x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int x^2 \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+4 \log \left (\frac {4}{x}\right )+\log (x)+4 \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx-\frac {1}{18} \int e^{e^x} x \log (x) \left (-18+6 x-24 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )-6 \log (x)+5 x \log (x)-24 \log \left (\frac {4}{x}\right ) \log (x)+12 x \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx-\frac {1}{6} \int x \left (-3+4 x-12 \log \left (\frac {4}{x}\right )+8 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{3} \int x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{2} \int x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx \\ & = \frac {1}{2} x^2 \log (x)-\frac {4}{27} x^3 \log (x)+\frac {1}{72} x^4 \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{18} \int x^3 \left (1+\log \left (\frac {4}{x}\right )\right ) \, dx+\frac {1}{18} \int \left (3 e^{2 e^x+x} x^2 \log ^2(x)+4 e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int \left (-3 x^2 \log ^2(x)+4 x^3 \log ^2(x)-12 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)+8 x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx-\frac {1}{18} \int \left (-3 e^{e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{e^x+x} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx+\frac {1}{18} \int e^{2 e^x} x \log (x) \left (3+\log (x)+4 \log \left (\frac {4}{x}\right ) (1+\log (x))\right ) \, dx-\frac {1}{18} \int e^{e^x} x \log (x) \left (6 (-3+x)+(-6+5 x) \log (x)+4 \log \left (\frac {4}{x}\right ) (2 (-3+x)+3 (-2+x) \log (x))\right ) \, dx-\frac {1}{6} \int \left (-3 x \log ^2(x)+4 x^2 \log ^2(x)-12 x \log \left (\frac {4}{x}\right ) \log ^2(x)+8 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {1}{3} \int \frac {1}{9} x^2 \left (13+12 \log \left (\frac {4}{x}\right )\right ) \, dx-\frac {1}{2} \int \frac {1}{2} x \left (5+4 \log \left (\frac {4}{x}\right )\right ) \, dx \\ & = -\frac {x^4}{288}-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )+\frac {1}{2} x^2 \log (x)-\frac {4}{27} x^3 \log (x)+\frac {1}{72} x^4 \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{27} \int x^2 \left (13+12 \log \left (\frac {4}{x}\right )\right ) \, dx-\frac {1}{18} \int e^{e^x+x} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int \left (e^{2 e^x} x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+e^{2 e^x} x \left (1+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx-\frac {1}{18} \int \left (2 e^{e^x} (-3+x) x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+e^{e^x} x \left (-6+5 x-24 \log \left (\frac {4}{x}\right )+12 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right ) \, dx-\frac {1}{6} \int x^2 \log ^2(x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx+\frac {1}{6} \int e^{e^x+x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {2}{9} \int x^3 \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {1}{4} \int x \left (5+4 \log \left (\frac {4}{x}\right )\right ) \, dx+\frac {4}{9} \int x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {1}{2} \int x \log ^2(x) \, dx-\frac {2}{3} \int x^2 \log ^2(x) \, dx-\frac {2}{3} \int x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {4}{3} \int x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+2 \int x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx \\ & = -\frac {x^2}{4}+\frac {4 x^3}{81}-\frac {x^4}{288}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )+\frac {1}{2} x^2 \log (x)-\frac {4}{27} x^3 \log (x)+\frac {1}{72} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{4} x^2 \log ^2(x)-\frac {5}{18} x^3 \log ^2(x)+\frac {1}{18} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{18} \int e^{2 e^x} x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{18} \int e^{2 e^x} x \left (1+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{18} \int e^{e^x} x \left (-6+5 x-24 \log \left (\frac {4}{x}\right )+12 x \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx-\frac {1}{18} \int \left (3 e^{e^x+x} x^3 \log ^2(x)+4 e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {1}{9} \int x^2 \log (x) \, dx-\frac {1}{9} \int x^3 \log (x) \, dx-\frac {1}{9} \int e^{e^x} (-3+x) x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx+\frac {1}{6} \int \left (3 e^{e^x+x} x^2 \log ^2(x)+4 e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {4}{9} \int x^2 \log (x) \, dx+\frac {4}{9} \int \frac {1}{32} x^3 \left (1-4 \log (x)+8 \log ^2(x)\right ) \, dx-\frac {1}{2} \int x \log (x) \, dx-\frac {2}{3} \int \frac {1}{27} x^2 \left (2-6 \log (x)+9 \log ^2(x)\right ) \, dx-\frac {4}{3} \int \frac {1}{27} x^2 \left (2-6 \log (x)+9 \log ^2(x)\right ) \, dx+2 \int \frac {1}{4} x \left (1-2 \log (x)+2 \log ^2(x)\right ) \, dx \\ & = -\frac {x^2}{8}-\frac {x^3}{81}+\frac {x^4}{288}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )+\frac {1}{4} x^2 \log (x)+\frac {1}{27} x^3 \log (x)-\frac {1}{72} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{4} x^2 \log ^2(x)-\frac {5}{18} x^3 \log ^2(x)+\frac {1}{18} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{72} \int x^3 \left (1-4 \log (x)+8 \log ^2(x)\right ) \, dx-\frac {2}{81} \int x^2 \left (2-6 \log (x)+9 \log ^2(x)\right ) \, dx-\frac {4}{81} \int x^2 \left (2-6 \log (x)+9 \log ^2(x)\right ) \, dx-\frac {1}{18} \int e^{e^x} x \left (-6+5 x+12 (-2+x) \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \, dx+\frac {1}{18} \int \left (3 e^{2 e^x} x \log (x)+4 e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx+\frac {1}{18} \int \left (e^{2 e^x} x \log ^2(x)+4 e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx-\frac {1}{9} \int \left (-3 e^{e^x} x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+e^{e^x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)\right ) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx-\frac {1}{6} \int e^{e^x+x} x^3 \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {1}{2} \int e^{e^x+x} x^2 \log ^2(x) \, dx+\frac {1}{2} \int x \left (1-2 \log (x)+2 \log ^2(x)\right ) \, dx+\frac {2}{3} \int e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx \\ & = -\frac {x^2}{8}-\frac {x^3}{81}+\frac {x^4}{288}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )+\frac {1}{4} x^2 \log (x)+\frac {1}{27} x^3 \log (x)-\frac {1}{72} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{4} x^2 \log ^2(x)-\frac {5}{18} x^3 \log ^2(x)+\frac {1}{18} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{72} \int \left (x^3-4 x^3 \log (x)+8 x^3 \log ^2(x)\right ) \, dx-\frac {2}{81} \int \left (2 x^2-6 x^2 \log (x)+9 x^2 \log ^2(x)\right ) \, dx-\frac {4}{81} \int \left (2 x^2-6 x^2 \log (x)+9 x^2 \log ^2(x)\right ) \, dx+\frac {1}{18} \int e^{2 e^x} x \log ^2(x) \, dx-\frac {1}{18} \int \left (-6 e^{e^x} x \log ^2(x)+5 e^{e^x} x^2 \log ^2(x)-24 e^{e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x)+12 e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)\right ) \, dx-\frac {1}{9} \int e^{e^x} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{6} \int e^{2 e^x} x \log (x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx-\frac {1}{6} \int e^{e^x+x} x^3 \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log (x) \, dx+\frac {2}{9} \int e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {1}{3} \int e^{e^x} x \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x) \, dx+\frac {1}{2} \int e^{e^x+x} x^2 \log ^2(x) \, dx+\frac {1}{2} \int \left (x-2 x \log (x)+2 x \log ^2(x)\right ) \, dx+\frac {2}{3} \int e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx \\ & = \frac {x^2}{8}-\frac {5 x^3}{81}+\frac {x^4}{144}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )+\frac {1}{4} x^2 \log (x)+\frac {1}{27} x^3 \log (x)-\frac {1}{72} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{4} x^2 \log ^2(x)-\frac {5}{18} x^3 \log ^2(x)+\frac {1}{18} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {1}{18} \int x^3 \log (x) \, dx+\frac {1}{18} \int e^{2 e^x} x \log ^2(x) \, dx+\frac {1}{9} \int x^3 \log ^2(x) \, dx-\frac {1}{9} \int \left (3 e^{e^x} x^2 \log (x)+4 e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx+\frac {4}{27} \int x^2 \log (x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx-\frac {1}{6} \int e^{e^x+x} x^3 \log ^2(x) \, dx-\frac {1}{6} \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx-\frac {2}{9} \int x^2 \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int \frac {\log \left (\frac {4}{x}\right ) \int e^{2 e^x} x \, dx}{x} \, dx+\frac {2}{9} \int \frac {\log (x) \int e^{2 e^x} x \, dx}{x} \, dx-\frac {5}{18} \int e^{e^x} x^2 \log ^2(x) \, dx+\frac {8}{27} \int x^2 \log (x) \, dx+\frac {1}{3} \int e^{e^x} x \log ^2(x) \, dx+\frac {1}{3} \int \left (3 e^{e^x} x \log (x)+4 e^{e^x} x \log \left (\frac {4}{x}\right ) \log (x)\right ) \, dx-\frac {4}{9} \int x^2 \log ^2(x) \, dx+\frac {1}{2} \int e^{e^x+x} x^2 \log ^2(x) \, dx-\frac {2}{3} \int e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{3} \int e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {4}{3} \int e^{e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {1}{6} \log (x) \int e^{2 e^x} x \, dx+\frac {1}{9} \left (2 \log \left (\frac {4}{x}\right ) \log (x)\right ) \int e^{2 e^x} x \, dx-\int x \log (x) \, dx+\int x \log ^2(x) \, dx \\ & = \frac {3 x^2}{8}-\frac {x^3}{9}+\frac {x^4}{96}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )-\frac {1}{4} x^2 \log (x)+\frac {5}{27} x^3 \log (x)-\frac {1}{36} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {3}{4} x^2 \log ^2(x)-\frac {1}{2} x^3 \log ^2(x)+\frac {1}{12} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {1}{18} \int x^3 \log (x) \, dx+\frac {1}{18} \int e^{2 e^x} x \log ^2(x) \, dx+\frac {4}{27} \int x^2 \log (x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx-\frac {1}{6} \int e^{e^x+x} x^3 \log ^2(x) \, dx-\frac {1}{6} \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx+\frac {2}{9} \int e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-2 \left (\frac {2}{9} \int \frac {\int \frac {\int e^{2 e^x} x \, dx}{x} \, dx}{x} \, dx\right )-\frac {5}{18} \int e^{e^x} x^2 \log ^2(x) \, dx+\frac {8}{27} \int x^2 \log (x) \, dx-\frac {1}{3} \int e^{e^x} x^2 \log (x) \, dx+\frac {1}{3} \int e^{e^x} x \log ^2(x) \, dx-\frac {4}{9} \int e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log (x) \, dx+\frac {1}{2} \int e^{e^x+x} x^2 \log ^2(x) \, dx-\frac {2}{3} \int e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{3} \int e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {4}{3} \int e^{e^x} x \log \left (\frac {4}{x}\right ) \log (x) \, dx+\frac {4}{3} \int e^{e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {1}{9} \left (2 \log \left (\frac {4}{x}\right )\right ) \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx+\frac {1}{6} \log (x) \int e^{2 e^x} x \, dx+\frac {1}{9} (2 \log (x)) \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx+\frac {1}{9} \left (2 \log \left (\frac {4}{x}\right ) \log (x)\right ) \int e^{2 e^x} x \, dx-\int x \log (x) \, dx+\int e^{e^x} x \log (x) \, dx \\ & = \frac {5 x^2}{8}-\frac {13 x^3}{81}+\frac {x^4}{72}+\frac {1}{2} x^2 \log \left (\frac {4}{x}\right )-\frac {4}{27} x^3 \log \left (\frac {4}{x}\right )+\frac {1}{72} x^4 \log \left (\frac {4}{x}\right )-\frac {1}{72} x^4 \left (1+\log \left (\frac {4}{x}\right )\right )-\frac {1}{8} x^2 \left (5+4 \log \left (\frac {4}{x}\right )\right )+\frac {1}{81} x^3 \left (13+12 \log \left (\frac {4}{x}\right )\right )-\frac {3}{4} x^2 \log (x)+\frac {1}{3} x^3 \log (x)-\frac {1}{24} x^4 \log (x)-x^2 \log \left (\frac {4}{x}\right ) \log (x)+\frac {4}{9} x^3 \log \left (\frac {4}{x}\right ) \log (x)-\frac {1}{18} x^4 \log \left (\frac {4}{x}\right ) \log (x)+\frac {1}{4} x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)-\frac {1}{9} x^3 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {1}{72} x^4 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log (x)+\frac {3}{4} x^2 \log ^2(x)-\frac {1}{2} x^3 \log ^2(x)+\frac {1}{12} x^4 \log ^2(x)+x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)-\frac {2}{3} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{9} x^4 \log \left (\frac {4}{x}\right ) \log ^2(x)+\frac {1}{18} \int e^{2 e^x} x \log ^2(x) \, dx+\frac {1}{6} \int e^{2 e^x+x} x^2 \log ^2(x) \, dx-\frac {1}{6} \int e^{e^x+x} x^3 \log ^2(x) \, dx-\frac {1}{6} \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx+\frac {2}{9} \int e^{2 e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{9} \int e^{2 e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {2}{9} \int e^{e^x+x} x^3 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-2 \left (\frac {2}{9} \int \frac {\int \frac {\int e^{2 e^x} x \, dx}{x} \, dx}{x} \, dx\right )-\frac {5}{18} \int e^{e^x} x^2 \log ^2(x) \, dx+\frac {1}{3} \int e^{e^x} x \log ^2(x) \, dx+\frac {1}{3} \int \frac {\int e^{e^x} x^2 \, dx}{x} \, dx+\frac {4}{9} \int \frac {\log \left (\frac {4}{x}\right ) \int e^{e^x} x^2 \, dx}{x} \, dx-\frac {4}{9} \int \frac {\log (x) \int e^{e^x} x^2 \, dx}{x} \, dx+\frac {1}{2} \int e^{e^x+x} x^2 \log ^2(x) \, dx-\frac {2}{3} \int e^{e^x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {2}{3} \int e^{e^x+x} x^2 \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx+\frac {4}{3} \int e^{e^x} x \log \left (\frac {4}{x}\right ) \log ^2(x) \, dx-\frac {4}{3} \int \frac {\log \left (\frac {4}{x}\right ) \int e^{e^x} x \, dx}{x} \, dx+\frac {4}{3} \int \frac {\log (x) \int e^{e^x} x \, dx}{x} \, dx-\frac {1}{9} \left (2 \log \left (\frac {4}{x}\right )\right ) \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx+\frac {1}{6} \log (x) \int e^{2 e^x} x \, dx+\frac {1}{9} (2 \log (x)) \int \frac {\int e^{2 e^x} x \, dx}{x} \, dx-\frac {1}{3} \log (x) \int e^{e^x} x^2 \, dx+\log (x) \int e^{e^x} x \, dx+\frac {1}{9} \left (2 \log \left (\frac {4}{x}\right ) \log (x)\right ) \int e^{2 e^x} x \, dx-\frac {1}{9} \left (4 \log \left (\frac {4}{x}\right ) \log (x)\right ) \int e^{e^x} x^2 \, dx+\frac {1}{3} \left (4 \log \left (\frac {4}{x}\right ) \log (x)\right ) \int e^{e^x} x \, dx-\int \frac {\int e^{e^x} x \, dx}{x} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.17 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.00 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\frac {1}{36} \left (3+e^{e^x}-x\right )^2 x^2 \left (3+4 \log \left (\frac {4}{x}\right )\right ) \log ^2(x) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(166\) vs. \(2(27)=54\).
Time = 6.82 (sec) , antiderivative size = 167, normalized size of antiderivative = 5.06
method | result | size |
parallelrisch | \(\frac {x^{4} \ln \left (x \right )^{2}}{12}-\frac {x^{3} \ln \left (x \right )^{2}}{2}+\frac {3 x^{2} \ln \left (x \right )^{2}}{4}+x^{2} \ln \left (\frac {4}{x}\right ) \ln \left (x \right )^{2}+\frac {{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{2}}{2}+\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{2}}{12}-\frac {{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{3}}{6}+\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \left (\frac {4}{x}\right ) x^{2} \ln \left (x \right )^{2}}{9}+\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (\frac {4}{x}\right ) x^{2} \ln \left (x \right )^{2}}{3}-\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (\frac {4}{x}\right ) \ln \left (x \right )^{2} x^{3}}{9}-\frac {2 \ln \left (\frac {4}{x}\right ) \ln \left (x \right )^{2} x^{3}}{3}+\frac {\ln \left (\frac {4}{x}\right ) \ln \left (x \right )^{2} x^{4}}{9}\) | \(167\) |
risch | \(-\frac {x^{3} \ln \left (x \right )^{2}}{2}+\frac {3 x^{2} \ln \left (x \right )^{2}}{4}+\frac {x^{4} \ln \left (x \right )^{2}}{12}+\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{2}}{12}-\frac {{\mathrm e}^{2 \,{\mathrm e}^{x}} x^{2} \ln \left (x \right )^{3}}{9}+\frac {2 \ln \left (x \right )^{2} \ln \left (2\right ) x^{4}}{9}+\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{3} x^{3}}{9}-\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{3} x^{2}}{3}-\frac {4 \ln \left (2\right ) \ln \left (x \right )^{2} x^{3}}{3}+2 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+\frac {{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{2}}{2}-\frac {{\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{3}}{6}+\frac {4 \ln \left (2\right ) {\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{2}}{3}+\frac {2 \,{\mathrm e}^{2 \,{\mathrm e}^{x}} \ln \left (2\right ) \ln \left (x \right )^{2} x^{2}}{9}-\frac {4 \ln \left (2\right ) {\mathrm e}^{{\mathrm e}^{x}} \ln \left (x \right )^{2} x^{3}}{9}-x^{2} \ln \left (x \right )^{3}+\frac {2 x^{3} \ln \left (x \right )^{3}}{3}-\frac {x^{4} \ln \left (x \right )^{3}}{9}\) | \(209\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 324 vs. \(2 (29) = 58\).
Time = 0.25 (sec) , antiderivative size = 324, normalized size of antiderivative = 9.82 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\frac {1}{9} \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{3} + \frac {1}{3} \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )^{2} + \frac {1}{36} \, {\left (3 \, x^{4} - 18 \, x^{3} + 27 \, x^{2} - 16 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (\frac {4}{x}\right )^{2} + \frac {1}{36} \, {\left (4 \, x^{2} \log \left (\frac {4}{x}\right )^{3} + 12 \, x^{2} \log \left (2\right )^{2} - {\left (16 \, x^{2} \log \left (2\right ) - 3 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{2} + 4 \, {\left (4 \, x^{2} \log \left (2\right )^{2} - 3 \, x^{2} \log \left (2\right )\right )} \log \left (\frac {4}{x}\right )\right )} e^{\left (2 \, e^{x}\right )} - \frac {1}{18} \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (\frac {4}{x}\right )^{3} + 12 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (2\right )^{2} + {\left (3 \, x^{3} - 9 \, x^{2} - 16 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (\frac {4}{x}\right )^{2} + 4 \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (2\right )^{2} - 3 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (\frac {4}{x}\right )\right )} e^{\left (e^{x}\right )} + \frac {1}{9} \, {\left (4 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )^{2} - 3 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (2\right )\right )} \log \left (\frac {4}{x}\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (27) = 54\).
Time = 5.61 (sec) , antiderivative size = 187, normalized size of antiderivative = 5.67 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\left (- \frac {x^{4}}{9} + \frac {2 x^{3}}{3} - x^{2}\right ) \log {\left (x \right )}^{3} + \frac {\left (- 72 x^{2} \log {\left (x \right )}^{3} + 54 x^{2} \log {\left (x \right )}^{2} + 144 x^{2} \log {\left (2 \right )} \log {\left (x \right )}^{2}\right ) e^{2 e^{x}}}{648} + \left (\frac {x^{4}}{12} + \frac {2 x^{4} \log {\left (2 \right )}}{9} - \frac {4 x^{3} \log {\left (2 \right )}}{3} - \frac {x^{3}}{2} + \frac {3 x^{2}}{4} + 2 x^{2} \log {\left (2 \right )}\right ) \log {\left (x \right )}^{2} + \frac {\left (144 x^{3} \log {\left (x \right )}^{3} - 288 x^{3} \log {\left (2 \right )} \log {\left (x \right )}^{2} - 108 x^{3} \log {\left (x \right )}^{2} - 432 x^{2} \log {\left (x \right )}^{3} + 324 x^{2} \log {\left (x \right )}^{2} + 864 x^{2} \log {\left (2 \right )} \log {\left (x \right )}^{2}\right ) e^{e^{x}}}{648} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 223 vs. \(2 (29) = 58\).
Time = 0.29 (sec) , antiderivative size = 223, normalized size of antiderivative = 6.76 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\frac {1}{36} \, {\left (3 \, x^{4} - 18 \, x^{3} + 27 \, x^{2} + 4 \, {\left (x^{4} - 6 \, x^{3} + 9 \, x^{2}\right )} \log \left (\frac {4}{x}\right )\right )} \log \left (x\right )^{2} + \frac {1}{36} \, {\left (x^{2} {\left (8 \, \log \left (2\right ) + 3\right )} \log \left (x\right )^{2} - 4 \, x^{2} \log \left (x\right )^{3}\right )} e^{\left (2 \, e^{x}\right )} + \frac {1}{18} \, {\left (4 \, {\left (x^{3} - 3 \, x^{2}\right )} \log \left (x\right )^{3} - {\left (x^{3} {\left (8 \, \log \left (2\right ) + 3\right )} - 3 \, x^{2} {\left (8 \, \log \left (2\right ) + 3\right )}\right )} \log \left (x\right )^{2}\right )} e^{\left (e^{x}\right )} - \frac {1}{108} \, {\left (6 \, x^{4} {\left (2 \, \log \left (2\right ) + 1\right )} - 4 \, x^{3} {\left (24 \, \log \left (2\right ) + 13\right )} + 27 \, x^{2} {\left (8 \, \log \left (2\right ) + 5\right )} - 6 \, {\left (x^{4} - 8 \, x^{3} + 18 \, x^{2}\right )} \log \left (x\right )\right )} \log \left (x\right ) + \frac {1}{108} \, {\left (6 \, x^{4} - 52 \, x^{3} + 135 \, x^{2} + 6 \, {\left (x^{4} - 8 \, x^{3} + 18 \, x^{2}\right )} \log \left (\frac {4}{x}\right )\right )} \log \left (x\right ) \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 227 vs. \(2 (29) = 58\).
Time = 0.31 (sec) , antiderivative size = 227, normalized size of antiderivative = 6.88 \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\frac {2}{9} \, x^{4} \log \left (2\right ) \log \left (x\right )^{2} - \frac {1}{9} \, x^{4} \log \left (x\right )^{3} + \frac {1}{12} \, x^{4} \log \left (x\right )^{2} - \frac {4}{3} \, x^{3} \log \left (2\right ) \log \left (x\right )^{2} + \frac {2}{9} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \left (2\right ) \log \left (x\right )^{2} + \frac {2}{3} \, x^{3} \log \left (x\right )^{3} - \frac {1}{9} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \left (x\right )^{3} - \frac {1}{2} \, x^{3} \log \left (x\right )^{2} + \frac {1}{12} \, x^{2} e^{\left (2 \, e^{x}\right )} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (2\right ) \log \left (x\right )^{2} - x^{2} \log \left (x\right )^{3} + \frac {3}{4} \, x^{2} \log \left (x\right )^{2} - \frac {1}{18} \, {\left (8 \, x^{3} e^{\left (x + e^{x}\right )} \log \left (2\right ) \log \left (x\right )^{2} - 4 \, x^{3} e^{\left (x + e^{x}\right )} \log \left (x\right )^{3} + 3 \, x^{3} e^{\left (x + e^{x}\right )} \log \left (x\right )^{2} - 24 \, x^{2} e^{\left (x + e^{x}\right )} \log \left (2\right ) \log \left (x\right )^{2} + 12 \, x^{2} e^{\left (x + e^{x}\right )} \log \left (x\right )^{3} - 9 \, x^{2} e^{\left (x + e^{x}\right )} \log \left (x\right )^{2}\right )} e^{\left (-x\right )} \]
[In]
[Out]
Timed out. \[ \int \frac {1}{18} \left (\left (27 x-18 x^2+3 x^3+\left (36 x-24 x^2+4 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (9 x-15 x^2+4 x^3+\left (36 x-36 x^2+8 x^3\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)+e^{2 e^x} \left (\left (3 x+4 x \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (x+3 e^x x^2+\left (4 x+4 e^x x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )+e^{e^x} \left (\left (18 x-6 x^2+\left (24 x-8 x^2\right ) \log \left (\frac {4}{x}\right )\right ) \log (x)+\left (6 x-5 x^2+e^x \left (9 x^2-3 x^3\right )+\left (24 x-12 x^2+e^x \left (12 x^2-4 x^3\right )\right ) \log \left (\frac {4}{x}\right )\right ) \log ^2(x)\right )\right ) \, dx=\int \frac {{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (\left (x+3\,x^2\,{\mathrm {e}}^x+\ln \left (\frac {4}{x}\right )\,\left (4\,x+4\,x^2\,{\mathrm {e}}^x\right )\right )\,{\ln \left (x\right )}^2+\left (3\,x+4\,x\,\ln \left (\frac {4}{x}\right )\right )\,\ln \left (x\right )\right )}{18}+\frac {\ln \left (x\right )\,\left (27\,x+\ln \left (\frac {4}{x}\right )\,\left (4\,x^3-24\,x^2+36\,x\right )-18\,x^2+3\,x^3\right )}{18}+\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left (\left (6\,x+{\mathrm {e}}^x\,\left (9\,x^2-3\,x^3\right )+\ln \left (\frac {4}{x}\right )\,\left (24\,x+{\mathrm {e}}^x\,\left (12\,x^2-4\,x^3\right )-12\,x^2\right )-5\,x^2\right )\,{\ln \left (x\right )}^2+\left (18\,x+\ln \left (\frac {4}{x}\right )\,\left (24\,x-8\,x^2\right )-6\,x^2\right )\,\ln \left (x\right )\right )}{18}+\frac {{\ln \left (x\right )}^2\,\left (9\,x+\ln \left (\frac {4}{x}\right )\,\left (8\,x^3-36\,x^2+36\,x\right )-15\,x^2+4\,x^3\right )}{18} \,d x \]
[In]
[Out]