Integrand size = 232, antiderivative size = 26 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=(1+x-\log (-5+x \log (4) \log (2-x) (x-\log (x))))^2 \] Output:
(x+1-ln(2*x*ln(2-x)*ln(2)*(x-ln(x))-5))^2
Leaf count is larger than twice the leaf count of optimal. \(88\) vs. \(2(26)=52\).
Time = 0.07 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.38 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=2 \left (x+\frac {x^2}{2}-x \log (-5+x \log (4) \log (2-x) (x-\log (x)))+\frac {1}{2} \log ^2(-5+x \log (4) \log (2-x) (x-\log (x)))-\log \left (5-x^2 \log (4) \log (2-x)+x \log (4) \log (2-x) \log (x)\right )\right ) \] Input:
Integrate[(-20 - 10*x + 10*x^2 + (2*x^2 + 2*x^3)*Log[4] + (4 - 6*x - 2*x^2 + 6*x^3 - 2*x^4)*Log[4]*Log[2 - x] + ((-2*x - 2*x^2)*Log[4] + (4 - 2*x - 4*x^2 + 2*x^3)*Log[4]*Log[2 - x])*Log[x] + (20 - 10*x - 2*x^2*Log[4] + (-4 + 10*x - 8*x^2 + 2*x^3)*Log[4]*Log[2 - x] + (2*x*Log[4] + (-4 + 6*x - 2*x ^2)*Log[4]*Log[2 - x])*Log[x])*Log[-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*L og[2 - x]*Log[x]])/(-10 + 5*x + (2*x^2 - x^3)*Log[4]*Log[2 - x] + (-2*x + x^2)*Log[4]*Log[2 - x]*Log[x]),x]
Output:
2*(x + x^2/2 - x*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])] + Log[-5 + x*L og[4]*Log[2 - x]*(x - Log[x])]^2/2 - Log[5 - x^2*Log[4]*Log[2 - x] + x*Log [4]*Log[2 - x]*Log[x]])
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {10 x^2+\left (\left (-2 x^2-2 x\right ) \log (4)+\left (2 x^3-4 x^2-2 x+4\right ) \log (4) \log (2-x)\right ) \log (x)+\left (-2 x^2 \log (4)+\left (\left (-2 x^2+6 x-4\right ) \log (4) \log (2-x)+2 x \log (4)\right ) \log (x)+\left (2 x^3-8 x^2+10 x-4\right ) \log (4) \log (2-x)-10 x+20\right ) \log \left (x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)-5\right )+\left (2 x^3+2 x^2\right ) \log (4)+\left (-2 x^4+6 x^3-2 x^2-6 x+4\right ) \log (4) \log (2-x)-10 x-20}{\left (x^2-2 x\right ) \log (4) \log (2-x) \log (x)+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+5 x-10} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (x^2 (-\log (4))+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)-5 x+x \log (4) \log (x)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x-\left (x^2-3 x+2\right ) \log (4) \log (2-x) (-x+\log (x)+1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 2 \int \left (-\frac {\log (x \log (4) \log (2-x) (x-\log (x))-5) \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {x \left (\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10\right )}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}+\frac {\log (4) \log (2-x) x^3-4 \log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x^2-\log (4) x^2+5 \log (4) \log (2-x) x+3 \log (4) \log (2-x) \log (x) x+\log (4) \log (x) x-5 x-2 \log (4) \log (2-x)-2 \log (4) \log (2-x) \log (x)+10}{(x-2) \left (\log (4) \log (2-x) x^2-\log (4) \log (2-x) \log (x) x-5\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 2 \int \frac {\left (-\log (4) x^2+\log (4) \log (x) x-5 x+\left (x^2-3 x+2\right ) \log (4) \log (2-x) (x-\log (x)-1)+10\right ) (x-\log (x \log (4) \log (2-x) (x-\log (x))-5)+1)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))}dx\) |
Input:
Int[(-20 - 10*x + 10*x^2 + (2*x^2 + 2*x^3)*Log[4] + (4 - 6*x - 2*x^2 + 6*x ^3 - 2*x^4)*Log[4]*Log[2 - x] + ((-2*x - 2*x^2)*Log[4] + (4 - 2*x - 4*x^2 + 2*x^3)*Log[4]*Log[2 - x])*Log[x] + (20 - 10*x - 2*x^2*Log[4] + (-4 + 10* x - 8*x^2 + 2*x^3)*Log[4]*Log[2 - x] + (2*x*Log[4] + (-4 + 6*x - 2*x^2)*Lo g[4]*Log[2 - x])*Log[x])*Log[-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*Log[2 - x]*Log[x]])/(-10 + 5*x + (2*x^2 - x^3)*Log[4]*Log[2 - x] + (-2*x + x^2)*L og[4]*Log[2 - x]*Log[x]),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(139\) vs. \(2(27)=54\).
Time = 81.65 (sec) , antiderivative size = 140, normalized size of antiderivative = 5.38
| method | result | size |
| parallelrisch | \(4+x^{2}-2 \ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right ) x +\ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right )^{2}+6 \ln \left (\frac {-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5}{2 \ln \left (2\right )}\right )+2 x -8 \ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right )\) | \(140\) |
Input:
int((((2*(-2*x^2+6*x-4)*ln(2)*ln(2-x)+4*x*ln(2))*ln(x)+2*(2*x^3-8*x^2+10*x -4)*ln(2)*ln(2-x)-4*x^2*ln(2)+20-10*x)*ln(-2*x*ln(2)*ln(2-x)*ln(x)+2*x^2*l n(2)*ln(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*ln(2)*ln(2-x)+2*(-2*x^2-2*x)*ln(2)) *ln(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*ln(2)*ln(2-x)+2*(2*x^3+2*x^2)*ln(2)+10 *x^2-10*x-20)/(2*(x^2-2*x)*ln(2)*ln(2-x)*ln(x)+2*(-x^3+2*x^2)*ln(2)*ln(2-x )+5*x-10),x,method=_RETURNVERBOSE)
Output:
4+x^2-2*ln(-2*x*ln(2)*ln(2-x)*ln(x)+2*x^2*ln(2)*ln(2-x)-5)*x+ln(-2*x*ln(2) *ln(2-x)*ln(x)+2*x^2*ln(2)*ln(2-x)-5)^2+6*ln(1/2*(-2*x*ln(2)*ln(2-x)*ln(x) +2*x^2*ln(2)*ln(2-x)-5)/ln(2))+2*x-8*ln(-2*x*ln(2)*ln(2-x)*ln(x)+2*x^2*ln( 2)*ln(2-x)-5)
Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (27) = 54\).
Time = 0.10 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.77 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=x^{2} - 2 \, {\left (x + 1\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) + \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right )^{2} + 2 \, x \] Input:
integrate((((2*(-2*x^2+6*x-4)*log(2)*log(2-x)+4*x*log(2))*log(x)+2*(2*x^3- 8*x^2+10*x-4)*log(2)*log(2-x)-4*x^2*log(2)+20-10*x)*log(-2*x*log(2)*log(2- x)*log(x)+2*x^2*log(2)*log(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*log(2)*log(2-x)+ 2*(-2*x^2-2*x)*log(2))*log(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*log(2)*log(2-x) +2*(2*x^3+2*x^2)*log(2)+10*x^2-10*x-20)/(2*(x^2-2*x)*log(2)*log(2-x)*log(x )+2*(-x^3+2*x^2)*log(2)*log(2-x)+5*x-10),x, algorithm="fricas")
Output:
x^2 - 2*(x + 1)*log(2*x^2*log(2)*log(-x + 2) - 2*x*log(2)*log(x)*log(-x + 2) - 5) + log(2*x^2*log(2)*log(-x + 2) - 2*x*log(2)*log(x)*log(-x + 2) - 5 )^2 + 2*x
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (24) = 48\).
Time = 3.52 (sec) , antiderivative size = 117, normalized size of antiderivative = 4.50 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=x^{2} - 2 x \log {\left (2 x^{2} \log {\left (2 \right )} \log {\left (2 - x \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )} \log {\left (2 - x \right )} - 5 \right )} + 2 x - 2 \log {\left (x \right )} - 2 \log {\left (- x + \log {\left (x \right )} \right )} - 2 \log {\left (\log {\left (2 - x \right )} - \frac {5}{2 x^{2} \log {\left (2 \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )}} \right )} + \log {\left (2 x^{2} \log {\left (2 \right )} \log {\left (2 - x \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )} \log {\left (2 - x \right )} - 5 \right )}^{2} \] Input:
integrate((((2*(-2*x**2+6*x-4)*ln(2)*ln(2-x)+4*x*ln(2))*ln(x)+2*(2*x**3-8* x**2+10*x-4)*ln(2)*ln(2-x)-4*x**2*ln(2)+20-10*x)*ln(-2*x*ln(2)*ln(2-x)*ln( x)+2*x**2*ln(2)*ln(2-x)-5)+(2*(2*x**3-4*x**2-2*x+4)*ln(2)*ln(2-x)+2*(-2*x* *2-2*x)*ln(2))*ln(x)+2*(-2*x**4+6*x**3-2*x**2-6*x+4)*ln(2)*ln(2-x)+2*(2*x* *3+2*x**2)*ln(2)+10*x**2-10*x-20)/(2*(x**2-2*x)*ln(2)*ln(2-x)*ln(x)+2*(-x* *3+2*x**2)*ln(2)*ln(2-x)+5*x-10),x)
Output:
x**2 - 2*x*log(2*x**2*log(2)*log(2 - x) - 2*x*log(2)*log(x)*log(2 - x) - 5 ) + 2*x - 2*log(x) - 2*log(-x + log(x)) - 2*log(log(2 - x) - 5/(2*x**2*log (2) - 2*x*log(2)*log(x))) + log(2*x**2*log(2)*log(2 - x) - 2*x*log(2)*log( x)*log(2 - x) - 5)**2
\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int { -\frac {2 \, {\left (2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right ) + {\left (2 \, x^{2} \log \left (2\right ) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - x \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x + 10\right )}}{2 \, {\left (x^{2} - 2 \, x\right )} \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 5 \, x - 10} \,d x } \] Input:
integrate((((2*(-2*x^2+6*x-4)*log(2)*log(2-x)+4*x*log(2))*log(x)+2*(2*x^3- 8*x^2+10*x-4)*log(2)*log(2-x)-4*x^2*log(2)+20-10*x)*log(-2*x*log(2)*log(2- x)*log(x)+2*x^2*log(2)*log(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*log(2)*log(2-x)+ 2*(-2*x^2-2*x)*log(2))*log(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*log(2)*log(2-x) +2*(2*x^3+2*x^2)*log(2)+10*x^2-10*x-20)/(2*(x^2-2*x)*log(2)*log(2-x)*log(x )+2*(-x^3+2*x^2)*log(2)*log(2-x)+5*x-10),x, algorithm="maxima")
Output:
-2*integrate((2*(x^4 - 3*x^3 + x^2 + 3*x - 2)*log(2)*log(-x + 2) - 5*x^2 - 2*(x^3 + x^2)*log(2) + (2*x^2*log(2) - 2*(x^3 - 4*x^2 + 5*x - 2)*log(2)*l og(-x + 2) + 2*((x^2 - 3*x + 2)*log(2)*log(-x + 2) - x*log(2))*log(x) + 5* x - 10)*log(2*x^2*log(2)*log(-x + 2) - 2*x*log(2)*log(x)*log(-x + 2) - 5) - 2*((x^3 - 2*x^2 - x + 2)*log(2)*log(-x + 2) - (x^2 + x)*log(2))*log(x) + 5*x + 10)/(2*(x^2 - 2*x)*log(2)*log(x)*log(-x + 2) - 2*(x^3 - 2*x^2)*log( 2)*log(-x + 2) + 5*x - 10), x)
\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int { -\frac {2 \, {\left (2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right ) + {\left (2 \, x^{2} \log \left (2\right ) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - x \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x + 10\right )}}{2 \, {\left (x^{2} - 2 \, x\right )} \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 5 \, x - 10} \,d x } \] Input:
integrate((((2*(-2*x^2+6*x-4)*log(2)*log(2-x)+4*x*log(2))*log(x)+2*(2*x^3- 8*x^2+10*x-4)*log(2)*log(2-x)-4*x^2*log(2)+20-10*x)*log(-2*x*log(2)*log(2- x)*log(x)+2*x^2*log(2)*log(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*log(2)*log(2-x)+ 2*(-2*x^2-2*x)*log(2))*log(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*log(2)*log(2-x) +2*(2*x^3+2*x^2)*log(2)+10*x^2-10*x-20)/(2*(x^2-2*x)*log(2)*log(2-x)*log(x )+2*(-x^3+2*x^2)*log(2)*log(2-x)+5*x-10),x, algorithm="giac")
Output:
integrate(-2*(2*(x^4 - 3*x^3 + x^2 + 3*x - 2)*log(2)*log(-x + 2) - 5*x^2 - 2*(x^3 + x^2)*log(2) + (2*x^2*log(2) - 2*(x^3 - 4*x^2 + 5*x - 2)*log(2)*l og(-x + 2) + 2*((x^2 - 3*x + 2)*log(2)*log(-x + 2) - x*log(2))*log(x) + 5* x - 10)*log(2*x^2*log(2)*log(-x + 2) - 2*x*log(2)*log(x)*log(-x + 2) - 5) - 2*((x^3 - 2*x^2 - x + 2)*log(2)*log(-x + 2) - (x^2 + x)*log(2))*log(x) + 5*x + 10)/(2*(x^2 - 2*x)*log(2)*log(x)*log(-x + 2) - 2*(x^3 - 2*x^2)*log( 2)*log(-x + 2) + 5*x - 10), x)
Timed out. \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int -\frac {10\,x-2\,\ln \left (2\right )\,\left (2\,x^3+2\,x^2\right )-10\,x^2-\ln \left (2\,x^2\,\ln \left (2\right )\,\ln \left (2-x\right )-2\,x\,\ln \left (2\right )\,\ln \left (2-x\right )\,\ln \left (x\right )-5\right )\,\left (\ln \left (x\right )\,\left (4\,x\,\ln \left (2\right )-2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^2-6\,x+4\right )\right )-4\,x^2\,\ln \left (2\right )-10\,x+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^3-8\,x^2+10\,x-4\right )+20\right )+\ln \left (x\right )\,\left (2\,\ln \left (2\right )\,\left (2\,x^2+2\,x\right )+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (-2\,x^3+4\,x^2+2\,x-4\right )\right )+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^4-6\,x^3+2\,x^2+6\,x-4\right )+20}{5\,x+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^2-x^3\right )-2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\ln \left (x\right )\,\left (2\,x-x^2\right )-10} \,d x \] Input:
int(-(10*x - 2*log(2)*(2*x^2 + 2*x^3) - 10*x^2 - log(2*x^2*log(2)*log(2 - x) - 2*x*log(2)*log(2 - x)*log(x) - 5)*(log(x)*(4*x*log(2) - 2*log(2)*log( 2 - x)*(2*x^2 - 6*x + 4)) - 4*x^2*log(2) - 10*x + 2*log(2)*log(2 - x)*(10* x - 8*x^2 + 2*x^3 - 4) + 20) + log(x)*(2*log(2)*(2*x + 2*x^2) + 2*log(2)*l og(2 - x)*(2*x + 4*x^2 - 2*x^3 - 4)) + 2*log(2)*log(2 - x)*(6*x + 2*x^2 - 6*x^3 + 2*x^4 - 4) + 20)/(5*x + 2*log(2)*log(2 - x)*(2*x^2 - x^3) - 2*log( 2)*log(2 - x)*log(x)*(2*x - x^2) - 10),x)
Output:
int(-(10*x - 2*log(2)*(2*x^2 + 2*x^3) - 10*x^2 - log(2*x^2*log(2)*log(2 - x) - 2*x*log(2)*log(2 - x)*log(x) - 5)*(log(x)*(4*x*log(2) - 2*log(2)*log( 2 - x)*(2*x^2 - 6*x + 4)) - 4*x^2*log(2) - 10*x + 2*log(2)*log(2 - x)*(10* x - 8*x^2 + 2*x^3 - 4) + 20) + log(x)*(2*log(2)*(2*x + 2*x^2) + 2*log(2)*l og(2 - x)*(2*x + 4*x^2 - 2*x^3 - 4)) + 2*log(2)*log(2 - x)*(6*x + 2*x^2 - 6*x^3 + 2*x^4 - 4) + 20)/(5*x + 2*log(2)*log(2 - x)*(2*x^2 - x^3) - 2*log( 2)*log(2 - x)*log(x)*(2*x - x^2) - 10), x)
\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int \frac {\left (\left (2 \left (-2 x^{2}+6 x -4\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )+4 \,\mathrm {log}\left (2\right ) x \right ) \mathrm {log}\left (x \right )+2 \left (2 x^{3}-8 x^{2}+10 x -4\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )-4 \,\mathrm {log}\left (2\right ) x^{2}+20-10 x \right ) \mathrm {log}\left (-2 x \,\mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right ) \mathrm {log}\left (x \right )+2 x^{2} \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )-5\right )+\left (2 \left (2 x^{3}-4 x^{2}-2 x +4\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )+2 \left (-2 x^{2}-2 x \right ) \mathrm {log}\left (2\right )\right ) \mathrm {log}\left (x \right )+2 \left (-2 x^{4}+6 x^{3}-2 x^{2}-6 x +4\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )+2 \left (2 x^{3}+2 x^{2}\right ) \mathrm {log}\left (2\right )+10 x^{2}-10 x -20}{2 \left (x^{2}-2 x \right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right ) \mathrm {log}\left (x \right )+2 \left (-x^{3}+2 x^{2}\right ) \mathrm {log}\left (2\right ) \mathrm {log}\left (-x +2\right )+5 x -10}d x \] Input:
int((((2*(-2*x^2+6*x-4)*log(2)*log(2-x)+4*x*log(2))*log(x)+2*(2*x^3-8*x^2+ 10*x-4)*log(2)*log(2-x)-4*x^2*log(2)+20-10*x)*log(-2*x*log(2)*log(2-x)*log (x)+2*x^2*log(2)*log(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*log(2)*log(2-x)+2*(-2* x^2-2*x)*log(2))*log(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*log(2)*log(2-x)+2*(2* x^3+2*x^2)*log(2)+10*x^2-10*x-20)/(2*(x^2-2*x)*log(2)*log(2-x)*log(x)+2*(- x^3+2*x^2)*log(2)*log(2-x)+5*x-10),x)
Output:
int((((2*(-2*x^2+6*x-4)*log(2)*log(2-x)+4*x*log(2))*log(x)+2*(2*x^3-8*x^2+ 10*x-4)*log(2)*log(2-x)-4*x^2*log(2)+20-10*x)*log(-2*x*log(2)*log(2-x)*log (x)+2*x^2*log(2)*log(2-x)-5)+(2*(2*x^3-4*x^2-2*x+4)*log(2)*log(2-x)+2*(-2* x^2-2*x)*log(2))*log(x)+2*(-2*x^4+6*x^3-2*x^2-6*x+4)*log(2)*log(2-x)+2*(2* x^3+2*x^2)*log(2)+10*x^2-10*x-20)/(2*(x^2-2*x)*log(2)*log(2-x)*log(x)+2*(- x^3+2*x^2)*log(2)*log(2-x)+5*x-10),x)