\(\int \frac {-20-10 x+10 x^2+(2 x^2+2 x^3) \log (4)+(4-6 x-2 x^2+6 x^3-2 x^4) \log (4) \log (2-x)+((-2 x-2 x^2) \log (4)+(4-2 x-4 x^2+2 x^3) \log (4) \log (2-x)) \log (x)+(20-10 x-2 x^2 \log (4)+(-4+10 x-8 x^2+2 x^3) \log (4) \log (2-x)+(2 x \log (4)+(-4+6 x-2 x^2) \log (4) \log (2-x)) \log (x)) \log (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x))}{-10+5 x+(2 x^2-x^3) \log (4) \log (2-x)+(-2 x+x^2) \log (4) \log (2-x) \log (x)} \, dx\) [7901]

Optimal result

Integrand size = 232, antiderivative size = 26 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=(1+x-\log (-5+x \log (4) \log (2-x) (x-\log (x))))^2 \]

[Out]

(x+1-ln(2*x*ln(2-x)*ln(2)*(x-ln(x))-5))^2

Rubi [F]

\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx \]

[In]

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 + 1
0*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]*Log[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]

[Out]

x^2 - 2*Log[x] - 6*Log[Log[2 - x]] + 2*LogIntegral[2 - x] - 10*Defer[Int][(-5 + x*Log[4]*Log[2 - x]*(x - Log[x
]))^(-1), x] - 10*Defer[Int][1/(x*(-5 + x*Log[4]*Log[2 - x]*(x - Log[x]))), x] - 10*Defer[Int][1/(Log[2 - x]*(
-5 + x*Log[4]*Log[2 - x]*(x - Log[x]))), x] - 18*Log[4]*Defer[Int][Log[2 - x]/(-5 + x*Log[4]*Log[2 - x]*(x - L
og[x])), x] + Log[16]*Defer[Int][Log[2 - x]/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] + 6*Log[64]*Defer[Int]
[Log[2 - x]/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] - 9*Log[4]*Defer[Int][(x*Log[2 - x])/(-5 + x*Log[4]*Lo
g[2 - x]*(x - Log[x])), x] + 3*Log[64]*Defer[Int][(x*Log[2 - x])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] -
2*Log[4]*Defer[Int][(x^2*Log[2 - x])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] - 30*Defer[Int][1/((-2 + x)*
Log[2 - x]*(-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*Log[2 - x]*Log[x])), x] - 36*Log[4]*Defer[Int][Log[2 - x]/((
-2 + x)*(-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*Log[2 - x]*Log[x])), x] + 12*Log[64]*Defer[Int][Log[2 - x]/((-2
+ x)*(-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*Log[2 - x]*Log[x])), x] + 10*Defer[Int][Log[-5 + x*Log[4]*Log[2 -
x]*(x - Log[x])]/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] + 4*Log[4]*Defer[Int][Log[-5 + x*Log[4]*Log[2 -
x]*(x - Log[x])]/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] + 2*Log[4]*Defer[Int][(x*Log[-5 + x*Log[4]*Log[2
- x]*(x - Log[x])])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] - 2*Log[4]*Defer[Int][(Log[2 - x]*Log[-5 + x*L
og[4]*Log[2 - x]*(x - Log[x])])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] + 4*Log[4]*Defer[Int][(x*Log[2 - x
]*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] - 2*Log[4]*Defer[Int
][(x^2*Log[2 - x]*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])])/(-5 + x*Log[4]*Log[2 - x]*(x - Log[x])), x] + 2*
Log[4]*Defer[Int][(x*Log[2 - x]*Log[x]*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])])/(-5 + x*Log[4]*Log[2 - x]*(
x - Log[x])), x] + 8*Log[4]*Defer[Int][Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])]/((-2 + x)*(-5 + x^2*Log[4]*L
og[2 - x] - x*Log[4]*Log[2 - x]*Log[x])), x] - 4*Log[4]*Defer[Int][(Log[x]*Log[-5 + x*Log[4]*Log[2 - x]*(x - L
og[x])])/((-2 + x)*(-5 + x^2*Log[4]*Log[2 - x] - x*Log[4]*Log[2 - x]*Log[x])), x] + 2*Log[4]*Defer[Int][(Log[x
]*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])])/(5 + x*Log[4]*Log[2 - x]*(-x + Log[x])), x] + 2*Log[4]*Defer[Int
][(Log[2 - x]*Log[x]*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])])/(5 + x*Log[4]*Log[2 - x]*(-x + Log[x])), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (10-5 x-x^2 \log (4)+\left (2-3 x+x^2\right ) \log (4) \log (2-x) (-1+x-\log (x))+x \log (4) \log (x)\right ) (1+x-\log (-5+x \log (4) \log (2-x) (x-\log (x))))}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))} \, dx \\ & = 2 \int \frac {\left (10-5 x-x^2 \log (4)+\left (2-3 x+x^2\right ) \log (4) \log (2-x) (-1+x-\log (x))+x \log (4) \log (x)\right ) (1+x-\log (-5+x \log (4) \log (2-x) (x-\log (x))))}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))} \, dx \\ & = 2 \int \left (\frac {10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}+\frac {x \left (10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)\right )}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {\left (10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)\right ) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}\right ) \, dx \\ & = 2 \int \frac {10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+2 \int \frac {x \left (10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)\right )}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-2 \int \frac {\left (10-5 x-x^2 \log (4)-2 \log (4) \log (2-x)+5 x \log (4) \log (2-x)-4 x^2 \log (4) \log (2-x)+x^3 \log (4) \log (2-x)+x \log (4) \log (x)-2 \log (4) \log (2-x) \log (x)+3 x \log (4) \log (2-x) \log (x)-x^2 \log (4) \log (2-x) \log (x)\right ) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx \\ & = 2 \int \frac {10-5 x-x^2 \log (4)+\left (2-3 x+x^2\right ) \log (4) \log (2-x) (-1+x-\log (x))+x \log (4) \log (x)}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))} \, dx+2 \int \frac {x \left (10-5 x-x^2 \log (4)+\left (2-3 x+x^2\right ) \log (4) \log (2-x) (-1+x-\log (x))+x \log (4) \log (x)\right )}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))} \, dx-2 \int \frac {\left (10-5 x-x^2 \log (4)+\left (2-3 x+x^2\right ) \log (4) \log (2-x) (-1+x-\log (x))+x \log (4) \log (x)\right ) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(2-x) (5-x \log (4) \log (2-x) (x-\log (x)))} \, dx \\ & = 2 \int \left (\frac {-x+2 \log (2-x)-3 x \log (2-x)+x^2 \log (2-x)}{(-2+x) \log (2-x)}+\frac {-5 x+10 \log (2-x)-5 x \log (2-x)-2 x \log (4) \log ^2(2-x)+3 x^2 \log (4) \log ^2(2-x)-x^3 \log (4) \log ^2(2-x)}{(-2+x) \log (2-x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}\right ) \, dx+2 \int \left (\frac {-x+2 \log (2-x)-3 x \log (2-x)+x^2 \log (2-x)}{(-2+x) x \log (2-x)}+\frac {-5 x+10 \log (2-x)-5 x \log (2-x)-2 x \log (4) \log ^2(2-x)+3 x^2 \log (4) \log ^2(2-x)-x^3 \log (4) \log ^2(2-x)}{(-2+x) x \log (2-x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}\right ) \, dx-2 \int \left (\frac {10 \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {5 x \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {x^2 \log (4) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {2 \log (4) \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}+\frac {5 x \log (4) \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {4 x^2 \log (4) \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}+\frac {x^3 \log (4) \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}+\frac {x \log (4) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {2 \log (4) \log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}+\frac {3 x \log (4) \log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}-\frac {x^2 \log (4) \log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}\right ) \, dx \\ & = 2 \int \frac {-x+2 \log (2-x)-3 x \log (2-x)+x^2 \log (2-x)}{(-2+x) \log (2-x)} \, dx+2 \int \frac {-x+2 \log (2-x)-3 x \log (2-x)+x^2 \log (2-x)}{(-2+x) x \log (2-x)} \, dx+2 \int \frac {-5 x+10 \log (2-x)-5 x \log (2-x)-2 x \log (4) \log ^2(2-x)+3 x^2 \log (4) \log ^2(2-x)-x^3 \log (4) \log ^2(2-x)}{(-2+x) \log (2-x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+2 \int \frac {-5 x+10 \log (2-x)-5 x \log (2-x)-2 x \log (4) \log ^2(2-x)+3 x^2 \log (4) \log ^2(2-x)-x^3 \log (4) \log ^2(2-x)}{(-2+x) x \log (2-x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+10 \int \frac {x \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-20 \int \frac {\log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+(2 \log (4)) \int \frac {x^2 \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-(2 \log (4)) \int \frac {x^3 \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-(2 \log (4)) \int \frac {x \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+(2 \log (4)) \int \frac {x^2 \log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+(4 \log (4)) \int \frac {\log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+(4 \log (4)) \int \frac {\log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-(6 \log (4)) \int \frac {x \log (2-x) \log (x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx+(8 \log (4)) \int \frac {x^2 \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx-(10 \log (4)) \int \frac {x \log (2-x) \log (-5+x \log (4) \log (2-x) (x-\log (x)))}{(-2+x) \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(88\) vs. \(2(26)=52\).

Time = 0.12 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.38 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=2 \left (x+\frac {x^2}{2}-x \log (-5+x \log (4) \log (2-x) (x-\log (x)))+\frac {1}{2} \log ^2(-5+x \log (4) \log (2-x) (x-\log (x)))-\log \left (5-x^2 \log (4) \log (2-x)+x \log (4) \log (2-x) \log (x)\right )\right ) \]

[In]

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]*Log[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]

[Out]

2*(x + x^2/2 - x*Log[-5 + x*Log[4]*Log[2 - x]*(x - Log[x])] + Log[-5 + x*Log[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]])

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(139\) vs. \(2(27)=54\).

Time = 96.53 (sec) , antiderivative size = 140, normalized size of antiderivative = 5.38

method	result	size
parallelrisch	\(4+x^{2}-2 \ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right ) x +\ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right )^{2}+6 \ln \left (\frac {-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5}{2 \ln \left (2\right )}\right )+2 x -8 \ln \left (-2 x \ln \left (2\right ) \ln \left (2-x \right ) \ln \left (x \right )+2 x^{2} \ln \left (2\right ) \ln \left (2-x \right )-5\right )\)	\(140\)

[In]

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*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)*l
n(2-x)*ln(x)+2*(-x^3+2*x^2)*ln(2)*ln(2-x)+5*x-10),x,method=_RETURNVERBOSE)

[Out]

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*l
n(2)*ln(2-x)-5)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (27) = 54\).

Time = 0.26 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.77 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=x^{2} - 2 \, {\left (x + 1\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) + \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right )^{2} + 2 \, x \]

[In]

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")

[Out]

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

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (24) = 48\).

Time = 3.43 (sec) , antiderivative size = 117, normalized size of antiderivative = 4.50 \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=x^{2} - 2 x \log {\left (2 x^{2} \log {\left (2 \right )} \log {\left (2 - x \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )} \log {\left (2 - x \right )} - 5 \right )} + 2 x - 2 \log {\left (x \right )} - 2 \log {\left (- x + \log {\left (x \right )} \right )} - 2 \log {\left (\log {\left (2 - x \right )} - \frac {5}{2 x^{2} \log {\left (2 \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )}} \right )} + \log {\left (2 x^{2} \log {\left (2 \right )} \log {\left (2 - x \right )} - 2 x \log {\left (2 \right )} \log {\left (x \right )} \log {\left (2 - x \right )} - 5 \right )}^{2} \]

[In]

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)

[Out]

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)*lo
g(x)*log(2 - x) - 5)**2

Maxima [F]

\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int { -\frac {2 \, {\left (2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right ) + {\left (2 \, x^{2} \log \left (2\right ) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - x \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x + 10\right )}}{2 \, {\left (x^{2} - 2 \, x\right )} \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 5 \, x - 10} \,d x } \]

[In]

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")

[Out]

-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)*log(-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)

Giac [F]

\[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int { -\frac {2 \, {\left (2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \left (2\right ) + {\left (2 \, x^{2} \log \left (2\right ) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - x \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \left (2\right ) \log \left (-x + 2\right ) - 2 \, x \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \left (2\right ) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \left (2\right )\right )} \log \left (x\right ) + 5 \, x + 10\right )}}{2 \, {\left (x^{2} - 2 \, x\right )} \log \left (2\right ) \log \left (x\right ) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \left (2\right ) \log \left (-x + 2\right ) + 5 \, x - 10} \,d x } \]

[In]

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")

[Out]

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)*log(-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)

Mupad [F(-1)]

Timed out. \[ \int \frac {-20-10 x+10 x^2+\left (2 x^2+2 x^3\right ) \log (4)+\left (4-6 x-2 x^2+6 x^3-2 x^4\right ) \log (4) \log (2-x)+\left (\left (-2 x-2 x^2\right ) \log (4)+\left (4-2 x-4 x^2+2 x^3\right ) \log (4) \log (2-x)\right ) \log (x)+\left (20-10 x-2 x^2 \log (4)+\left (-4+10 x-8 x^2+2 x^3\right ) \log (4) \log (2-x)+\left (2 x \log (4)+\left (-4+6 x-2 x^2\right ) \log (4) \log (2-x)\right ) \log (x)\right ) \log \left (-5+x^2 \log (4) \log (2-x)-x \log (4) \log (2-x) \log (x)\right )}{-10+5 x+\left (2 x^2-x^3\right ) \log (4) \log (2-x)+\left (-2 x+x^2\right ) \log (4) \log (2-x) \log (x)} \, dx=\int -\frac {10\,x-2\,\ln \left (2\right )\,\left (2\,x^3+2\,x^2\right )-10\,x^2-\ln \left (2\,x^2\,\ln \left (2\right )\,\ln \left (2-x\right )-2\,x\,\ln \left (2\right )\,\ln \left (2-x\right )\,\ln \left (x\right )-5\right )\,\left (\ln \left (x\right )\,\left (4\,x\,\ln \left (2\right )-2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^2-6\,x+4\right )\right )-4\,x^2\,\ln \left (2\right )-10\,x+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^3-8\,x^2+10\,x-4\right )+20\right )+\ln \left (x\right )\,\left (2\,\ln \left (2\right )\,\left (2\,x^2+2\,x\right )+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (-2\,x^3+4\,x^2+2\,x-4\right )\right )+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^4-6\,x^3+2\,x^2+6\,x-4\right )+20}{5\,x+2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\left (2\,x^2-x^3\right )-2\,\ln \left (2\right )\,\ln \left (2-x\right )\,\ln \left (x\right )\,\left (2\,x-x^2\right )-10} \,d x \]

[In]

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)*(1
0*x - 8*x^2 + 2*x^3 - 4) + 20) + log(x)*(2*log(2)*(2*x + 2*x^2) + 2*log(2)*log(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)

[Out]

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)*(1
0*x - 8*x^2 + 2*x^3 - 4) + 20) + log(x)*(2*log(2)*(2*x + 2*x^2) + 2*log(2)*log(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)