Optimal. Leaf size=26 \[ (1+x-\log (-5+x \log (4) \log (2-x) (x-\log (x))))^2 \]
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Rubi [F] time = 54.38, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.13, size = 88, normalized size = 3.38 \begin {gather*} 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 ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 72, normalized size = 2.77 \begin {gather*} x^{2} - 2 \, {\left (x + 1\right )} \log \left (2 \, x^{2} \log \relax (2) \log \left (-x + 2\right ) - 2 \, x \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 5\right ) + \log \left (2 \, x^{2} \log \relax (2) \log \left (-x + 2\right ) - 2 \, x \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 5\right )^{2} + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {2 \, {\left (2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \relax (2) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \relax (2) + {\left (2 \, x^{2} \log \relax (2) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \relax (2) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \relax (2) \log \left (-x + 2\right ) - x \log \relax (2)\right )} \log \relax (x) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \relax (2) \log \left (-x + 2\right ) - 2 \, x \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \relax (2) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \relax (2)\right )} \log \relax (x) + 5 \, x + 10\right )}}{2 \, {\left (x^{2} - 2 \, x\right )} \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \relax (2) \log \left (-x + 2\right ) + 5 \, x - 10}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 \left (-2 x^{2}+6 x -4\right ) \ln \relax (2) \ln \left (2-x \right )+4 x \ln \relax (2)\right ) \ln \relax (x )+2 \left (2 x^{3}-8 x^{2}+10 x -4\right ) \ln \relax (2) \ln \left (2-x \right )-4 x^{2} \ln \relax (2)+20-10 x \right ) \ln \left (-2 x \ln \relax (2) \ln \left (2-x \right ) \ln \relax (x )+2 x^{2} \ln \relax (2) \ln \left (2-x \right )-5\right )+\left (2 \left (2 x^{3}-4 x^{2}-2 x +4\right ) \ln \relax (2) \ln \left (2-x \right )+2 \left (-2 x^{2}-2 x \right ) \ln \relax (2)\right ) \ln \relax (x )+2 \left (-2 x^{4}+6 x^{3}-2 x^{2}-6 x +4\right ) \ln \relax (2) \ln \left (2-x \right )+2 \left (2 x^{3}+2 x^{2}\right ) \ln \relax (2)+10 x^{2}-10 x -20}{2 \left (x^{2}-2 x \right ) \ln \relax (2) \ln \left (2-x \right ) \ln \relax (x )+2 \left (-x^{3}+2 x^{2}\right ) \ln \relax (2) \ln \left (2-x \right )+5 x -10}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -2 \, \int \frac {2 \, {\left (x^{4} - 3 \, x^{3} + x^{2} + 3 \, x - 2\right )} \log \relax (2) \log \left (-x + 2\right ) - 5 \, x^{2} - 2 \, {\left (x^{3} + x^{2}\right )} \log \relax (2) + {\left (2 \, x^{2} \log \relax (2) - 2 \, {\left (x^{3} - 4 \, x^{2} + 5 \, x - 2\right )} \log \relax (2) \log \left (-x + 2\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x + 2\right )} \log \relax (2) \log \left (-x + 2\right ) - x \log \relax (2)\right )} \log \relax (x) + 5 \, x - 10\right )} \log \left (2 \, x^{2} \log \relax (2) \log \left (-x + 2\right ) - 2 \, x \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 5\right ) - 2 \, {\left ({\left (x^{3} - 2 \, x^{2} - x + 2\right )} \log \relax (2) \log \left (-x + 2\right ) - {\left (x^{2} + x\right )} \log \relax (2)\right )} \log \relax (x) + 5 \, x + 10}{2 \, {\left (x^{2} - 2 \, x\right )} \log \relax (2) \log \relax (x) \log \left (-x + 2\right ) - 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \relax (2) \log \left (-x + 2\right ) + 5 \, x - 10}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {10\,x-2\,\ln \relax (2)\,\left (2\,x^3+2\,x^2\right )-10\,x^2-\ln \left (2\,x^2\,\ln \relax (2)\,\ln \left (2-x\right )-2\,x\,\ln \relax (2)\,\ln \left (2-x\right )\,\ln \relax (x)-5\right )\,\left (\ln \relax (x)\,\left (4\,x\,\ln \relax (2)-2\,\ln \relax (2)\,\ln \left (2-x\right )\,\left (2\,x^2-6\,x+4\right )\right )-4\,x^2\,\ln \relax (2)-10\,x+2\,\ln \relax (2)\,\ln \left (2-x\right )\,\left (2\,x^3-8\,x^2+10\,x-4\right )+20\right )+\ln \relax (x)\,\left (2\,\ln \relax (2)\,\left (2\,x^2+2\,x\right )+2\,\ln \relax (2)\,\ln \left (2-x\right )\,\left (-2\,x^3+4\,x^2+2\,x-4\right )\right )+2\,\ln \relax (2)\,\ln \left (2-x\right )\,\left (2\,x^4-6\,x^3+2\,x^2+6\,x-4\right )+20}{5\,x+2\,\ln \relax (2)\,\ln \left (2-x\right )\,\left (2\,x^2-x^3\right )-2\,\ln \relax (2)\,\ln \left (2-x\right )\,\ln \relax (x)\,\left (2\,x-x^2\right )-10} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 8.06, size = 117, normalized size = 4.50 \begin {gather*} x^{2} - 2 x \log {\left (2 x^{2} \log {\relax (2 )} \log {\left (2 - x \right )} - 2 x \log {\relax (2 )} \log {\relax (x )} \log {\left (2 - x \right )} - 5 \right )} + 2 x - 2 \log {\relax (x )} - 2 \log {\left (- x + \log {\relax (x )} \right )} - 2 \log {\left (\log {\left (2 - x \right )} - \frac {5}{2 x^{2} \log {\relax (2 )} - 2 x \log {\relax (2 )} \log {\relax (x )}} \right )} + \log {\left (2 x^{2} \log {\relax (2 )} \log {\left (2 - x \right )} - 2 x \log {\relax (2 )} \log {\relax (x )} \log {\left (2 - x \right )} - 5 \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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