Optimal. Leaf size=27 \[ \frac {3}{x \left (x+\log \left (\frac {x}{(4-x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \]
________________________________________________________________________________________
Rubi [F] time = 4.02, 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 {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (2 (-4+x)+\log \left (\frac {2}{x^2}\right ) \left (2 \left (-2-4 x+x^2\right )+(-4+x) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )\right )}{(4-x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx\\ &=3 \int \frac {2 (-4+x)+\log \left (\frac {2}{x^2}\right ) \left (2 \left (-2-4 x+x^2\right )+(-4+x) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )}{(4-x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx\\ &=3 \int \left (\frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )}\right ) \, dx\\ &=3 \int \frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\\ &=-\left (3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\right )+3 \int \left (\frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{16 (-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{4 x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{16 x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx\\ &=\frac {3}{16} \int \frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{16} \int \frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\\ &=\frac {3}{16} \int \frac {2 (-4+x)+\left (-4-4 x+x^2\right ) \log \left (\frac {2}{x^2}\right )}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{16} \int \left (\frac {4}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {4 x}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {x^2}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {8}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {2 x}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{4} \int \frac {2 (-4+x)+\left (-4-4 x+x^2\right ) \log \left (\frac {2}{x^2}\right )}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\\ &=-\left (\frac {3}{16} \int \frac {x^2}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx\right )+\frac {3}{16} \int \left (-\frac {4}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {x}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {2}{\log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {8}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx-\frac {3}{8} \int \frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {1}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {x}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \left (\frac {1}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {8}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {2}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{2} \int \frac {1}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.11, size = 26, normalized size = 0.96 \begin {gather*} \frac {3}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 27, normalized size = 1.00 \begin {gather*} \frac {3}{x^{2} + x \log \left (-\frac {x}{{\left (x - 4\right )} \log \left (\frac {2}{x^{2}}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [C] time = 4.99, size = 699, normalized size = 25.89 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {\left (-3 x +12\right ) \ln \left (\frac {2}{x^{2}}\right ) \ln \left (-\frac {x}{\left (x -4\right ) \ln \left (\frac {2}{x^{2}}\right )}\right )+\left (-6 x^{2}+24 x +12\right ) \ln \left (\frac {2}{x^{2}}\right )-6 x +24}{\left (x^{3}-4 x^{2}\right ) \ln \left (\frac {2}{x^{2}}\right ) \ln \left (-\frac {x}{\left (x -4\right ) \ln \left (\frac {2}{x^{2}}\right )}\right )^{2}+\left (2 x^{4}-8 x^{3}\right ) \ln \left (\frac {2}{x^{2}}\right ) \ln \left (-\frac {x}{\left (x -4\right ) \ln \left (\frac {2}{x^{2}}\right )}\right )+\left (x^{5}-4 x^{4}\right ) \ln \left (\frac {2}{x^{2}}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 32, normalized size = 1.19 \begin {gather*} \frac {3}{x^{2} - x \log \left (x - 4\right ) + x \log \relax (x) - x \log \left (-\log \relax (2) + 2 \, \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {6\,x-\ln \left (\frac {2}{x^2}\right )\,\left (-6\,x^2+24\,x+12\right )+\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )\,\ln \left (\frac {2}{x^2}\right )\,\left (3\,x-12\right )-24}{\ln \left (\frac {2}{x^2}\right )\,\left (4\,x^2-x^3\right )\,{\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )}^2+\ln \left (\frac {2}{x^2}\right )\,\left (8\,x^3-2\,x^4\right )\,\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )+\ln \left (\frac {2}{x^2}\right )\,\left (4\,x^4-x^5\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.42, size = 20, normalized size = 0.74 \begin {gather*} \frac {3}{x^{2} + x \log {\left (- \frac {x}{\left (x - 4\right ) \log {\left (\frac {2}{x^{2}} \right )}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________