Optimal. Leaf size=19 \[ \log \left (\frac {3 \log \left (x (-x-\log (2))^2\right )}{x}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 0.53, 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 {3 x+\log (2)+(-x-\log (2)) \log \left (x^3+2 x^2 \log (2)+x \log ^2(2)\right )}{\left (x^2+x \log (2)\right ) \log \left (x^3+2 x^2 \log (2)+x \log ^2(2)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 x+\log (2)+(-x-\log (2)) \log \left (x^3+2 x^2 \log (2)+x \log ^2(2)\right )}{x (x+\log (2)) \log \left (x^3+2 x^2 \log (2)+x \log ^2(2)\right )} \, dx\\ &=\int \frac {3 x+\log (2)-(x+\log (2)) \log \left (x (x+\log (2))^2\right )}{x (x+\log (2)) \log \left (x (x+\log (2))^2\right )} \, dx\\ &=\int \left (-\frac {1}{x}+\frac {3 x+\log (2)}{x (x+\log (2)) \log \left (x (x+\log (2))^2\right )}\right ) \, dx\\ &=-\log (x)+\int \frac {3 x+\log (2)}{x (x+\log (2)) \log \left (x (x+\log (2))^2\right )} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.51, size = 15, normalized size = 0.79 \begin {gather*} -\log (x)+\log \left (\log \left (x (x+\log (2))^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.74, size = 24, normalized size = 1.26 \begin {gather*} -\log \relax (x) + \log \left (\log \left (x^{3} + 2 \, x^{2} \log \relax (2) + x \log \relax (2)^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 24, normalized size = 1.26 \begin {gather*} -\log \relax (x) + \log \left (\log \left (x^{3} + 2 \, x^{2} \log \relax (2) + x \log \relax (2)^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 25, normalized size = 1.32
method | result | size |
default | \(\ln \left (\ln \left (x \ln \relax (2)^{2}+2 x^{2} \ln \relax (2)+x^{3}\right )\right )-\ln \relax (x )\) | \(25\) |
norman | \(\ln \left (\ln \left (x \ln \relax (2)^{2}+2 x^{2} \ln \relax (2)+x^{3}\right )\right )-\ln \relax (x )\) | \(25\) |
risch | \(\ln \left (\ln \left (x \ln \relax (2)^{2}+2 x^{2} \ln \relax (2)+x^{3}\right )\right )-\ln \relax (x )\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 16, normalized size = 0.84 \begin {gather*} -\log \relax (x) + \log \left (\log \left (x + \log \relax (2)\right ) + \frac {1}{2} \, \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.64, size = 24, normalized size = 1.26 \begin {gather*} \ln \left (\ln \left (x^3+2\,\ln \relax (2)\,x^2+{\ln \relax (2)}^2\,x\right )\right )-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.19, size = 24, normalized size = 1.26 \begin {gather*} - \log {\relax (x )} + \log {\left (\log {\left (x^{3} + 2 x^{2} \log {\relax (2 )} + x \log {\relax (2 )}^{2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________