Optimal. Leaf size=23 \[ \log \left (-2+x-10 \left (3-\log \left (\frac {4}{3}\right )-\log \left (\log \left (3+x^2\right )\right )\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.19, antiderivative size = 22, normalized size of antiderivative = 0.96, number of steps used = 2, number of rules used = 2, integrand size = 74, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6688, 6684} \begin {gather*} \log \left (10 \log \left (\log \left (x^2+3\right )\right )+x-2 \left (16-5 \log \left (\frac {4}{3}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6684
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20 x+\left (3+x^2\right ) \log \left (3+x^2\right )}{\left (3+x^2\right ) \log \left (3+x^2\right ) \left (x-32 \left (1-\frac {5}{16} \log \left (\frac {4}{3}\right )\right )+10 \log \left (\log \left (3+x^2\right )\right )\right )} \, dx\\ &=\log \left (x-2 \left (16-5 \log \left (\frac {4}{3}\right )\right )+10 \log \left (\log \left (3+x^2\right )\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 1.10, size = 21, normalized size = 0.91 \begin {gather*} \log \left (32-x-10 \log \left (\frac {4}{3}\right )-10 \log \left (\log \left (3+x^2\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.60, size = 17, normalized size = 0.74 \begin {gather*} \log \left (x - 10 \, \log \left (\frac {3}{4}\right ) + 10 \, \log \left (\log \left (x^{2} + 3\right )\right ) - 32\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.50, size = 21, normalized size = 0.91 \begin {gather*} \log \left (x - 10 \, \log \relax (3) + 20 \, \log \relax (2) + 10 \, \log \left (\log \left (x^{2} + 3\right )\right ) - 32\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 22, normalized size = 0.96
method | result | size |
risch | \(\ln \left (-\ln \relax (3)+2 \ln \relax (2)+\frac {x}{10}+\ln \left (\ln \left (x^{2}+3\right )\right )-\frac {16}{5}\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.69, size = 21, normalized size = 0.91 \begin {gather*} \log \left (\frac {1}{10} \, x - \log \relax (3) + 2 \, \log \relax (2) + \log \left (\log \left (x^{2} + 3\right )\right ) - \frac {16}{5}\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 {20\,x+\ln \left (x^2+3\right )\,\left (x^2+3\right )}{\ln \left (x^2+3\right )\,\left (\ln \left (\frac {3}{4}\right )\,\left (10\,x^2+30\right )-3\,x+32\,x^2-x^3+96\right )-\ln \left (\ln \left (x^2+3\right )\right )\,\ln \left (x^2+3\right )\,\left (10\,x^2+30\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.53, size = 24, normalized size = 1.04 \begin {gather*} \log {\left (\frac {x}{10} + \log {\left (\log {\left (x^{2} + 3 \right )} \right )} - \frac {16}{5} - \log {\relax (3 )} + 2 \log {\relax (2 )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________