Optimal. Leaf size=13 \[ \frac {1}{8} \log \left (4 \log ^2(x)+1\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {203, 260} \[ \frac {1}{8} \log \left (4 \log ^2(x)+1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 203
Rule 260
Rubi steps
\begin {align*} \int \frac {\log (x)}{x+4 x \log ^2(x)} \, dx &=\operatorname {Subst}\left (\int \frac {x}{1+4 x^2} \, dx,x,\log (x)\right )\\ &=\frac {1}{8} \log \left (1+4 \log ^2(x)\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 13, normalized size = 1.00 \[ \frac {1}{8} \log \left (4 \log ^2(x)+1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.43, size = 11, normalized size = 0.85 \[ \frac {1}{8} \, \log \left (4 \, \log \relax (x)^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 11, normalized size = 0.85 \[ \frac {1}{8} \, \log \left (4 \, \log \relax (x)^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 12, normalized size = 0.92 \[ \frac {\ln \left (4 \ln \relax (x )^{2}+1\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.79, size = 9, normalized size = 0.69 \[ \frac {1}{8} \, \log \left (\log \relax (x)^{2} + \frac {1}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.46, size = 11, normalized size = 0.85 \[ \frac {\ln \left (4\,{\ln \relax (x)}^2+1\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 10, normalized size = 0.77 \[ \frac {\log {\left (\log {\relax (x )}^{2} + \frac {1}{4} \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________