Optimal. Leaf size=29 \[ \log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0215285, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {2296, 2295} \[ \log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2296
Rule 2295
Rubi steps
\begin{align*} \int \frac{\log ^3(\log (x))}{x} \, dx &=\operatorname{Subst}\left (\int \log ^3(x) \, dx,x,\log (x)\right )\\ &=\log (x) \log ^3(\log (x))-3 \operatorname{Subst}\left (\int \log ^2(x) \, dx,x,\log (x)\right )\\ &=-3 \log (x) \log ^2(\log (x))+\log (x) \log ^3(\log (x))+6 \operatorname{Subst}(\int \log (x) \, dx,x,\log (x))\\ &=-6 \log (x)+6 \log (x) \log (\log (x))-3 \log (x) \log ^2(\log (x))+\log (x) \log ^3(\log (x))\\ \end{align*}
Mathematica [A] time = 0.0088646, size = 29, normalized size = 1. \[ \log (x) \log ^3(\log (x))-3 \log (x) \log ^2(\log (x))+6 \log (x) \log (\log (x))-6 \log (x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 30, normalized size = 1. \begin{align*} -6\,\ln \left ( x \right ) +6\,\ln \left ( x \right ) \ln \left ( \ln \left ( x \right ) \right ) -3\,\ln \left ( x \right ) \left ( \ln \left ( \ln \left ( x \right ) \right ) \right ) ^{2}+\ln \left ( x \right ) \left ( \ln \left ( \ln \left ( x \right ) \right ) \right ) ^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.04443, size = 30, normalized size = 1.03 \begin{align*}{\left (\log \left (\log \left (x\right )\right )^{3} - 3 \, \log \left (\log \left (x\right )\right )^{2} + 6 \, \log \left (\log \left (x\right )\right ) - 6\right )} \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.32822, size = 109, normalized size = 3.76 \begin{align*} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{3} - 3 \, \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} + 6 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 6 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.356041, size = 36, normalized size = 1.24 \begin{align*} \log{\left (x \right )} \log{\left (\log{\left (x \right )} \right )}^{3} - 3 \log{\left (x \right )} \log{\left (\log{\left (x \right )} \right )}^{2} + 6 \log{\left (x \right )} \log{\left (\log{\left (x \right )} \right )} - 6 \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.06163, size = 39, normalized size = 1.34 \begin{align*} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{3} - 3 \, \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} + 6 \, \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 6 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]