Optimal. Leaf size=12 \[ 10 \log (\log (x)+3)-\log (x) \]
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Rubi [A] time = 0.0362636, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2365, 43} \[ 10 \log (\log (x)+3)-\log (x) \]
Antiderivative was successfully verified.
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Rule 2365
Rule 43
Rubi steps
\begin{align*} \int \frac{7-\log (x)}{x (3+\log (x))} \, dx &=\operatorname{Subst}\left (\int \frac{7-x}{3+x} \, dx,x,\log (x)\right )\\ &=\operatorname{Subst}\left (\int \left (-1+\frac{10}{3+x}\right ) \, dx,x,\log (x)\right )\\ &=-\log (x)+10 \log (3+\log (x))\\ \end{align*}
Mathematica [A] time = 0.0257176, size = 12, normalized size = 1. \[ 10 \log (\log (x)+3)-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 13, normalized size = 1.1 \begin{align*} -\ln \left ( x \right ) +10\,\ln \left ( 3+\ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09944, size = 16, normalized size = 1.33 \begin{align*} -\log \left (x\right ) + 10 \, \log \left (\log \left (x\right ) + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.03898, size = 41, normalized size = 3.42 \begin{align*} -\log \left (x\right ) + 10 \, \log \left (\log \left (x\right ) + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.107148, size = 10, normalized size = 0.83 \begin{align*} - \log{\left (x \right )} + 10 \log{\left (\log{\left (x \right )} + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.25913, size = 36, normalized size = 3. \begin{align*} 5 \, \log \left (\frac{1}{4} \, \pi ^{2}{\left (\mathrm{sgn}\left (x\right ) - 1\right )}^{2} +{\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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