Optimal. Leaf size=12 \[ 10 \log (\log (x)+3)-\log (x) \]
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Rubi [A] time = 0.04, antiderivative size = 12, normalized size of antiderivative = 1.00, 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 43
Rule 2365
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*}
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Mathematica [A] time = 0.03, size = 12, normalized size = 1.00 \[ 10 \log (\log (x)+3)-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 12, normalized size = 1.00 \[ -\log \relax (x) + 10 \, \log \left (\log \relax (x) + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 27, normalized size = 2.25 \[ 5 \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\relax (x) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 13, normalized size = 1.08 \[ -\ln \relax (x )+10 \ln \left (\ln \relax (x )+3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 12, normalized size = 1.00 \[ -\log \relax (x) + 10 \, \log \left (\log \relax (x) + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 12, normalized size = 1.00 \[ 10\,\ln \left (\ln \relax (x)+3\right )-\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 0.83 \[ - \log {\relax (x )} + 10 \log {\left (\log {\relax (x )} + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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