Optimal. Leaf size=14 \[ -3-\log \left (\frac {16 \log ^2(3)}{x^4}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 4, normalized size of antiderivative = 0.29, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 29} \begin {gather*} 4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 \int \frac {1}{x} \, dx\\ &=4 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 0.29 \begin {gather*} 4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.01, size = 4, normalized size = 0.29 \begin {gather*} 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 5, normalized size = 0.36 \begin {gather*} 4 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 5, normalized size = 0.36
method | result | size |
default | \(4 \ln \relax (x )\) | \(5\) |
norman | \(4 \ln \relax (x )\) | \(5\) |
risch | \(4 \ln \relax (x )\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 4, normalized size = 0.29 \begin {gather*} 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.01, size = 4, normalized size = 0.29 \begin {gather*} 4\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 3, normalized size = 0.21 \begin {gather*} 4 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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