Optimal. Leaf size=8 \[ \log \left (\frac {55 x^2}{3}\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 4, normalized size of antiderivative = 0.50, 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*} 2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int \frac {1}{x} \, dx\\ &=2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 4, normalized size = 0.50 \begin {gather*} 2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 5, normalized size = 0.62
method | result | size |
default | \(2 \ln \left (x \right )\) | \(5\) |
norman | \(2 \ln \left (x \right )\) | \(5\) |
risch | \(2 \ln \left (x \right )\) | \(5\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 4, normalized size = 0.50 \begin {gather*} 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 4, normalized size = 0.50 \begin {gather*} 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 3, normalized size = 0.38 \begin {gather*} 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 5, normalized size = 0.62 \begin {gather*} 2 \, \log \left ({\left | x \right |}\right ) \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 = 0.50 \begin {gather*} 2\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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