Optimal. Leaf size=13 \[ -\frac {x}{2}+6 (3+x)+\log (x) \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 0.62, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 43} \begin {gather*} \frac {11 x}{2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 43
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {2+11 x}{x} \, dx\\ &=\frac {1}{2} \int \left (11+\frac {2}{x}\right ) \, dx\\ &=\frac {11 x}{2}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} \frac {11 x}{2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 6, normalized size = 0.46 \begin {gather*} \frac {11}{2} \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 7, normalized size = 0.54 \begin {gather*} \frac {11}{2} \, x + \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 = 0.01, size = 7, normalized size = 0.54
method | result | size |
default | \(\frac {11 x}{2}+\ln \relax (x )\) | \(7\) |
norman | \(\frac {11 x}{2}+\ln \relax (x )\) | \(7\) |
risch | \(\frac {11 x}{2}+\ln \relax (x )\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 6, normalized size = 0.46 \begin {gather*} \frac {11}{2} \, x + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 6, normalized size = 0.46 \begin {gather*} \frac {11\,x}{2}+\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 7, normalized size = 0.54 \begin {gather*} \frac {11 x}{2} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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