Optimal. Leaf size=11 \[ 5-\frac {2}{9 x}+\log (x) \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.91, 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, 45}
\begin {gather*} \log (x)-\frac {2}{9 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \int \frac {2+9 x}{x^2} \, dx\\ &=\frac {1}{9} \int \left (\frac {2}{x^2}+\frac {9}{x}\right ) \, dx\\ &=-\frac {2}{9 x}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.27 \begin {gather*} \frac {1}{9} \left (-\frac {2}{x}+9 \log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 9, normalized size = 0.82
method | result | size |
default | \(-\frac {2}{9 x}+\ln \left (x \right )\) | \(9\) |
norman | \(-\frac {2}{9 x}+\ln \left (x \right )\) | \(9\) |
risch | \(-\frac {2}{9 x}+\ln \left (x \right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 8, normalized size = 0.73 \begin {gather*} -\frac {2}{9 \, x} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 12, normalized size = 1.09 \begin {gather*} \frac {9 \, x \log \left (x\right ) - 2}{9 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.64 \begin {gather*} \log {\left (x \right )} - \frac {2}{9 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 9, normalized size = 0.82 \begin {gather*} -\frac {2}{9 \, x} + \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 = 0.02, size = 8, normalized size = 0.73 \begin {gather*} \ln \left (x\right )-\frac {2}{9\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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