Optimal. Leaf size=9 \[ -6-2 x+\log \left (x^2\right ) \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.89, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} 2 \log (x)-2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {2}{x}\right ) \, dx\\ &=-2 x+2 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 0.89 \begin {gather*} -2 x+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 9, normalized size = 1.00
method | result | size |
default | \(2 \ln \left (x \right )-2 x\) | \(9\) |
norman | \(2 \ln \left (x \right )-2 x\) | \(9\) |
risch | \(2 \ln \left (x \right )-2 x\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 8, normalized size = 0.89 \begin {gather*} -2 \, x + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 8, normalized size = 0.89 \begin {gather*} -2 \, x + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} - 2 x + 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 9, normalized size = 1.00 \begin {gather*} -2 \, x + 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 = 0.02, size = 8, normalized size = 0.89 \begin {gather*} 2\,\ln \left (x\right )-2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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