Optimal. Leaf size=30 \[ -x+\log \left (\left (2+\frac {5 e^2}{2}\right ) \left (2+x-\frac {x^2}{2-x}\right )\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 20, normalized size of antiderivative = 0.67, number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2074, 260} \begin {gather*} \log \left (2-x^2\right )-x-\log (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 260
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {1}{2-x}+\frac {2 x}{-2+x^2}\right ) \, dx\\ &=-x-\log (2-x)+2 \int \frac {x}{-2+x^2} \, dx\\ &=-x-\log (2-x)+\log \left (2-x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 0.67 \begin {gather*} -x-\log (2-x)+\log \left (2-x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 16, normalized size = 0.53 \begin {gather*} -x + \log \left (x^{2} - 2\right ) - \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 18, normalized size = 0.60 \begin {gather*} -x + \log \left ({\left | x^{2} - 2 \right |}\right ) - \log \left ({\left | x - 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.57
method | result | size |
default | \(-x +\ln \left (x^{2}-2\right )-\ln \left (x -2\right )\) | \(17\) |
norman | \(-x +\ln \left (x^{2}-2\right )-\ln \left (x -2\right )\) | \(17\) |
risch | \(-x +\ln \left (x^{2}-2\right )-\ln \left (x -2\right )\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 16, normalized size = 0.53 \begin {gather*} -x + \log \left (x^{2} - 2\right ) - \log \left (x - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.03, size = 16, normalized size = 0.53 \begin {gather*} \ln \left (x^2-2\right )-\ln \left (x-2\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.40 \begin {gather*} - x - \log {\left (x - 2 \right )} + \log {\left (x^{2} - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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