Optimal. Leaf size=17 \[ -x+\frac {1}{5} \log \left (\frac {100 x}{-2+x}\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1593, 893} \begin {gather*} -x-\frac {1}{5} \log (2-x)+\frac {\log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 893
Rule 1593
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2+10 x-5 x^2}{x (-10+5 x)} \, dx\\ &=\int \left (-1-\frac {1}{5 (-2+x)}+\frac {1}{5 x}\right ) \, dx\\ &=-x-\frac {1}{5} \log (2-x)+\frac {\log (x)}{5}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.18 \begin {gather*} -x-\frac {1}{5} \log (2-x)+\frac {\log (x)}{5} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 14, normalized size = 0.82 \begin {gather*} -x - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 16, normalized size = 0.94 \begin {gather*} -x - \frac {1}{5} \, \log \left ({\left | x - 2 \right |}\right ) + \frac {1}{5} \, \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 = 0.46, size = 15, normalized size = 0.88
method | result | size |
default | \(-x +\frac {\ln \relax (x )}{5}-\frac {\ln \left (x -2\right )}{5}\) | \(15\) |
norman | \(-x +\frac {\ln \relax (x )}{5}-\frac {\ln \left (x -2\right )}{5}\) | \(15\) |
risch | \(-x +\frac {\ln \relax (x )}{5}-\frac {\ln \left (x -2\right )}{5}\) | \(15\) |
meijerg | \(\frac {\ln \relax (x )}{5}-\frac {\ln \relax (2)}{5}+\frac {i \pi }{5}-\frac {\ln \left (1-\frac {x}{2}\right )}{5}-x\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 14, normalized size = 0.82 \begin {gather*} -x - \frac {1}{5} \, \log \left (x - 2\right ) + \frac {1}{5} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.73, size = 10, normalized size = 0.59 \begin {gather*} \frac {2\,\mathrm {atanh}\left (x-1\right )}{5}-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 = 0.71 \begin {gather*} - x + \frac {\log {\relax (x )}}{5} - \frac {\log {\left (x - 2 \right )}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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