Optimal. Leaf size=21 \[ \frac {1}{4} \log (5-x)-\frac {1}{4} \log (1-x) \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {616, 31} \[ \frac {1}{4} \log (5-x)-\frac {1}{4} \log (1-x) \]
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rubi steps
\begin {align*} \int \frac {1}{5-6 x+x^2} \, dx &=\frac {1}{4} \int \frac {1}{-5+x} \, dx-\frac {1}{4} \int \frac {1}{-1+x} \, dx\\ &=-\frac {1}{4} \log (1-x)+\frac {1}{4} \log (5-x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ \frac {1}{4} \log (5-x)-\frac {1}{4} \log (1-x) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 14, normalized size = 0.67 \[ \frac {1}{2} \tanh ^{-1}\left (\frac {3}{2}-\frac {x}{2}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 13, normalized size = 0.62 \[ -\frac {1}{4} \, \log \left (x - 1\right ) + \frac {1}{4} \, \log \left (x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 15, normalized size = 0.71 \[ -\frac {1}{4} \, \log \left ({\left | x - 1 \right |}\right ) + \frac {1}{4} \, \log \left ({\left | x - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.31, size = 14, normalized size = 0.67
method | result | size |
default | \(\frac {\ln \left (-5+x \right )}{4}-\frac {\ln \left (-1+x \right )}{4}\) | \(14\) |
norman | \(\frac {\ln \left (-5+x \right )}{4}-\frac {\ln \left (-1+x \right )}{4}\) | \(14\) |
risch | \(\frac {\ln \left (-5+x \right )}{4}-\frac {\ln \left (-1+x \right )}{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 13, normalized size = 0.62 \[ -\frac {1}{4} \, \log \left (x - 1\right ) + \frac {1}{4} \, \log \left (x - 5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.26, size = 8, normalized size = 0.38 \[ -\frac {\mathrm {atanh}\left (\frac {x}{2}-\frac {3}{2}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.57 \[ \frac {\log {\left (x - 5 \right )}}{4} - \frac {\log {\left (x - 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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