Optimal. Leaf size=21 \[ \frac{1}{4} \log (5-x)-\frac{1}{4} \log (1-x) \]
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Rubi [A] time = 0.0041527, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, 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 616
Rule 31
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*}
Mathematica [A] time = 0.0028664, size = 21, normalized size = 1. \[ \frac{1}{4} \log (5-x)-\frac{1}{4} \log (1-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \begin{align*}{\frac{\ln \left ( -5+x \right ) }{4}}-{\frac{\ln \left ( -1+x \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967044, size = 18, normalized size = 0.86 \begin{align*} -\frac{1}{4} \, \log \left (x - 1\right ) + \frac{1}{4} \, \log \left (x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.86827, size = 46, normalized size = 2.19 \begin{align*} -\frac{1}{4} \, \log \left (x - 1\right ) + \frac{1}{4} \, \log \left (x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089792, size = 12, normalized size = 0.57 \begin{align*} \frac{\log{\left (x - 5 \right )}}{4} - \frac{\log{\left (x - 1 \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06522, size = 20, normalized size = 0.95 \begin{align*} -\frac{1}{4} \, \log \left ({\left | x - 1 \right |}\right ) + \frac{1}{4} \, \log \left ({\left | x - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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