Optimal. Leaf size=19 \[ \frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+3) \]
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Rubi [A] time = 0.0037085, antiderivative size = 19, 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} \[ \frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{-3+2 x+x^2} \, dx &=\frac{1}{4} \int \frac{1}{-1+x} \, dx-\frac{1}{4} \int \frac{1}{3+x} \, dx\\ &=\frac{1}{4} \log (1-x)-\frac{1}{4} \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0023606, size = 19, normalized size = 1. \[ \frac{1}{4} \log (1-x)-\frac{1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 0.7 \begin{align*} -{\frac{\ln \left ( 3+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 = 0.926453, size = 18, normalized size = 0.95 \begin{align*} -\frac{1}{4} \, \log \left (x + 3\right ) + \frac{1}{4} \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.80742, size = 46, normalized size = 2.42 \begin{align*} -\frac{1}{4} \, \log \left (x + 3\right ) + \frac{1}{4} \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.088556, size = 12, normalized size = 0.63 \begin{align*} \frac{\log{\left (x - 1 \right )}}{4} - \frac{\log{\left (x + 3 \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05974, size = 20, normalized size = 1.05 \begin{align*} -\frac{1}{4} \, \log \left ({\left | x + 3 \right |}\right ) + \frac{1}{4} \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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