Optimal. Leaf size=19 \[ \frac{7}{4} \log (1-x)+\frac{1}{4} \log (x+3) \]
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Rubi [A] time = 0.0044599, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {632, 31} \[ \frac{7}{4} \log (1-x)+\frac{1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{5+2 x}{-3+2 x+x^2} \, dx &=\frac{1}{4} \int \frac{1}{3+x} \, dx+\frac{7}{4} \int \frac{1}{-1+x} \, dx\\ &=\frac{7}{4} \log (1-x)+\frac{1}{4} \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0032404, size = 19, normalized size = 1. \[ \frac{7}{4} \log (1-x)+\frac{1}{4} \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \begin{align*}{\frac{7\,\ln \left ( -1+x \right ) }{4}}+{\frac{\ln \left ( 3+x \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.931335, size = 18, normalized size = 0.95 \begin{align*} \frac{1}{4} \, \log \left (x + 3\right ) + \frac{7}{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 = 0.635538, size = 45, normalized size = 2.37 \begin{align*} \frac{1}{4} \, \log \left (x + 3\right ) + \frac{7}{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 = 0.096212, size = 14, normalized size = 0.74 \begin{align*} \frac{7 \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 = 1.0666, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{4} \, \log \left ({\left | x + 3 \right |}\right ) + \frac{7}{4} \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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