Optimal. Leaf size=15 \[ 2 \log (1-x)+3 \log (x+3) \]
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Rubi [A] time = 0.004191, antiderivative size = 15, 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} \[ 2 \log (1-x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{3+5 x}{-3+2 x+x^2} \, dx &=2 \int \frac{1}{-1+x} \, dx+3 \int \frac{1}{3+x} \, dx\\ &=2 \log (1-x)+3 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0034669, size = 15, normalized size = 1. \[ 2 \log (1-x)+3 \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 14, normalized size = 0.9 \begin{align*} 2\,\ln \left ( -1+x \right ) +3\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929475, size = 18, normalized size = 1.2 \begin{align*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.673259, size = 39, normalized size = 2.6 \begin{align*} 3 \, \log \left (x + 3\right ) + 2 \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.093474, size = 12, normalized size = 0.8 \begin{align*} 2 \log{\left (x - 1 \right )} + 3 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07378, size = 20, normalized size = 1.33 \begin{align*} 3 \, \log \left ({\left | x + 3 \right |}\right ) + 2 \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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