Optimal. Leaf size=12 \[ 3 x-7 \log (2 x+3) \]
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Rubi [A] time = 0.005847, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ 3 x-7 \log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{-5+6 x}{3+2 x} \, dx &=\int \left (3-\frac{14}{3+2 x}\right ) \, dx\\ &=3 x-7 \log (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.0029611, size = 15, normalized size = 1.25 \[ 3 x-7 \log (2 x+3)+\frac{9}{2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 1.1 \begin{align*} 3\,x-7\,\ln \left ( 3+2\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.920511, size = 16, normalized size = 1.33 \begin{align*} 3 \, x - 7 \, \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81019, size = 30, normalized size = 2.5 \begin{align*} 3 \, x - 7 \, \log \left (2 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.070079, size = 10, normalized size = 0.83 \begin{align*} 3 x - 7 \log{\left (2 x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06254, size = 18, normalized size = 1.5 \begin{align*} 3 \, x - 7 \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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