Optimal. Leaf size=10 \[ x-2 \log (2 x+3) \]
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Rubi [A] time = 0.0050317, antiderivative size = 10, 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} \[ x-2 \log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{-1+2 x}{3+2 x} \, dx &=\int \left (1-\frac{4}{3+2 x}\right ) \, dx\\ &=x-2 \log (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.0017653, size = 10, normalized size = 1. \[ x-2 \log (2 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 1.1 \begin{align*} x-2\,\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 = 0.941657, size = 14, normalized size = 1.4 \begin{align*} x - 2 \, \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 = 2.07079, size = 27, normalized size = 2.7 \begin{align*} x - 2 \, \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 = 0.072634, size = 8, normalized size = 0.8 \begin{align*} x - 2 \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 = 1.04953, size = 15, normalized size = 1.5 \begin{align*} x - 2 \, \log \left ({\left | 2 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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