Optimal. Leaf size=21 \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]
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Rubi [A] time = 0.0098538, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {72} \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x) (2+3 x)} \, dx &=\int \left (-\frac{11}{7 (-1+2 x)}-\frac{1}{7 (2+3 x)}\right ) \, dx\\ &=-\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0043201, size = 21, normalized size = 1. \[ -\frac{11}{14} \log (1-2 x)-\frac{1}{21} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*} -{\frac{11\,\ln \left ( 2\,x-1 \right ) }{14}}-{\frac{\ln \left ( 2+3\,x \right ) }{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.83039, size = 23, normalized size = 1.1 \begin{align*} -\frac{1}{21} \, \log \left (3 \, x + 2\right ) - \frac{11}{14} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.17874, size = 55, normalized size = 2.62 \begin{align*} -\frac{1}{21} \, \log \left (3 \, x + 2\right ) - \frac{11}{14} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.106297, size = 19, normalized size = 0.9 \begin{align*} - \frac{11 \log{\left (x - \frac{1}{2} \right )}}{14} - \frac{\log{\left (x + \frac{2}{3} \right )}}{21} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.82513, size = 26, normalized size = 1.24 \begin{align*} -\frac{1}{21} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{11}{14} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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