Optimal. Leaf size=21 \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
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Rubi [A] time = 0.0104349, 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} \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac{7}{11 (-1+2 x)}+\frac{1}{11 (3+5 x)}\right ) \, dx\\ &=-\frac{7}{22} \log (1-2 x)+\frac{1}{55} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.004192, size = 21, normalized size = 1. \[ \frac{1}{55} \log (5 x+3)-\frac{7}{22} \log (1-2 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 18, normalized size = 0.9 \begin{align*} -{\frac{7\,\ln \left ( 2\,x-1 \right ) }{22}}+{\frac{\ln \left ( 3+5\,x \right ) }{55}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.14937, size = 23, normalized size = 1.1 \begin{align*} \frac{1}{55} \, \log \left (5 \, x + 3\right ) - \frac{7}{22} \, \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 = 1.23127, size = 53, normalized size = 2.52 \begin{align*} \frac{1}{55} \, \log \left (5 \, x + 3\right ) - \frac{7}{22} \, \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 = 0.10671, size = 17, normalized size = 0.81 \begin{align*} - \frac{7 \log{\left (x - \frac{1}{2} \right )}}{22} + \frac{\log{\left (x + \frac{3}{5} \right )}}{55} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.21171, size = 26, normalized size = 1.24 \begin{align*} \frac{1}{55} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{7}{22} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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