Optimal. Leaf size=32 \[ \frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3) \]
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Rubi [A] time = 0.0135686, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac{49}{22 (-1+2 x)^2}+\frac{217}{242 (-1+2 x)}+\frac{1}{121 (3+5 x)}\right ) \, dx\\ &=\frac{49}{44 (1-2 x)}+\frac{217}{484} \log (1-2 x)+\frac{1}{605} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0134924, size = 40, normalized size = 1.25 \[ -\frac{245}{44 (2 (5 x+3)-11)}+\frac{1}{605} \log (5 x+3)+\frac{217}{484} \log (11-2 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 27, normalized size = 0.8 \begin{align*} -{\frac{49}{88\,x-44}}+{\frac{217\,\ln \left ( 2\,x-1 \right ) }{484}}+{\frac{\ln \left ( 3+5\,x \right ) }{605}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 3.03536, size = 35, normalized size = 1.09 \begin{align*} -\frac{49}{44 \,{\left (2 \, x - 1\right )}} + \frac{1}{605} \, \log \left (5 \, x + 3\right ) + \frac{217}{484} \, \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 = 1.30369, size = 111, normalized size = 3.47 \begin{align*} \frac{4 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 1085 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2695}{2420 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125175, size = 24, normalized size = 0.75 \begin{align*} \frac{217 \log{\left (x - \frac{1}{2} \right )}}{484} + \frac{\log{\left (x + \frac{3}{5} \right )}}{605} - \frac{49}{88 x - 44} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.46496, size = 58, normalized size = 1.81 \begin{align*} -\frac{49}{44 \,{\left (2 \, x - 1\right )}} - \frac{9}{20} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{605} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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