Optimal. Leaf size=32 \[ -\frac{1}{55 (5 x+3)}-\frac{7}{121} \log (1-2 x)+\frac{7}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0130007, antiderivative size = 32, 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 = {77} \[ -\frac{1}{55 (5 x+3)}-\frac{7}{121} \log (1-2 x)+\frac{7}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac{14}{121 (-1+2 x)}+\frac{1}{11 (3+5 x)^2}+\frac{35}{121 (3+5 x)}\right ) \, dx\\ &=-\frac{1}{55 (3+5 x)}-\frac{7}{121} \log (1-2 x)+\frac{7}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0140118, size = 30, normalized size = 0.94 \[ \frac{1}{605} \left (-\frac{11}{5 x+3}-35 \log (5-10 x)+35 \log (5 x+3)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*} -{\frac{7\,\ln \left ( 2\,x-1 \right ) }{121}}-{\frac{1}{165+275\,x}}+{\frac{7\,\ln \left ( 3+5\,x \right ) }{121}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06481, size = 35, normalized size = 1.09 \begin{align*} -\frac{1}{55 \,{\left (5 \, x + 3\right )}} + \frac{7}{121} \, \log \left (5 \, x + 3\right ) - \frac{7}{121} \, \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 = 1.54965, size = 105, normalized size = 3.28 \begin{align*} \frac{35 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 35 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 11}{605 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.118017, size = 26, normalized size = 0.81 \begin{align*} - \frac{7 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{7 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{275 x + 165} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.77226, size = 34, normalized size = 1.06 \begin{align*} -\frac{1}{55 \,{\left (5 \, x + 3\right )}} - \frac{7}{121} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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