Optimal. Leaf size=43 \[ -\frac{11}{49 (3 x+2)}+\frac{1}{42 (3 x+2)^2}-\frac{22}{343} \log (1-2 x)+\frac{22}{343} \log (3 x+2) \]
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Rubi [A] time = 0.0173423, antiderivative size = 43, 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} \[ -\frac{11}{49 (3 x+2)}+\frac{1}{42 (3 x+2)^2}-\frac{22}{343} \log (1-2 x)+\frac{22}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x) (2+3 x)^3} \, dx &=\int \left (-\frac{44}{343 (-1+2 x)}-\frac{1}{7 (2+3 x)^3}+\frac{33}{49 (2+3 x)^2}+\frac{66}{343 (2+3 x)}\right ) \, dx\\ &=\frac{1}{42 (2+3 x)^2}-\frac{11}{49 (2+3 x)}-\frac{22}{343} \log (1-2 x)+\frac{22}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0177354, size = 35, normalized size = 0.81 \[ \frac{-\frac{7 (198 x+125)}{(3 x+2)^2}-132 \log (3-6 x)+132 \log (3 x+2)}{2058} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{22\,\ln \left ( 2\,x-1 \right ) }{343}}+{\frac{1}{42\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{11}{98+147\,x}}+{\frac{22\,\ln \left ( 2+3\,x \right ) }{343}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01526, size = 49, normalized size = 1.14 \begin{align*} -\frac{198 \, x + 125}{294 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{22}{343} \, \log \left (3 \, x + 2\right ) - \frac{22}{343} \, \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 = 1.35527, size = 159, normalized size = 3.7 \begin{align*} \frac{132 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 132 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) - 1386 \, x - 875}{2058 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.135448, size = 34, normalized size = 0.79 \begin{align*} - \frac{198 x + 125}{2646 x^{2} + 3528 x + 1176} - \frac{22 \log{\left (x - \frac{1}{2} \right )}}{343} + \frac{22 \log{\left (x + \frac{2}{3} \right )}}{343} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.39976, size = 45, normalized size = 1.05 \begin{align*} -\frac{198 \, x + 125}{294 \,{\left (3 \, x + 2\right )}^{2}} + \frac{22}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{22}{343} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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