Optimal. Leaf size=43 \[ -\frac{1}{49 (1-2 x)}+\frac{11}{28 (1-2 x)^2}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (3 x+2) \]
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Rubi [A] time = 0.021647, 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} \[ -\frac{1}{49 (1-2 x)}+\frac{11}{28 (1-2 x)^2}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac{11}{7 (-1+2 x)^3}-\frac{2}{49 (-1+2 x)^2}+\frac{6}{343 (-1+2 x)}-\frac{9}{343 (2+3 x)}\right ) \, dx\\ &=\frac{11}{28 (1-2 x)^2}-\frac{1}{49 (1-2 x)}+\frac{3}{343} \log (1-2 x)-\frac{3}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0181143, size = 35, normalized size = 0.81 \[ \frac{\frac{7 (8 x+73)}{(1-2 x)^2}+12 \log (1-2 x)-12 \log (6 x+4)}{1372} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 36, normalized size = 0.8 \begin{align*}{\frac{11}{28\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{1}{98\,x-49}}+{\frac{3\,\ln \left ( 2\,x-1 \right ) }{343}}-{\frac{3\,\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 = 2.29175, size = 49, normalized size = 1.14 \begin{align*} \frac{8 \, x + 73}{196 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{3}{343} \, \log \left (3 \, x + 2\right ) + \frac{3}{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 = 1.27989, size = 151, normalized size = 3.51 \begin{align*} -\frac{12 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 12 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 56 \, x - 511}{1372 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.132194, size = 34, normalized size = 0.79 \begin{align*} \frac{8 x + 73}{784 x^{2} - 784 x + 196} + \frac{3 \log{\left (x - \frac{1}{2} \right )}}{343} - \frac{3 \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 = 3.86074, size = 45, normalized size = 1.05 \begin{align*} \frac{8 \, x + 73}{196 \,{\left (2 \, x - 1\right )}^{2}} - \frac{3}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac{3}{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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