Optimal. Leaf size=22 \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]
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Rubi [A] time = 0.0086518, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^2} \, dx &=\int \left (\frac{11}{2 (-1+2 x)^2}+\frac{5}{2 (-1+2 x)}\right ) \, dx\\ &=\frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0053687, size = 22, normalized size = 1. \[ \frac{11}{4 (1-2 x)}+\frac{5}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 19, normalized size = 0.9 \begin{align*}{\frac{5\,\ln \left ( 2\,x-1 \right ) }{4}}-{\frac{11}{8\,x-4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.45118, size = 24, normalized size = 1.09 \begin{align*} -\frac{11}{4 \,{\left (2 \, x - 1\right )}} + \frac{5}{4} \, \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 = 1.15786, size = 63, normalized size = 2.86 \begin{align*} \frac{5 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{4 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.088426, size = 15, normalized size = 0.68 \begin{align*} \frac{5 \log{\left (2 x - 1 \right )}}{4} - \frac{11}{8 x - 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.36421, size = 38, normalized size = 1.73 \begin{align*} -\frac{11}{4 \,{\left (2 \, x - 1\right )}} - \frac{5}{4} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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