Optimal. Leaf size=16 \[ -\frac{5 x}{2}-\frac{11}{4} \log (1-2 x) \]
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Rubi [A] time = 0.0070926, antiderivative size = 16, 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} \[ -\frac{5 x}{2}-\frac{11}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+5 x}{1-2 x} \, dx &=\int \left (-\frac{5}{2}-\frac{11}{2 (-1+2 x)}\right ) \, dx\\ &=-\frac{5 x}{2}-\frac{11}{4} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0026952, size = 17, normalized size = 1.06 \[ \frac{1}{4} (-10 x-11 \log (1-2 x)+5) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 0.8 \begin{align*} -{\frac{5\,x}{2}}-{\frac{11\,\ln \left ( 2\,x-1 \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02367, size = 16, normalized size = 1. \begin{align*} -\frac{5}{2} \, x - \frac{11}{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 = 1.23041, size = 38, normalized size = 2.38 \begin{align*} -\frac{5}{2} \, x - \frac{11}{4} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.076542, size = 15, normalized size = 0.94 \begin{align*} - \frac{5 x}{2} - \frac{11 \log{\left (2 x - 1 \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.95619, size = 18, normalized size = 1.12 \begin{align*} -\frac{5}{2} \, x - \frac{11}{4} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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