Optimal. Leaf size=27 \[ \frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x) \]
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Rubi [A] time = 0.0118792, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ \frac{15 x}{4}+\frac{77}{8 (1-2 x)}+\frac{17}{2} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)}{(1-2 x)^2} \, dx &=\int \left (\frac{15}{4}+\frac{77}{4 (-1+2 x)^2}+\frac{17}{-1+2 x}\right ) \, dx\\ &=\frac{77}{8 (1-2 x)}+\frac{15 x}{4}+\frac{17}{2} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.009845, size = 26, normalized size = 0.96 \[ \frac{1}{8} \left (30 x+\frac{77}{1-2 x}+68 \log (1-2 x)-15\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 22, normalized size = 0.8 \begin{align*}{\frac{15\,x}{4}}+{\frac{17\,\ln \left ( 2\,x-1 \right ) }{2}}-{\frac{77}{16\,x-8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04119, size = 28, normalized size = 1.04 \begin{align*} \frac{15}{4} \, x - \frac{77}{8 \,{\left (2 \, x - 1\right )}} + \frac{17}{2} \, \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 = 1.2741, size = 86, normalized size = 3.19 \begin{align*} \frac{60 \, x^{2} + 68 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 30 \, x - 77}{8 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089469, size = 20, normalized size = 0.74 \begin{align*} \frac{15 x}{4} + \frac{17 \log{\left (2 x - 1 \right )}}{2} - \frac{77}{16 x - 8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.65171, size = 43, normalized size = 1.59 \begin{align*} \frac{15}{4} \, x - \frac{77}{8 \,{\left (2 \, x - 1\right )}} - \frac{17}{2} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{15}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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