Optimal. Leaf size=34 \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0146051, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{175}{2}+\frac{125 x}{4}+\frac{1331}{8 (-1+2 x)^2}+\frac{1815}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{1331}{16 (1-2 x)}+\frac{175 x}{2}+\frac{125 x^2}{8}+\frac{1815}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.00736, size = 36, normalized size = 1.06 \[ \frac{1000 x^3+5100 x^2-5850 x+3630 (2 x-1) \log (1-2 x)-1137}{64 x-32} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*}{\frac{125\,{x}^{2}}{8}}+{\frac{175\,x}{2}}+{\frac{1815\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{1331}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1324, size = 35, normalized size = 1.03 \begin{align*} \frac{125}{8} \, x^{2} + \frac{175}{2} \, x - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} + \frac{1815}{16} \, \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 = 1.24352, size = 112, normalized size = 3.29 \begin{align*} \frac{500 \, x^{3} + 2550 \, x^{2} + 1815 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1400 \, x - 1331}{16 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.092911, size = 27, normalized size = 0.79 \begin{align*} \frac{125 x^{2}}{8} + \frac{175 x}{2} + \frac{1815 \log{\left (2 x - 1 \right )}}{16} - \frac{1331}{32 x - 16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.49988, size = 65, normalized size = 1.91 \begin{align*} \frac{25}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{66}{2 \, x - 1} + 5\right )} - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} - \frac{1815}{16} \, \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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