Optimal. Leaf size=41 \[ \frac{125 x^3}{4}+\frac{325 x^2}{2}+\frac{8245 x}{16}+\frac{9317}{32 (1-2 x)}+\frac{8349}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0188122, antiderivative size = 41, 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} \[ \frac{125 x^3}{4}+\frac{325 x^2}{2}+\frac{8245 x}{16}+\frac{9317}{32 (1-2 x)}+\frac{8349}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{8245}{16}+325 x+\frac{375 x^2}{4}+\frac{9317}{16 (-1+2 x)^2}+\frac{8349}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{9317}{32 (1-2 x)}+\frac{8245 x}{16}+\frac{325 x^2}{2}+\frac{125 x^3}{4}+\frac{8349}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.010294, size = 41, normalized size = 1. \[ \frac{2000 x^4+9400 x^3+27780 x^2-35830 x+16698 (2 x-1) \log (1-2 x)+353}{64 x-32} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*}{\frac{125\,{x}^{3}}{4}}+{\frac{325\,{x}^{2}}{2}}+{\frac{8245\,x}{16}}+{\frac{8349\,\ln \left ( 2\,x-1 \right ) }{16}}-{\frac{9317}{64\,x-32}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.9824, size = 42, normalized size = 1.02 \begin{align*} \frac{125}{4} \, x^{3} + \frac{325}{2} \, x^{2} + \frac{8245}{16} \, x - \frac{9317}{32 \,{\left (2 \, x - 1\right )}} + \frac{8349}{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 = 1.32849, size = 132, normalized size = 3.22 \begin{align*} \frac{2000 \, x^{4} + 9400 \, x^{3} + 27780 \, x^{2} + 16698 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 16490 \, x - 9317}{32 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09808, size = 34, normalized size = 0.83 \begin{align*} \frac{125 x^{3}}{4} + \frac{325 x^{2}}{2} + \frac{8245 x}{16} + \frac{8349 \log{\left (2 x - 1 \right )}}{16} - \frac{9317}{64 x - 32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.24848, size = 77, normalized size = 1.88 \begin{align*} \frac{5}{32} \,{\left (2 \, x - 1\right )}^{3}{\left (\frac{335}{2 \, x - 1} + \frac{2244}{{\left (2 \, x - 1\right )}^{2}} + 25\right )} - \frac{9317}{32 \,{\left (2 \, x - 1\right )}} - \frac{8349}{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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