Optimal. Leaf size=55 \[ \frac{675 x^5}{4}+\frac{2025 x^4}{2}+\frac{47535 x^3}{16}+\frac{194881 x^2}{32}+\frac{766807 x}{64}+\frac{456533}{128 (1-2 x)}+\frac{302379}{32} \log (1-2 x) \]
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Rubi [A] time = 0.027731, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{675 x^5}{4}+\frac{2025 x^4}{2}+\frac{47535 x^3}{16}+\frac{194881 x^2}{32}+\frac{766807 x}{64}+\frac{456533}{128 (1-2 x)}+\frac{302379}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac{766807}{64}+\frac{194881 x}{16}+\frac{142605 x^2}{16}+4050 x^3+\frac{3375 x^4}{4}+\frac{456533}{64 (-1+2 x)^2}+\frac{302379}{16 (-1+2 x)}\right ) \, dx\\ &=\frac{456533}{128 (1-2 x)}+\frac{766807 x}{64}+\frac{194881 x^2}{32}+\frac{47535 x^3}{16}+\frac{2025 x^4}{2}+\frac{675 x^5}{4}+\frac{302379}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0135269, size = 54, normalized size = 0.98 \[ \frac{43200 x^6+237600 x^5+630960 x^4+1178768 x^3+2287704 x^2-3569610 x+1209516 (2 x-1) \log (1-2 x)+561465}{128 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 42, normalized size = 0.8 \begin{align*}{\frac{675\,{x}^{5}}{4}}+{\frac{2025\,{x}^{4}}{2}}+{\frac{47535\,{x}^{3}}{16}}+{\frac{194881\,{x}^{2}}{32}}+{\frac{766807\,x}{64}}+{\frac{302379\,\ln \left ( 2\,x-1 \right ) }{32}}-{\frac{456533}{256\,x-128}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05615, size = 55, normalized size = 1. \begin{align*} \frac{675}{4} \, x^{5} + \frac{2025}{2} \, x^{4} + \frac{47535}{16} \, x^{3} + \frac{194881}{32} \, x^{2} + \frac{766807}{64} \, x - \frac{456533}{128 \,{\left (2 \, x - 1\right )}} + \frac{302379}{32} \, \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 = 1.28632, size = 185, normalized size = 3.36 \begin{align*} \frac{43200 \, x^{6} + 237600 \, x^{5} + 630960 \, x^{4} + 1178768 \, x^{3} + 2287704 \, x^{2} + 1209516 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1533614 \, x - 456533}{128 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.107356, size = 48, normalized size = 0.87 \begin{align*} \frac{675 x^{5}}{4} + \frac{2025 x^{4}}{2} + \frac{47535 x^{3}}{16} + \frac{194881 x^{2}}{32} + \frac{766807 x}{64} + \frac{302379 \log{\left (2 x - 1 \right )}}{32} - \frac{456533}{256 x - 128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.03721, size = 101, normalized size = 1.84 \begin{align*} \frac{1}{128} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{11475}{2 \, x - 1} + \frac{86685}{{\left (2 \, x - 1\right )}^{2}} + \frac{392836}{{\left (2 \, x - 1\right )}^{3}} + \frac{1334949}{{\left (2 \, x - 1\right )}^{4}} + 675\right )} - \frac{456533}{128 \,{\left (2 \, x - 1\right )}} - \frac{302379}{32} \, \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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