Optimal. Leaf size=59 \[ -\frac{3375 x^4}{32}-\frac{11925 x^3}{16}-\frac{44595 x^2}{16}-\frac{284071 x}{32}-\frac{302379}{32 (1-2 x)}+\frac{456533}{256 (1-2 x)^2}-\frac{1334949}{128} \log (1-2 x) \]
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Rubi [A] time = 0.0305795, antiderivative size = 59, 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} \[ -\frac{3375 x^4}{32}-\frac{11925 x^3}{16}-\frac{44595 x^2}{16}-\frac{284071 x}{32}-\frac{302379}{32 (1-2 x)}+\frac{456533}{256 (1-2 x)^2}-\frac{1334949}{128} \log (1-2 x) \]
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)^3} \, dx &=\int \left (-\frac{284071}{32}-\frac{44595 x}{8}-\frac{35775 x^2}{16}-\frac{3375 x^3}{8}-\frac{456533}{64 (-1+2 x)^3}-\frac{302379}{16 (-1+2 x)^2}-\frac{1334949}{64 (-1+2 x)}\right ) \, dx\\ &=\frac{456533}{256 (1-2 x)^2}-\frac{302379}{32 (1-2 x)}-\frac{284071 x}{32}-\frac{44595 x^2}{16}-\frac{11925 x^3}{16}-\frac{3375 x^4}{32}-\frac{1334949}{128} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0183163, size = 56, normalized size = 0.95 \[ -\frac{216000 x^6+1310400 x^5+4235760 x^4+12853984 x^3-27475116 x^2+5590620 x+5339796 (1-2 x)^2 \log (1-2 x)+1244595}{512 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 46, normalized size = 0.8 \begin{align*} -{\frac{3375\,{x}^{4}}{32}}-{\frac{11925\,{x}^{3}}{16}}-{\frac{44595\,{x}^{2}}{16}}-{\frac{284071\,x}{32}}-{\frac{1334949\,\ln \left ( 2\,x-1 \right ) }{128}}+{\frac{456533}{256\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{302379}{64\,x-32}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08799, size = 62, normalized size = 1.05 \begin{align*} -\frac{3375}{32} \, x^{4} - \frac{11925}{16} \, x^{3} - \frac{44595}{16} \, x^{2} - \frac{284071}{32} \, x + \frac{5929 \,{\left (816 \, x - 331\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1334949}{128} \, \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 = 1.5124, size = 212, normalized size = 3.59 \begin{align*} -\frac{108000 \, x^{6} + 655200 \, x^{5} + 2117880 \, x^{4} + 6426992 \, x^{3} - 8376752 \, x^{2} + 2669898 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 2565496 \, x + 1962499}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.126038, size = 49, normalized size = 0.83 \begin{align*} - \frac{3375 x^{4}}{32} - \frac{11925 x^{3}}{16} - \frac{44595 x^{2}}{16} - \frac{284071 x}{32} + \frac{4838064 x - 1962499}{1024 x^{2} - 1024 x + 256} - \frac{1334949 \log{\left (2 x - 1 \right )}}{128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.60364, size = 57, normalized size = 0.97 \begin{align*} -\frac{3375}{32} \, x^{4} - \frac{11925}{16} \, x^{3} - \frac{44595}{16} \, x^{2} - \frac{284071}{32} \, x + \frac{5929 \,{\left (816 \, x - 331\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1334949}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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