Optimal. Leaf size=38 \[ -\frac{45 x}{8}-\frac{707}{16 (1-2 x)}+\frac{539}{32 (1-2 x)^2}-\frac{309}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0277792, antiderivative size = 38, 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} \[ -\frac{45 x}{8}-\frac{707}{16 (1-2 x)}+\frac{539}{32 (1-2 x)^2}-\frac{309}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac{45}{8}-\frac{539}{8 (-1+2 x)^3}-\frac{707}{8 (-1+2 x)^2}-\frac{309}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{539}{32 (1-2 x)^2}-\frac{707}{16 (1-2 x)}-\frac{45 x}{8}-\frac{309}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0215737, size = 34, normalized size = 0.89 \[ \frac{1}{32} \left (\frac{360 x^2+2468 x-785}{(1-2 x)^2}-180 x-618 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 31, normalized size = 0.8 \begin{align*} -{\frac{45\,x}{8}}-{\frac{309\,\ln \left ( 2\,x-1 \right ) }{16}}+{\frac{539}{32\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{707}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07712, size = 42, normalized size = 1.11 \begin{align*} -\frac{45}{8} \, x + \frac{7 \,{\left (404 \, x - 125\right )}}{32 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{309}{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 = 1.33014, size = 131, normalized size = 3.45 \begin{align*} -\frac{720 \, x^{3} - 720 \, x^{2} + 618 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 2648 \, x + 875}{32 \,{\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 = 0.116651, size = 29, normalized size = 0.76 \begin{align*} - \frac{45 x}{8} + \frac{2828 x - 875}{128 x^{2} - 128 x + 32} - \frac{309 \log{\left (2 x - 1 \right )}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 5.90088, size = 36, normalized size = 0.95 \begin{align*} -\frac{45}{8} \, x + \frac{7 \,{\left (404 \, x - 125\right )}}{32 \,{\left (2 \, x - 1\right )}^{2}} - \frac{309}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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