Optimal. Leaf size=38 \[ -\frac{75 x}{8}-\frac{1133}{16 (1-2 x)}+\frac{847}{32 (1-2 x)^2}-\frac{505}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0153867, 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} \[ -\frac{75 x}{8}-\frac{1133}{16 (1-2 x)}+\frac{847}{32 (1-2 x)^2}-\frac{505}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{75}{8}-\frac{847}{8 (-1+2 x)^3}-\frac{1133}{8 (-1+2 x)^2}-\frac{505}{8 (-1+2 x)}\right ) \, dx\\ &=\frac{847}{32 (1-2 x)^2}-\frac{1133}{16 (1-2 x)}-\frac{75 x}{8}-\frac{505}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0217107, size = 34, normalized size = 0.89 \[ \frac{1}{32} \left (\frac{600 x^2+3932 x-1269}{(1-2 x)^2}-300 x-1010 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 31, normalized size = 0.8 \begin{align*} -{\frac{75\,x}{8}}-{\frac{505\,\ln \left ( 2\,x-1 \right ) }{16}}+{\frac{847}{32\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{1133}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.33125, size = 42, normalized size = 1.11 \begin{align*} -\frac{75}{8} \, x + \frac{11 \,{\left (412 \, x - 129\right )}}{32 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{505}{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 = 1.54826, size = 136, normalized size = 3.58 \begin{align*} -\frac{1200 \, x^{3} - 1200 \, x^{2} + 1010 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 4232 \, x + 1419}{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 = 0.11723, size = 29, normalized size = 0.76 \begin{align*} - \frac{75 x}{8} + \frac{4532 x - 1419}{128 x^{2} - 128 x + 32} - \frac{505 \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 = 3.04248, size = 36, normalized size = 0.95 \begin{align*} -\frac{75}{8} \, x + \frac{11 \,{\left (412 \, x - 129\right )}}{32 \,{\left (2 \, x - 1\right )}^{2}} - \frac{505}{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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