Optimal. Leaf size=30 \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0102759, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{125 x^3}{6}-\frac{575 x^2}{8}-\frac{1115 x}{8}-\frac{1331}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{1115}{8}-\frac{575 x}{4}-\frac{125 x^2}{2}-\frac{1331}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac{1115 x}{8}-\frac{575 x^2}{8}-\frac{125 x^3}{6}-\frac{1331}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0074629, size = 30, normalized size = 1. \[ \frac{1}{96} \left (-5 \left (400 x^3+1380 x^2+2676 x-1733\right )-7986 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 23, normalized size = 0.8 \begin{align*} -{\frac{125\,{x}^{3}}{6}}-{\frac{575\,{x}^{2}}{8}}-{\frac{1115\,x}{8}}-{\frac{1331\,\ln \left ( 2\,x-1 \right ) }{16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06698, size = 30, normalized size = 1. \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{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 = 1.31803, size = 78, normalized size = 2.6 \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{16} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.0832, size = 29, normalized size = 0.97 \begin{align*} - \frac{125 x^{3}}{6} - \frac{575 x^{2}}{8} - \frac{1115 x}{8} - \frac{1331 \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 = 2.30156, size = 31, normalized size = 1.03 \begin{align*} -\frac{125}{6} \, x^{3} - \frac{575}{8} \, x^{2} - \frac{1115}{8} \, x - \frac{1331}{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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