Optimal. Leaf size=45 \[ -\frac{375 x^2}{16}-\frac{2975 x}{16}-\frac{8349}{16 (1-2 x)}+\frac{9317}{64 (1-2 x)^2}-\frac{2805}{8} \log (1-2 x) \]
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Rubi [A] time = 0.0209593, antiderivative size = 45, 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} \[ -\frac{375 x^2}{16}-\frac{2975 x}{16}-\frac{8349}{16 (1-2 x)}+\frac{9317}{64 (1-2 x)^2}-\frac{2805}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{2975}{16}-\frac{375 x}{8}-\frac{9317}{16 (-1+2 x)^3}-\frac{8349}{8 (-1+2 x)^2}-\frac{2805}{4 (-1+2 x)}\right ) \, dx\\ &=\frac{9317}{64 (1-2 x)^2}-\frac{8349}{16 (1-2 x)}-\frac{2975 x}{16}-\frac{375 x^2}{16}-\frac{2805}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.01306, size = 46, normalized size = 1.02 \[ -\frac{3000 x^4+20800 x^3-35700 x^2-14796 x+11220 (1-2 x)^2 \log (1-2 x)+8877}{32 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{375\,{x}^{2}}{16}}-{\frac{2975\,x}{16}}-{\frac{2805\,\ln \left ( 2\,x-1 \right ) }{8}}+{\frac{9317}{64\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{8349}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.11124, size = 49, normalized size = 1.09 \begin{align*} -\frac{375}{16} \, x^{2} - \frac{2975}{16} \, x + \frac{121 \,{\left (552 \, x - 199\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{2805}{8} \, \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 = 1.40517, size = 158, normalized size = 3.51 \begin{align*} -\frac{6000 \, x^{4} + 41600 \, x^{3} - 46100 \, x^{2} + 22440 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 54892 \, x + 24079}{64 \,{\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 = 0.123523, size = 36, normalized size = 0.8 \begin{align*} - \frac{375 x^{2}}{16} - \frac{2975 x}{16} + \frac{66792 x - 24079}{256 x^{2} - 256 x + 64} - \frac{2805 \log{\left (2 x - 1 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.6649, size = 43, normalized size = 0.96 \begin{align*} -\frac{375}{16} \, x^{2} - \frac{2975}{16} \, x + \frac{121 \,{\left (552 \, x - 199\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{2805}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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