Optimal. Leaf size=37 \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]
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Rubi [A] time = 0.0136059, antiderivative size = 37, 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} \[ -\frac{375 x^4}{8}-\frac{2225 x^3}{12}-\frac{5645 x^2}{16}-\frac{8453 x}{16}-\frac{9317}{32} \log (1-2 x) \]
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} \, dx &=\int \left (-\frac{8453}{16}-\frac{5645 x}{8}-\frac{2225 x^2}{4}-\frac{375 x^3}{2}-\frac{9317}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac{8453 x}{16}-\frac{5645 x^2}{16}-\frac{2225 x^3}{12}-\frac{375 x^4}{8}-\frac{9317}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0112771, size = 32, normalized size = 0.86 \[ \frac{1}{384} \left (-18000 x^4-71200 x^3-135480 x^2-202872 x-111804 \log (1-2 x)+145331\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 28, normalized size = 0.8 \begin{align*} -{\frac{375\,{x}^{4}}{8}}-{\frac{2225\,{x}^{3}}{12}}-{\frac{5645\,{x}^{2}}{16}}-{\frac{8453\,x}{16}}-{\frac{9317\,\ln \left ( 2\,x-1 \right ) }{32}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01314, size = 36, normalized size = 0.97 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \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 = 1.28684, size = 101, normalized size = 2.73 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \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 = 0.091192, size = 36, normalized size = 0.97 \begin{align*} - \frac{375 x^{4}}{8} - \frac{2225 x^{3}}{12} - \frac{5645 x^{2}}{16} - \frac{8453 x}{16} - \frac{9317 \log{\left (2 x - 1 \right )}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.77631, size = 38, normalized size = 1.03 \begin{align*} -\frac{375}{8} \, x^{4} - \frac{2225}{12} \, x^{3} - \frac{5645}{16} \, x^{2} - \frac{8453}{16} \, x - \frac{9317}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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