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 = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.89, size = 27, normalized size = 0.73 \[ -\frac {375}{8} \, x^{4} - \frac {2225}{12} \, x^{3} - \frac {5645}{16} \, x^{2} - \frac {8453}{16} \, x - \frac {9317}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 28, normalized size = 0.76 \[ -\frac {375}{8} \, x^{4} - \frac {2225}{12} \, x^{3} - \frac {5645}{16} \, x^{2} - \frac {8453}{16} \, x - \frac {9317}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {375 x^{4}}{8}-\frac {2225 x^{3}}{12}-\frac {5645 x^{2}}{16}-\frac {8453 x}{16}-\frac {9317 \ln \left (2 x -1\right )}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 27, normalized size = 0.73 \[ -\frac {375}{8} \, x^{4} - \frac {2225}{12} \, x^{3} - \frac {5645}{16} \, x^{2} - \frac {8453}{16} \, x - \frac {9317}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 25, normalized size = 0.68 \[ -\frac {8453\,x}{16}-\frac {9317\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {5645\,x^2}{16}-\frac {2225\,x^3}{12}-\frac {375\,x^4}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 36, normalized size = 0.97 \[ - \frac {375 x^{4}}{8} - \frac {2225 x^{3}}{12} - \frac {5645 x^{2}}{16} - \frac {8453 x}{16} - \frac {9317 \log {\left (2 x - 1 \right )}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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