Optimal. Leaf size=37 \[ -\frac {135 x^4}{8}-\frac {279 x^3}{4}-\frac {2205 x^2}{16}-\frac {3389 x}{16}-\frac {3773}{32} \log (1-2 x) \]
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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} \[ -\frac {135 x^4}{8}-\frac {279 x^3}{4}-\frac {2205 x^2}{16}-\frac {3389 x}{16}-\frac {3773}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {3389}{16}-\frac {2205 x}{8}-\frac {837 x^2}{4}-\frac {135 x^3}{2}-\frac {3773}{16 (-1+2 x)}\right ) \, dx\\ &=-\frac {3389 x}{16}-\frac {2205 x^2}{16}-\frac {279 x^3}{4}-\frac {135 x^4}{8}-\frac {3773}{32} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 32, normalized size = 0.86 \[ \frac {1}{128} \left (-2160 x^4-8928 x^3-17640 x^2-27112 x-15092 \log (1-2 x)+19217\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 27, normalized size = 0.73 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 28, normalized size = 0.76 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {135 x^{4}}{8}-\frac {279 x^{3}}{4}-\frac {2205 x^{2}}{16}-\frac {3389 x}{16}-\frac {3773 \ln \left (2 x -1\right )}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 27, normalized size = 0.73 \[ -\frac {135}{8} \, x^{4} - \frac {279}{4} \, x^{3} - \frac {2205}{16} \, x^{2} - \frac {3389}{16} \, x - \frac {3773}{32} \, \log \left (2 \, x - 1\right ) \]
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 \[ -\frac {3389\,x}{16}-\frac {3773\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {2205\,x^2}{16}-\frac {279\,x^3}{4}-\frac {135\,x^4}{8} \]
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 \[ - \frac {135 x^{4}}{8} - \frac {279 x^{3}}{4} - \frac {2205 x^{2}}{16} - \frac {3389 x}{16} - \frac {3773 \log {\left (2 x - 1 \right )}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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