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 = 0.0139055, 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} \[ -\frac{135 x^4}{8}-\frac{279 x^3}{4}-\frac{2205 x^2}{16}-\frac{3389 x}{16}-\frac{3773}{32} \log (1-2 x) \]
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*}
Mathematica [A] time = 0.0113969, 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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Maple [A] time = 0.002, size = 28, normalized size = 0.8 \begin{align*} -{\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05818, size = 36, normalized size = 0.97 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31611, size = 99, normalized size = 2.68 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089228, size = 36, normalized size = 0.97 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.43337, size = 38, normalized size = 1.03 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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