Optimal. Leaf size=37 \[ -\frac{27 x^4}{10}-\frac{81 x^3}{25}+\frac{279 x^2}{250}+\frac{1663 x}{625}+\frac{11 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0127903, 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} \[ -\frac{27 x^4}{10}-\frac{81 x^3}{25}+\frac{279 x^2}{250}+\frac{1663 x}{625}+\frac{11 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^3}{3+5 x} \, dx &=\int \left (\frac{1663}{625}+\frac{279 x}{125}-\frac{243 x^2}{25}-\frac{54 x^3}{5}+\frac{11}{625 (3+5 x)}\right ) \, dx\\ &=\frac{1663 x}{625}+\frac{279 x^2}{250}-\frac{81 x^3}{25}-\frac{27 x^4}{10}+\frac{11 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0118916, size = 35, normalized size = 0.95 \[ \frac{5 \left (-3375 x^4-4050 x^3+1395 x^2+3326 x+1056\right )+22 \log (5 x+3)}{6250} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 0.8 \begin{align*}{\frac{1663\,x}{625}}+{\frac{279\,{x}^{2}}{250}}-{\frac{81\,{x}^{3}}{25}}-{\frac{27\,{x}^{4}}{10}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14828, size = 36, normalized size = 0.97 \begin{align*} -\frac{27}{10} \, x^{4} - \frac{81}{25} \, x^{3} + \frac{279}{250} \, x^{2} + \frac{1663}{625} \, x + \frac{11}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48107, size = 100, normalized size = 2.7 \begin{align*} -\frac{27}{10} \, x^{4} - \frac{81}{25} \, x^{3} + \frac{279}{250} \, x^{2} + \frac{1663}{625} \, x + \frac{11}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.085246, size = 34, normalized size = 0.92 \begin{align*} - \frac{27 x^{4}}{10} - \frac{81 x^{3}}{25} + \frac{279 x^{2}}{250} + \frac{1663 x}{625} + \frac{11 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.10521, size = 38, normalized size = 1.03 \begin{align*} -\frac{27}{10} \, x^{4} - \frac{81}{25} \, x^{3} + \frac{279}{250} \, x^{2} + \frac{1663}{625} \, x + \frac{11}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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