Optimal. Leaf size=37 \[ -\frac{6 x^4}{5}+\frac{172 x^3}{75}-\frac{183 x^2}{125}-\frac{27 x}{625}+\frac{1331 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0131486, 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} \[ -\frac{6 x^4}{5}+\frac{172 x^3}{75}-\frac{183 x^2}{125}-\frac{27 x}{625}+\frac{1331 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)}{3+5 x} \, dx &=\int \left (-\frac{27}{625}-\frac{366 x}{125}+\frac{172 x^2}{25}-\frac{24 x^3}{5}+\frac{1331}{625 (3+5 x)}\right ) \, dx\\ &=-\frac{27 x}{625}-\frac{183 x^2}{125}+\frac{172 x^3}{75}-\frac{6 x^4}{5}+\frac{1331 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0128692, size = 35, normalized size = 0.95 \[ \frac{3993 \log (5 x+3)-5 \left (2250 x^4-4300 x^3+2745 x^2+81 x-2160\right )}{9375} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 0.8 \begin{align*} -{\frac{27\,x}{625}}-{\frac{183\,{x}^{2}}{125}}+{\frac{172\,{x}^{3}}{75}}-{\frac{6\,{x}^{4}}{5}}+{\frac{1331\,\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 = 1.05946, size = 36, normalized size = 0.97 \begin{align*} -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{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 = 1.52552, size = 99, normalized size = 2.68 \begin{align*} -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{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 = 0.085847, size = 34, normalized size = 0.92 \begin{align*} - \frac{6 x^{4}}{5} + \frac{172 x^{3}}{75} - \frac{183 x^{2}}{125} - \frac{27 x}{625} + \frac{1331 \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 = 2.23316, size = 38, normalized size = 1.03 \begin{align*} -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{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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