Optimal. Leaf size=44 \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0191101, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{40 x^5}{3}+\frac{145 x^4}{9}+\frac{82 x^3}{81}-\frac{1433 x^2}{162}+\frac{922 x}{243}+\frac{343}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac{922}{243}-\frac{1433 x}{81}+\frac{82 x^2}{27}+\frac{580 x^3}{9}-\frac{200 x^4}{3}+\frac{343}{243 (2+3 x)}\right ) \, dx\\ &=\frac{922 x}{243}-\frac{1433 x^2}{162}+\frac{82 x^3}{81}+\frac{145 x^4}{9}-\frac{40 x^5}{3}+\frac{343}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0105508, size = 37, normalized size = 0.84 \[ \frac{-58320 x^5+70470 x^4+4428 x^3-38691 x^2+16596 x+2058 \log (3 x+2)+7972}{4374} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 33, normalized size = 0.8 \begin{align*}{\frac{922\,x}{243}}-{\frac{1433\,{x}^{2}}{162}}+{\frac{82\,{x}^{3}}{81}}+{\frac{145\,{x}^{4}}{9}}-{\frac{40\,{x}^{5}}{3}}+{\frac{343\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994317, size = 43, normalized size = 0.98 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28992, size = 115, normalized size = 2.61 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091572, size = 41, normalized size = 0.93 \begin{align*} - \frac{40 x^{5}}{3} + \frac{145 x^{4}}{9} + \frac{82 x^{3}}{81} - \frac{1433 x^{2}}{162} + \frac{922 x}{243} + \frac{343 \log{\left (3 x + 2 \right )}}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.41679, size = 45, normalized size = 1.02 \begin{align*} -\frac{40}{3} \, x^{5} + \frac{145}{9} \, x^{4} + \frac{82}{81} \, x^{3} - \frac{1433}{162} \, x^{2} + \frac{922}{243} \, x + \frac{343}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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