Optimal. Leaf size=23 \[ -\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2) \]
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Rubi [A] time = 0.0101749, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{5 x^2}{3}+\frac{17 x}{9}-\frac{7}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)}{2+3 x} \, dx &=\int \left (\frac{17}{9}-\frac{10 x}{3}-\frac{7}{9 (2+3 x)}\right ) \, dx\\ &=\frac{17 x}{9}-\frac{5 x^2}{3}-\frac{7}{27} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0053774, size = 22, normalized size = 0.96 \[ \frac{1}{27} \left (-45 x^2+51 x-7 \log (3 x+2)+54\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.8 \begin{align*}{\frac{17\,x}{9}}-{\frac{5\,{x}^{2}}{3}}-{\frac{7\,\ln \left ( 2+3\,x \right ) }{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10713, size = 23, normalized size = 1. \begin{align*} -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \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 = 1.46491, size = 53, normalized size = 2.3 \begin{align*} -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \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 = 0.076814, size = 20, normalized size = 0.87 \begin{align*} - \frac{5 x^{2}}{3} + \frac{17 x}{9} - \frac{7 \log{\left (3 x + 2 \right )}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.33405, size = 24, normalized size = 1.04 \begin{align*} -\frac{5}{3} \, x^{2} + \frac{17}{9} \, x - \frac{7}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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