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 = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.91, size = 17, normalized size = 0.74 \[ -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.12, size = 18, normalized size = 0.78 \[ -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ -\frac {5 x^{2}}{3}+\frac {17 x}{9}-\frac {7 \ln \left (3 x +2\right )}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 17, normalized size = 0.74 \[ -\frac {5}{3} \, x^{2} + \frac {17}{9} \, x - \frac {7}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.65 \[ \frac {17\,x}{9}-\frac {7\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {5\,x^2}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 20, normalized size = 0.87 \[ - \frac {5 x^{2}}{3} + \frac {17 x}{9} - \frac {7 \log {\left (3 x + 2 \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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