Optimal. Leaf size=41 \[ -\frac {40 x^3}{27}+\frac {134 x^2}{27}-\frac {286 x}{27}+\frac {343}{243 (3 x+2)}+\frac {2009}{243} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 41, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {40 x^3}{27}+\frac {134 x^2}{27}-\frac {286 x}{27}+\frac {343}{243 (3 x+2)}+\frac {2009}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac {286}{27}+\frac {268 x}{27}-\frac {40 x^2}{9}-\frac {343}{81 (2+3 x)^2}+\frac {2009}{81 (2+3 x)}\right ) \, dx\\ &=-\frac {286 x}{27}+\frac {134 x^2}{27}-\frac {40 x^3}{27}+\frac {343}{243 (2+3 x)}+\frac {2009}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 44, normalized size = 1.07 \[ \frac {-2160 x^4+5796 x^3-10620 x^2-4113 x+4018 (3 x+2) \log (6 x+4)+4808}{486 (3 x+2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 42, normalized size = 1.02 \[ -\frac {1080 \, x^{4} - 2898 \, x^{3} + 5310 \, x^{2} - 2009 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 5148 \, x - 343}{243 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.95, size = 57, normalized size = 1.39 \[ \frac {2}{729} \, {\left (3 \, x + 2\right )}^{3} {\left (\frac {321}{3 \, x + 2} - \frac {2331}{{\left (3 \, x + 2\right )}^{2}} - 20\right )} + \frac {343}{243 \, {\left (3 \, x + 2\right )}} - \frac {2009}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 32, normalized size = 0.78 \[ -\frac {40 x^{3}}{27}+\frac {134 x^{2}}{27}-\frac {286 x}{27}+\frac {2009 \ln \left (3 x +2\right )}{243}+\frac {343}{243 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 31, normalized size = 0.76 \[ -\frac {40}{27} \, x^{3} + \frac {134}{27} \, x^{2} - \frac {286}{27} \, x + \frac {343}{243 \, {\left (3 \, x + 2\right )}} + \frac {2009}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.71 \[ \frac {2009\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {286\,x}{27}+\frac {343}{729\,\left (x+\frac {2}{3}\right )}+\frac {134\,x^2}{27}-\frac {40\,x^3}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 34, normalized size = 0.83 \[ - \frac {40 x^{3}}{27} + \frac {134 x^{2}}{27} - \frac {286 x}{27} + \frac {2009 \log {\left (3 x + 2 \right )}}{243} + \frac {343}{729 x + 486} \]
Verification of antiderivative is not currently implemented for this CAS.
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