Optimal. Leaf size=45 \[ -\frac {20 x^2}{27}+\frac {116 x}{27}-\frac {2009}{243 (3 x+2)}+\frac {343}{486 (3 x+2)^2}-\frac {518}{81} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 45, 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} \[ -\frac {20 x^2}{27}+\frac {116 x}{27}-\frac {2009}{243 (3 x+2)}+\frac {343}{486 (3 x+2)^2}-\frac {518}{81} \log (3 x+2) \]
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)^3} \, dx &=\int \left (\frac {116}{27}-\frac {40 x}{27}-\frac {343}{81 (2+3 x)^3}+\frac {2009}{81 (2+3 x)^2}-\frac {518}{27 (2+3 x)}\right ) \, dx\\ &=\frac {116 x}{27}-\frac {20 x^2}{27}+\frac {343}{486 (2+3 x)^2}-\frac {2009}{243 (2+3 x)}-\frac {518}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 1.02 \[ -\frac {3240 x^4-14472 x^3-15030 x^2+15150 x+3108 (3 x+2)^2 \log (6 x+4)+11509}{486 (3 x+2)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 52, normalized size = 1.16 \[ -\frac {3240 \, x^{4} - 14472 \, x^{3} - 23616 \, x^{2} + 3108 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 3702 \, x + 7693}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.98, size = 32, normalized size = 0.71 \[ -\frac {20}{27} \, x^{2} + \frac {116}{27} \, x - \frac {49 \, {\left (246 \, x + 157\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} - \frac {518}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.80 \[ -\frac {20 x^{2}}{27}+\frac {116 x}{27}-\frac {518 \ln \left (3 x +2\right )}{81}+\frac {343}{486 \left (3 x +2\right )^{2}}-\frac {2009}{243 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 36, normalized size = 0.80 \[ -\frac {20}{27} \, x^{2} + \frac {116}{27} \, x - \frac {49 \, {\left (246 \, x + 157\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {518}{81} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 32, normalized size = 0.71 \[ \frac {116\,x}{27}-\frac {518\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {\frac {2009\,x}{729}+\frac {7693}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {20\,x^2}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 36, normalized size = 0.80 \[ - \frac {20 x^{2}}{27} + \frac {116 x}{27} - \frac {12054 x + 7693}{4374 x^{2} + 5832 x + 1944} - \frac {518 \log {\left (3 x + 2 \right )}}{81} \]
Verification of antiderivative is not currently implemented for this CAS.
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