Optimal. Leaf size=34 \[ \frac {10 x^2}{9}-\frac {104 x}{27}+\frac {49}{81 (3 x+2)}+\frac {91}{27} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 34, 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} \[ \frac {10 x^2}{9}-\frac {104 x}{27}+\frac {49}{81 (3 x+2)}+\frac {91}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac {104}{27}+\frac {20 x}{9}-\frac {49}{27 (2+3 x)^2}+\frac {91}{9 (2+3 x)}\right ) \, dx\\ &=-\frac {104 x}{27}+\frac {10 x^2}{9}+\frac {49}{81 (2+3 x)}+\frac {91}{27} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 39, normalized size = 1.15 \[ \frac {540 x^3-1512 x^2-447 x+546 (3 x+2) \log (6 x+4)+632}{162 (3 x+2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 37, normalized size = 1.09 \[ \frac {270 \, x^{3} - 756 \, x^{2} + 273 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 624 \, x + 49}{81 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 48, normalized size = 1.41 \[ -\frac {2}{81} \, {\left (3 \, x + 2\right )}^{2} {\left (\frac {72}{3 \, x + 2} - 5\right )} + \frac {49}{81 \, {\left (3 \, x + 2\right )}} - \frac {91}{27} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.79 \[ \frac {10 x^{2}}{9}-\frac {104 x}{27}+\frac {91 \ln \left (3 x +2\right )}{27}+\frac {49}{81 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 26, normalized size = 0.76 \[ \frac {10}{9} \, x^{2} - \frac {104}{27} \, x + \frac {49}{81 \, {\left (3 \, x + 2\right )}} + \frac {91}{27} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.71 \[ \frac {91\,\ln \left (x+\frac {2}{3}\right )}{27}-\frac {104\,x}{27}+\frac {49}{243\,\left (x+\frac {2}{3}\right )}+\frac {10\,x^2}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 27, normalized size = 0.79 \[ \frac {10 x^{2}}{9} - \frac {104 x}{27} + \frac {91 \log {\left (3 x + 2 \right )}}{27} + \frac {49}{243 x + 162} \]
Verification of antiderivative is not currently implemented for this CAS.
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