Optimal. Leaf size=45 \[ -\frac {125 x^2}{27}+\frac {175 x}{27}-\frac {107}{243 (3 x+2)}+\frac {7}{486 (3 x+2)^2}-\frac {185}{81} \log (3 x+2) \]
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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} \[ -\frac {125 x^2}{27}+\frac {175 x}{27}-\frac {107}{243 (3 x+2)}+\frac {7}{486 (3 x+2)^2}-\frac {185}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx &=\int \left (\frac {175}{27}-\frac {250 x}{27}-\frac {7}{81 (2+3 x)^3}+\frac {107}{81 (2+3 x)^2}-\frac {185}{27 (2+3 x)}\right ) \, dx\\ &=\frac {175 x}{27}-\frac {125 x^2}{27}+\frac {7}{486 (2+3 x)^2}-\frac {107}{243 (2+3 x)}-\frac {185}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 1.02 \[ \frac {-6750 x^4+450 x^3+18900 x^2+16386 x-370 (3 x+2)^2 \log (3 x+2)+3993}{162 (3 x+2)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 52, normalized size = 1.16 \[ -\frac {20250 \, x^{4} - 1350 \, x^{3} - 28800 \, x^{2} + 1110 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 11958 \, x + 421}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 32, normalized size = 0.71 \[ -\frac {125}{27} \, x^{2} + \frac {175}{27} \, x - \frac {642 \, x + 421}{486 \, {\left (3 \, x + 2\right )}^{2}} - \frac {185}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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 \[ -\frac {125 x^{2}}{27}+\frac {175 x}{27}-\frac {185 \ln \left (3 x +2\right )}{81}+\frac {7}{486 \left (3 x +2\right )^{2}}-\frac {107}{243 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 36, normalized size = 0.80 \[ -\frac {125}{27} \, x^{2} + \frac {175}{27} \, x - \frac {642 \, x + 421}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {185}{81} \, \log \left (3 \, x + 2\right ) \]
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 \[ \frac {175\,x}{27}-\frac {185\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {\frac {107\,x}{729}+\frac {421}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {125\,x^2}{27} \]
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 \[ - \frac {125 x^{2}}{27} + \frac {175 x}{27} - \frac {642 x + 421}{4374 x^{2} + 5832 x + 1944} - \frac {185 \log {\left (3 x + 2 \right )}}{81} \]
Verification of antiderivative is not currently implemented for this CAS.
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