Optimal. Leaf size=44 \[ -\frac {40 x^5}{3}+\frac {145 x^4}{9}+\frac {82 x^3}{81}-\frac {1433 x^2}{162}+\frac {922 x}{243}+\frac {343}{729} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {40 x^5}{3}+\frac {145 x^4}{9}+\frac {82 x^3}{81}-\frac {1433 x^2}{162}+\frac {922 x}{243}+\frac {343}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac {922}{243}-\frac {1433 x}{81}+\frac {82 x^2}{27}+\frac {580 x^3}{9}-\frac {200 x^4}{3}+\frac {343}{243 (2+3 x)}\right ) \, dx\\ &=\frac {922 x}{243}-\frac {1433 x^2}{162}+\frac {82 x^3}{81}+\frac {145 x^4}{9}-\frac {40 x^5}{3}+\frac {343}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 37, normalized size = 0.84 \[ \frac {-58320 x^5+70470 x^4+4428 x^3-38691 x^2+16596 x+2058 \log (3 x+2)+7972}{4374} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 32, normalized size = 0.73 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 33, normalized size = 0.75 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.75 \[ -\frac {40 x^{5}}{3}+\frac {145 x^{4}}{9}+\frac {82 x^{3}}{81}-\frac {1433 x^{2}}{162}+\frac {922 x}{243}+\frac {343 \ln \left (3 x +2\right )}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 32, normalized size = 0.73 \[ -\frac {40}{3} \, x^{5} + \frac {145}{9} \, x^{4} + \frac {82}{81} \, x^{3} - \frac {1433}{162} \, x^{2} + \frac {922}{243} \, x + \frac {343}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 30, normalized size = 0.68 \[ \frac {922\,x}{243}+\frac {343\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1433\,x^2}{162}+\frac {82\,x^3}{81}+\frac {145\,x^4}{9}-\frac {40\,x^5}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 41, normalized size = 0.93 \[ - \frac {40 x^{5}}{3} + \frac {145 x^{4}}{9} + \frac {82 x^{3}}{81} - \frac {1433 x^{2}}{162} + \frac {922 x}{243} + \frac {343 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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