Optimal. Leaf size=49 \[ -\frac {40 x}{81}+\frac {518}{81 (3 x+2)}-\frac {2009}{486 (3 x+2)^2}+\frac {343}{729 (3 x+2)^3}+\frac {428}{243} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 49, 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} \[ -\frac {40 x}{81}+\frac {518}{81 (3 x+2)}-\frac {2009}{486 (3 x+2)^2}+\frac {343}{729 (3 x+2)^3}+\frac {428}{243} \log (3 x+2) \]
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)^4} \, dx &=\int \left (-\frac {40}{81}-\frac {343}{81 (2+3 x)^4}+\frac {2009}{81 (2+3 x)^3}-\frac {518}{27 (2+3 x)^2}+\frac {428}{81 (2+3 x)}\right ) \, dx\\ &=-\frac {40 x}{81}+\frac {343}{729 (2+3 x)^3}-\frac {2009}{486 (2+3 x)^2}+\frac {518}{81 (2+3 x)}+\frac {428}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 46, normalized size = 0.94 \[ \frac {-19440 x^4-51840 x^3+32076 x^2+70767 x+2568 (3 x+2)^3 \log (3 x+2)+22088}{1458 (3 x+2)^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 62, normalized size = 1.27 \[ -\frac {19440 \, x^{4} + 38880 \, x^{3} - 57996 \, x^{2} - 2568 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 88047 \, x - 25928}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.80, size = 32, normalized size = 0.65 \[ -\frac {40}{81} \, x + \frac {7 \, {\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \, {\left (3 \, x + 2\right )}^{3}} + \frac {428}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 40, normalized size = 0.82 \[ -\frac {40 x}{81}+\frac {428 \ln \left (3 x +2\right )}{243}+\frac {343}{729 \left (3 x +2\right )^{3}}-\frac {2009}{486 \left (3 x +2\right )^{2}}+\frac {518}{81 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 41, normalized size = 0.84 \[ -\frac {40}{81} \, x + \frac {7 \, {\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {428}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 36, normalized size = 0.73 \[ \frac {428\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {40\,x}{81}+\frac {\frac {518\,x^2}{243}+\frac {10423\,x}{4374}+\frac {12964}{19683}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 41, normalized size = 0.84 \[ - \frac {40 x}{81} - \frac {- 83916 x^{2} - 93807 x - 25928}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac {428 \log {\left (3 x + 2 \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
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