Optimal. Leaf size=30 \[ \frac {20 x^3}{9}-\frac {32 x^2}{9}+\frac {65 x}{27}-\frac {49}{81} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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} \begin {gather*} \frac {20 x^3}{9}-\frac {32 x^2}{9}+\frac {65 x}{27}-\frac {49}{81} \log (3 x+2) \end {gather*}
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} \, dx &=\int \left (\frac {65}{27}-\frac {64 x}{9}+\frac {20 x^2}{3}-\frac {49}{27 (2+3 x)}\right ) \, dx\\ &=\frac {65 x}{27}-\frac {32 x^2}{9}+\frac {20 x^3}{9}-\frac {49}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.90 \begin {gather*} \frac {1}{243} \left (540 x^3-864 x^2+585 x-147 \log (3 x+2)+934\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2 (3+5 x)}{2+3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.65, size = 22, normalized size = 0.73 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.18, size = 23, normalized size = 0.77 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.77 \begin {gather*} \frac {20 x^{3}}{9}-\frac {32 x^{2}}{9}+\frac {65 x}{27}-\frac {49 \ln \left (3 x +2\right )}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 22, normalized size = 0.73 \begin {gather*} \frac {20}{9} \, x^{3} - \frac {32}{9} \, x^{2} + \frac {65}{27} \, x - \frac {49}{81} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.67 \begin {gather*} \frac {65\,x}{27}-\frac {49\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {32\,x^2}{9}+\frac {20\,x^3}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 27, normalized size = 0.90 \begin {gather*} \frac {20 x^{3}}{9} - \frac {32 x^{2}}{9} + \frac {65 x}{27} - \frac {49 \log {\left (3 x + 2 \right )}}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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