Optimal. Leaf size=37 \[ -\frac {125 x^4}{6}-\frac {475 x^3}{27}+\frac {545 x^2}{54}+\frac {1097 x}{81}-\frac {7}{243} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 37, 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} \[ -\frac {125 x^4}{6}-\frac {475 x^3}{27}+\frac {545 x^2}{54}+\frac {1097 x}{81}-\frac {7}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac {1097}{81}+\frac {545 x}{27}-\frac {475 x^2}{9}-\frac {250 x^3}{3}-\frac {7}{81 (2+3 x)}\right ) \, dx\\ &=\frac {1097 x}{81}+\frac {545 x^2}{54}-\frac {475 x^3}{27}-\frac {125 x^4}{6}-\frac {7}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 32, normalized size = 0.86 \[ \frac {-30375 x^4-25650 x^3+14715 x^2+19746 x-42 \log (3 x+2)+5024}{1458} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 27, normalized size = 0.73 \[ -\frac {125}{6} \, x^{4} - \frac {475}{27} \, x^{3} + \frac {545}{54} \, x^{2} + \frac {1097}{81} \, x - \frac {7}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 28, normalized size = 0.76 \[ -\frac {125}{6} \, x^{4} - \frac {475}{27} \, x^{3} + \frac {545}{54} \, x^{2} + \frac {1097}{81} \, x - \frac {7}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 0.76 \[ -\frac {125 x^{4}}{6}-\frac {475 x^{3}}{27}+\frac {545 x^{2}}{54}+\frac {1097 x}{81}-\frac {7 \ln \left (3 x +2\right )}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 27, normalized size = 0.73 \[ -\frac {125}{6} \, x^{4} - \frac {475}{27} \, x^{3} + \frac {545}{54} \, x^{2} + \frac {1097}{81} \, x - \frac {7}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 25, normalized size = 0.68 \[ \frac {1097\,x}{81}-\frac {7\,\ln \left (x+\frac {2}{3}\right )}{243}+\frac {545\,x^2}{54}-\frac {475\,x^3}{27}-\frac {125\,x^4}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 34, normalized size = 0.92 \[ - \frac {125 x^{4}}{6} - \frac {475 x^{3}}{27} + \frac {545 x^{2}}{54} + \frac {1097 x}{81} - \frac {7 \log {\left (3 x + 2 \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
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