Optimal. Leaf size=34 \[ -\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4 \]
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Rubi [A] time = 0.0144945, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{5}{81} (3 x+2)^6+\frac{37}{135} (3 x+2)^5-\frac{7}{108} (3 x+2)^4 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^3 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^3+\frac{37}{9} (2+3 x)^4-\frac{10}{9} (2+3 x)^5\right ) \, dx\\ &=-\frac{7}{108} (2+3 x)^4+\frac{37}{135} (2+3 x)^5-\frac{5}{81} (2+3 x)^6\\ \end{align*}
Mathematica [A] time = 0.0009359, size = 35, normalized size = 1.03 \[ -45 x^6-\frac{567 x^5}{5}-\frac{333 x^4}{4}+\frac{46 x^3}{3}+50 x^2+24 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 0.9 \begin{align*} -45\,{x}^{6}-{\frac{567\,{x}^{5}}{5}}-{\frac{333\,{x}^{4}}{4}}+{\frac{46\,{x}^{3}}{3}}+50\,{x}^{2}+24\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09581, size = 39, normalized size = 1.15 \begin{align*} -45 \, x^{6} - \frac{567}{5} \, x^{5} - \frac{333}{4} \, x^{4} + \frac{46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28403, size = 81, normalized size = 2.38 \begin{align*} -45 x^{6} - \frac{567}{5} x^{5} - \frac{333}{4} x^{4} + \frac{46}{3} x^{3} + 50 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058004, size = 32, normalized size = 0.94 \begin{align*} - 45 x^{6} - \frac{567 x^{5}}{5} - \frac{333 x^{4}}{4} + \frac{46 x^{3}}{3} + 50 x^{2} + 24 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.48673, size = 39, normalized size = 1.15 \begin{align*} -45 \, x^{6} - \frac{567}{5} \, x^{5} - \frac{333}{4} \, x^{4} + \frac{46}{3} \, x^{3} + 50 \, x^{2} + 24 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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