Optimal. Leaf size=34 \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]
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Rubi [A] time = 0.0193035, 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} \[ -\frac{10}{243} (3 x+2)^9+\frac{37}{216} (3 x+2)^8-\frac{1}{27} (3 x+2)^7 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx &=\int \left (-\frac{7}{9} (2+3 x)^6+\frac{37}{9} (2+3 x)^7-\frac{10}{9} (2+3 x)^8\right ) \, dx\\ &=-\frac{1}{27} (2+3 x)^7+\frac{37}{216} (2+3 x)^8-\frac{10}{243} (2+3 x)^9\\ \end{align*}
Mathematica [A] time = 0.0023265, size = 48, normalized size = 1.41 \[ -810 x^9-\frac{29889 x^8}{8}-7047 x^7-6552 x^6-2268 x^5+1260 x^4+\frac{5264 x^3}{3}+832 x^2+192 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 45, normalized size = 1.3 \begin{align*} -810\,{x}^{9}-{\frac{29889\,{x}^{8}}{8}}-7047\,{x}^{7}-6552\,{x}^{6}-2268\,{x}^{5}+1260\,{x}^{4}+{\frac{5264\,{x}^{3}}{3}}+832\,{x}^{2}+192\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.1865, size = 59, normalized size = 1.74 \begin{align*} -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28706, size = 134, normalized size = 3.94 \begin{align*} -810 x^{9} - \frac{29889}{8} x^{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264}{3} x^{3} + 832 x^{2} + 192 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065316, size = 46, normalized size = 1.35 \begin{align*} - 810 x^{9} - \frac{29889 x^{8}}{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac{5264 x^{3}}{3} + 832 x^{2} + 192 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.5213, size = 59, normalized size = 1.74 \begin{align*} -810 \, x^{9} - \frac{29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac{5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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