Optimal. Leaf size=45 \[ -\frac{5}{81} (3 x+2)^{10}+\frac{65}{243} (3 x+2)^9-\frac{1}{9} (3 x+2)^8+\frac{1}{81} (3 x+2)^7 \]
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Rubi [A] time = 0.0242123, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{5}{81} (3 x+2)^{10}+\frac{65}{243} (3 x+2)^9-\frac{1}{9} (3 x+2)^8+\frac{1}{81} (3 x+2)^7 \]
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)^2 \, dx &=\int \left (\frac{7}{27} (2+3 x)^6-\frac{8}{3} (2+3 x)^7+\frac{65}{9} (2+3 x)^8-\frac{50}{27} (2+3 x)^9\right ) \, dx\\ &=\frac{1}{81} (2+3 x)^7-\frac{1}{9} (2+3 x)^8+\frac{65}{243} (2+3 x)^9-\frac{5}{81} (2+3 x)^{10}\\ \end{align*}
Mathematica [A] time = 0.0021809, size = 51, normalized size = 1.13 \[ -3645 x^{10}-19035 x^9-42039 x^8-49221 x^7-29106 x^6-1764 x^5+10360 x^4+\frac{24112 x^3}{3}+2976 x^2+576 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 50, normalized size = 1.1 \begin{align*} -3645\,{x}^{10}-19035\,{x}^{9}-42039\,{x}^{8}-49221\,{x}^{7}-29106\,{x}^{6}-1764\,{x}^{5}+10360\,{x}^{4}+{\frac{24112\,{x}^{3}}{3}}+2976\,{x}^{2}+576\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.26269, size = 66, normalized size = 1.47 \begin{align*} -3645 \, x^{10} - 19035 \, x^{9} - 42039 \, x^{8} - 49221 \, x^{7} - 29106 \, x^{6} - 1764 \, x^{5} + 10360 \, x^{4} + \frac{24112}{3} \, x^{3} + 2976 \, x^{2} + 576 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.38196, size = 157, normalized size = 3.49 \begin{align*} -3645 x^{10} - 19035 x^{9} - 42039 x^{8} - 49221 x^{7} - 29106 x^{6} - 1764 x^{5} + 10360 x^{4} + \frac{24112}{3} x^{3} + 2976 x^{2} + 576 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.067348, size = 49, normalized size = 1.09 \begin{align*} - 3645 x^{10} - 19035 x^{9} - 42039 x^{8} - 49221 x^{7} - 29106 x^{6} - 1764 x^{5} + 10360 x^{4} + \frac{24112 x^{3}}{3} + 2976 x^{2} + 576 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.54822, size = 66, normalized size = 1.47 \begin{align*} -3645 \, x^{10} - 19035 \, x^{9} - 42039 \, x^{8} - 49221 \, x^{7} - 29106 \, x^{6} - 1764 \, x^{5} + 10360 \, x^{4} + \frac{24112}{3} \, x^{3} + 2976 \, x^{2} + 576 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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