Optimal. Leaf size=34 \[ -\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4 \]
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Rubi [A] time = 0.0143311, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{25}{48} (1-2 x)^6+\frac{11}{4} (1-2 x)^5-\frac{121}{32} (1-2 x)^4 \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^3 (3+5 x)^2 \, dx &=\int \left (\frac{121}{4} (1-2 x)^3-\frac{55}{2} (1-2 x)^4+\frac{25}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac{121}{32} (1-2 x)^4+\frac{11}{4} (1-2 x)^5-\frac{25}{48} (1-2 x)^6\\ \end{align*}
Mathematica [A] time = 0.0008315, size = 35, normalized size = 1.03 \[ -\frac{100 x^6}{3}+12 x^5+\frac{69 x^4}{2}-\frac{47 x^3}{3}-12 x^2+9 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 30, normalized size = 0.9 \begin{align*} -{\frac{100\,{x}^{6}}{3}}+12\,{x}^{5}+{\frac{69\,{x}^{4}}{2}}-{\frac{47\,{x}^{3}}{3}}-12\,{x}^{2}+9\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.88086, size = 39, normalized size = 1.15 \begin{align*} -\frac{100}{3} \, x^{6} + 12 \, x^{5} + \frac{69}{2} \, x^{4} - \frac{47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.09641, size = 78, normalized size = 2.29 \begin{align*} -\frac{100}{3} x^{6} + 12 x^{5} + \frac{69}{2} x^{4} - \frac{47}{3} x^{3} - 12 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.061568, size = 32, normalized size = 0.94 \begin{align*} - \frac{100 x^{6}}{3} + 12 x^{5} + \frac{69 x^{4}}{2} - \frac{47 x^{3}}{3} - 12 x^{2} + 9 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.61225, size = 39, normalized size = 1.15 \begin{align*} -\frac{100}{3} \, x^{6} + 12 \, x^{5} + \frac{69}{2} \, x^{4} - \frac{47}{3} \, x^{3} - 12 \, x^{2} + 9 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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