Optimal. Leaf size=34 \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]
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Rubi [A] time = 0.0144095, 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} \[ -\frac{5}{16} (1-2 x)^6+\frac{17}{10} (1-2 x)^5-\frac{77}{32} (1-2 x)^4 \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x) (3+5 x) \, dx &=\int \left (\frac{77}{4} (1-2 x)^3-17 (1-2 x)^4+\frac{15}{4} (1-2 x)^5\right ) \, dx\\ &=-\frac{77}{32} (1-2 x)^4+\frac{17}{10} (1-2 x)^5-\frac{5}{16} (1-2 x)^6\\ \end{align*}
Mathematica [A] time = 0.0007683, size = 35, normalized size = 1.03 \[ -20 x^6+\frac{28 x^5}{5}+\frac{45 x^4}{2}-9 x^3-\frac{17 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 0.9 \begin{align*} -20\,{x}^{6}+{\frac{28\,{x}^{5}}{5}}+{\frac{45\,{x}^{4}}{2}}-9\,{x}^{3}-{\frac{17\,{x}^{2}}{2}}+6\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.28086, size = 39, normalized size = 1.15 \begin{align*} -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.13918, size = 76, normalized size = 2.24 \begin{align*} -20 x^{6} + \frac{28}{5} x^{5} + \frac{45}{2} x^{4} - 9 x^{3} - \frac{17}{2} x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05735, size = 32, normalized size = 0.94 \begin{align*} - 20 x^{6} + \frac{28 x^{5}}{5} + \frac{45 x^{4}}{2} - 9 x^{3} - \frac{17 x^{2}}{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.32989, size = 39, normalized size = 1.15 \begin{align*} -20 \, x^{6} + \frac{28}{5} \, x^{5} + \frac{45}{2} \, x^{4} - 9 \, x^{3} - \frac{17}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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