Optimal. Leaf size=23 \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]
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Rubi [A] time = 0.0080378, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int (1-2 x)^2 (3+5 x) \, dx &=\int \left (3-7 x-8 x^2+20 x^3\right ) \, dx\\ &=3 x-\frac{7 x^2}{2}-\frac{8 x^3}{3}+5 x^4\\ \end{align*}
Mathematica [A] time = 0.0006351, size = 23, normalized size = 1. \[ 5 x^4-\frac{8 x^3}{3}-\frac{7 x^2}{2}+3 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 20, normalized size = 0.9 \begin{align*} 3\,x-{\frac{7\,{x}^{2}}{2}}-{\frac{8\,{x}^{3}}{3}}+5\,{x}^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.51226, size = 26, normalized size = 1.13 \begin{align*} 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33897, size = 45, normalized size = 1.96 \begin{align*} 5 x^{4} - \frac{8}{3} x^{3} - \frac{7}{2} x^{2} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.057019, size = 20, normalized size = 0.87 \begin{align*} 5 x^{4} - \frac{8 x^{3}}{3} - \frac{7 x^{2}}{2} + 3 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.03925, size = 26, normalized size = 1.13 \begin{align*} 5 \, x^{4} - \frac{8}{3} \, x^{3} - \frac{7}{2} \, x^{2} + 3 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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