Optimal. Leaf size=35 \[ 30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x \]
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Rubi [A] time = 0.0134748, antiderivative size = 35, 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} \[ 30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^2 (2+3 x)^2 (3+5 x) \, dx &=\int \left (12+8 x-89 x^2-79 x^3+168 x^4+180 x^5\right ) \, dx\\ &=12 x+4 x^2-\frac{89 x^3}{3}-\frac{79 x^4}{4}+\frac{168 x^5}{5}+30 x^6\\ \end{align*}
Mathematica [A] time = 0.0014862, size = 35, normalized size = 1. \[ 30 x^6+\frac{168 x^5}{5}-\frac{79 x^4}{4}-\frac{89 x^3}{3}+4 x^2+12 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 30, normalized size = 0.9 \begin{align*} 12\,x+4\,{x}^{2}-{\frac{89\,{x}^{3}}{3}}-{\frac{79\,{x}^{4}}{4}}+{\frac{168\,{x}^{5}}{5}}+30\,{x}^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07669, size = 39, normalized size = 1.11 \begin{align*} 30 \, x^{6} + \frac{168}{5} \, x^{5} - \frac{79}{4} \, x^{4} - \frac{89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31742, size = 77, normalized size = 2.2 \begin{align*} 30 x^{6} + \frac{168}{5} x^{5} - \frac{79}{4} x^{4} - \frac{89}{3} x^{3} + 4 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.059202, size = 32, normalized size = 0.91 \begin{align*} 30 x^{6} + \frac{168 x^{5}}{5} - \frac{79 x^{4}}{4} - \frac{89 x^{3}}{3} + 4 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.664, size = 39, normalized size = 1.11 \begin{align*} 30 \, x^{6} + \frac{168}{5} \, x^{5} - \frac{79}{4} \, x^{4} - \frac{89}{3} \, x^{3} + 4 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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