Optimal. Leaf size=40 \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]
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Rubi [A] time = 0.0172792, antiderivative size = 40, 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} \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx &=\int \left (12-16 x-105 x^2+99 x^3+326 x^4-156 x^5-360 x^6\right ) \, dx\\ &=12 x-8 x^2-35 x^3+\frac{99 x^4}{4}+\frac{326 x^5}{5}-26 x^6-\frac{360 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0008698, size = 40, normalized size = 1. \[ -\frac{360 x^7}{7}-26 x^6+\frac{326 x^5}{5}+\frac{99 x^4}{4}-35 x^3-8 x^2+12 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 35, normalized size = 0.9 \begin{align*} 12\,x-8\,{x}^{2}-35\,{x}^{3}+{\frac{99\,{x}^{4}}{4}}+{\frac{326\,{x}^{5}}{5}}-26\,{x}^{6}-{\frac{360\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.14528, size = 46, normalized size = 1.15 \begin{align*} -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19916, size = 92, normalized size = 2.3 \begin{align*} -\frac{360}{7} x^{7} - 26 x^{6} + \frac{326}{5} x^{5} + \frac{99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060783, size = 37, normalized size = 0.92 \begin{align*} - \frac{360 x^{7}}{7} - 26 x^{6} + \frac{326 x^{5}}{5} + \frac{99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.98691, size = 46, normalized size = 1.15 \begin{align*} -\frac{360}{7} \, x^{7} - 26 \, x^{6} + \frac{326}{5} \, x^{5} + \frac{99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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