Optimal. Leaf size=42 \[ \frac{20 x^7}{7}-\frac{17 x^6}{6}+\frac{17 x^5}{5}-x^4+7 x^3+\frac{7 x^2}{2}+6 x \]
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Rubi [A] time = 0.0248029, antiderivative size = 42, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.034, Rules used = {1657} \[ \frac{20 x^7}{7}-\frac{17 x^6}{6}+\frac{17 x^5}{5}-x^4+7 x^3+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin{align*} \int \left (3+2 x+5 x^2\right ) \left (2+x+3 x^2-5 x^3+4 x^4\right ) \, dx &=\int \left (6+7 x+21 x^2-4 x^3+17 x^4-17 x^5+20 x^6\right ) \, dx\\ &=6 x+\frac{7 x^2}{2}+7 x^3-x^4+\frac{17 x^5}{5}-\frac{17 x^6}{6}+\frac{20 x^7}{7}\\ \end{align*}
Mathematica [A] time = 0.0014784, size = 42, normalized size = 1. \[ \frac{20 x^7}{7}-\frac{17 x^6}{6}+\frac{17 x^5}{5}-x^4+7 x^3+\frac{7 x^2}{2}+6 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 35, normalized size = 0.8 \begin{align*} 6\,x+{\frac{7\,{x}^{2}}{2}}+7\,{x}^{3}-{x}^{4}+{\frac{17\,{x}^{5}}{5}}-{\frac{17\,{x}^{6}}{6}}+{\frac{20\,{x}^{7}}{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.969959, size = 46, normalized size = 1.1 \begin{align*} \frac{20}{7} \, x^{7} - \frac{17}{6} \, x^{6} + \frac{17}{5} \, x^{5} - x^{4} + 7 \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.868683, size = 84, normalized size = 2. \begin{align*} \frac{20}{7} x^{7} - \frac{17}{6} x^{6} + \frac{17}{5} x^{5} - x^{4} + 7 x^{3} + \frac{7}{2} x^{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.063344, size = 37, normalized size = 0.88 \begin{align*} \frac{20 x^{7}}{7} - \frac{17 x^{6}}{6} + \frac{17 x^{5}}{5} - x^{4} + 7 x^{3} + \frac{7 x^{2}}{2} + 6 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14635, size = 46, normalized size = 1.1 \begin{align*} \frac{20}{7} \, x^{7} - \frac{17}{6} \, x^{6} + \frac{17}{5} \, x^{5} - x^{4} + 7 \, x^{3} + \frac{7}{2} \, x^{2} + 6 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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