Optimal. Leaf size=12 \[ \frac{1}{3} x^3 (x+2)^6 \]
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Rubi [A] time = 0.0012158, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {74} \[ \frac{1}{3} x^3 (x+2)^6 \]
Antiderivative was successfully verified.
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Rule 74
Rubi steps
\begin{align*} \int x^2 (2+x)^5 (2+3 x) \, dx &=\frac{1}{3} x^3 (2+x)^6\\ \end{align*}
Mathematica [B] time = 0.0019626, size = 42, normalized size = 3.5 \[ \frac{x^9}{3}+4 x^8+20 x^7+\frac{160 x^6}{3}+80 x^5+64 x^4+\frac{64 x^3}{3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 37, normalized size = 3.1 \begin{align*}{\frac{{x}^{9}}{3}}+4\,{x}^{8}+20\,{x}^{7}+{\frac{160\,{x}^{6}}{3}}+80\,{x}^{5}+64\,{x}^{4}+{\frac{64\,{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.02013, size = 49, normalized size = 4.08 \begin{align*} \frac{1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac{160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac{64}{3} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.2694, size = 90, normalized size = 7.5 \begin{align*} \frac{1}{3} x^{9} + 4 x^{8} + 20 x^{7} + \frac{160}{3} x^{6} + 80 x^{5} + 64 x^{4} + \frac{64}{3} x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.068323, size = 37, normalized size = 3.08 \begin{align*} \frac{x^{9}}{3} + 4 x^{8} + 20 x^{7} + \frac{160 x^{6}}{3} + 80 x^{5} + 64 x^{4} + \frac{64 x^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.1728, size = 49, normalized size = 4.08 \begin{align*} \frac{1}{3} \, x^{9} + 4 \, x^{8} + 20 \, x^{7} + \frac{160}{3} \, x^{6} + 80 \, x^{5} + 64 \, x^{4} + \frac{64}{3} \, x^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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