Optimal. Leaf size=15 \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]
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Rubi [A] time = 0.0030355, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {261} \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^2 \left (27+8 x^3\right )^{2/3} \, dx &=\frac{1}{40} \left (27+8 x^3\right )^{5/3}\\ \end{align*}
Mathematica [A] time = 0.0033828, size = 15, normalized size = 1. \[ \frac{1}{40} \left (8 x^3+27\right )^{5/3} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.005, size = 27, normalized size = 1.8 \begin{align*}{\frac{ \left ( 3+2\,x \right ) \left ( 4\,{x}^{2}-6\,x+9 \right ) }{40} \left ( 8\,{x}^{3}+27 \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.950064, size = 15, normalized size = 1. \begin{align*} \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.42443, size = 34, normalized size = 2.27 \begin{align*} \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.349162, size = 27, normalized size = 1.8 \begin{align*} \frac{x^{3} \left (8 x^{3} + 27\right )^{\frac{2}{3}}}{5} + \frac{27 \left (8 x^{3} + 27\right )^{\frac{2}{3}}}{40} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09399, size = 15, normalized size = 1. \begin{align*} \frac{1}{40} \,{\left (8 \, x^{3} + 27\right )}^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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