Optimal. Leaf size=16 \[ \frac{\left (a+b x^3\right )^3}{9 b} \]
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Rubi [A] time = 0.0026883, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ \frac{\left (a+b x^3\right )^3}{9 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^2 \left (a+b x^3\right )^2 \, dx &=\frac{\left (a+b x^3\right )^3}{9 b}\\ \end{align*}
Mathematica [A] time = 0.0006582, size = 30, normalized size = 1.88 \[ \frac{a^2 x^3}{3}+\frac{1}{3} a b x^6+\frac{b^2 x^9}{9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 25, normalized size = 1.6 \begin{align*}{\frac{{b}^{2}{x}^{9}}{9}}+{\frac{ab{x}^{6}}{3}}+{\frac{{x}^{3}{a}^{2}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993242, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{3}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48137, size = 55, normalized size = 3.44 \begin{align*} \frac{1}{9} x^{9} b^{2} + \frac{1}{3} x^{6} b a + \frac{1}{3} x^{3} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.058779, size = 24, normalized size = 1.5 \begin{align*} \frac{a^{2} x^{3}}{3} + \frac{a b x^{6}}{3} + \frac{b^{2} x^{9}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.55848, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{3}}{9 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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