Optimal. Leaf size=16 \[ \frac{\left (a+b x^3\right )^4}{12 b} \]
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Rubi [A] time = 0.0029147, 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} \[ \frac{\left (a+b x^3\right )^4}{12 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^2 \left (a+b x^3\right )^3 \, dx &=\frac{\left (a+b x^3\right )^4}{12 b}\\ \end{align*}
Mathematica [B] time = 0.0016595, size = 43, normalized size = 2.69 \[ \frac{1}{2} a^2 b x^6+\frac{a^3 x^3}{3}+\frac{1}{3} a b^2 x^9+\frac{b^3 x^{12}}{12} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 36, normalized size = 2.3 \begin{align*}{\frac{{b}^{3}{x}^{12}}{12}}+{\frac{a{b}^{2}{x}^{9}}{3}}+{\frac{{a}^{2}b{x}^{6}}{2}}+{\frac{{a}^{3}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.957055, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{4}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.43057, size = 82, normalized size = 5.12 \begin{align*} \frac{1}{12} x^{12} b^{3} + \frac{1}{3} x^{9} b^{2} a + \frac{1}{2} x^{6} b a^{2} + \frac{1}{3} x^{3} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.094796, size = 36, normalized size = 2.25 \begin{align*} \frac{a^{3} x^{3}}{3} + \frac{a^{2} b x^{6}}{2} + \frac{a b^{2} x^{9}}{3} + \frac{b^{3} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12702, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{3} + a\right )}^{4}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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