Optimal. Leaf size=16 \[ \frac {\left (a+b x^3\right )^3}{9 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, 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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fricas [A] time = 0.66, size = 24, normalized size = 1.50 \[ \frac {1}{9} x^{9} b^{2} + \frac {1}{3} x^{6} b a + \frac {1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{3}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 1.56 \[ \frac {1}{9} b^{2} x^{9}+\frac {1}{3} a b \,x^{6}+\frac {1}{3} a^{2} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.26, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{3}}{9 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 1.50 \[ \frac {a^2\,x^3}{3}+\frac {a\,b\,x^6}{3}+\frac {b^2\,x^9}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 24, normalized size = 1.50 \[ \frac {a^{2} x^{3}}{3} + \frac {a b x^{6}}{3} + \frac {b^{2} x^{9}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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