Optimal. Leaf size=16 \[ \frac {\left (a+b x^3\right )^4}{12 b} \]
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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} \[ \frac {\left (a+b x^3\right )^4}{12 b} \]
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*}
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Mathematica [B] time = 0.00, size = 43, normalized size = 2.69 \[ \frac {a^3 x^3}{3}+\frac {1}{2} a^2 b x^6+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{12}}{12} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.78, size = 35, normalized size = 2.19 \[ \frac {1}{12} x^{12} b^{3} + \frac {1}{3} x^{9} b^{2} a + \frac {1}{2} x^{6} b a^{2} + \frac {1}{3} x^{3} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{4}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 36, normalized size = 2.25 \[ \frac {1}{12} b^{3} x^{12}+\frac {1}{3} a \,b^{2} x^{9}+\frac {1}{2} a^{2} b \,x^{6}+\frac {1}{3} a^{3} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.27, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{3} + a\right )}^{4}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 2.19 \[ \frac {a^3\,x^3}{3}+\frac {a^2\,b\,x^6}{2}+\frac {a\,b^2\,x^9}{3}+\frac {b^3\,x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 36, normalized size = 2.25 \[ \frac {a^{3} x^{3}}{3} + \frac {a^{2} b x^{6}}{2} + \frac {a b^{2} x^{9}}{3} + \frac {b^{3} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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