Optimal. Leaf size=16 \[ \frac{\left (a+b x^4\right )^3}{12 b} \]
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Rubi [A] time = 0.0029175, 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} \[ \frac{\left (a+b x^4\right )^3}{12 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^3 \left (a+b x^4\right )^2 \, dx &=\frac{\left (a+b x^4\right )^3}{12 b}\\ \end{align*}
Mathematica [A] time = 0.0006971, size = 30, normalized size = 1.88 \[ \frac{a^2 x^4}{4}+\frac{1}{4} a b x^8+\frac{b^2 x^{12}}{12} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 1.6 \begin{align*}{\frac{{b}^{2}{x}^{12}}{12}}+{\frac{ab{x}^{8}}{4}}+{\frac{{a}^{2}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962192, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{3}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27111, size = 58, normalized size = 3.62 \begin{align*} \frac{1}{12} x^{12} b^{2} + \frac{1}{4} x^{8} b a + \frac{1}{4} x^{4} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.084215, size = 24, normalized size = 1.5 \begin{align*} \frac{a^{2} x^{4}}{4} + \frac{a b x^{8}}{4} + \frac{b^{2} x^{12}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0959, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{3}}{12 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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