Optimal. Leaf size=16 \[ \frac{\left (a+b x^4\right )^4}{16 b} \]
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Rubi [A] time = 0.0029122, 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} \[ \frac{\left (a+b x^4\right )^4}{16 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x^3 \left (a+b x^4\right )^3 \, dx &=\frac{\left (a+b x^4\right )^4}{16 b}\\ \end{align*}
Mathematica [B] time = 0.001719, size = 43, normalized size = 2.69 \[ \frac{3}{8} a^2 b x^8+\frac{a^3 x^4}{4}+\frac{1}{4} a b^2 x^{12}+\frac{b^3 x^{16}}{16} \]
Antiderivative was successfully verified.
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Maple [B] time = 0., size = 36, normalized size = 2.3 \begin{align*}{\frac{{b}^{3}{x}^{16}}{16}}+{\frac{a{b}^{2}{x}^{12}}{4}}+{\frac{3\,{a}^{2}b{x}^{8}}{8}}+{\frac{{a}^{3}{x}^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.970116, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{4}}{16 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.22993, size = 84, normalized size = 5.25 \begin{align*} \frac{1}{16} x^{16} b^{3} + \frac{1}{4} x^{12} b^{2} a + \frac{3}{8} x^{8} b a^{2} + \frac{1}{4} x^{4} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.068845, size = 37, normalized size = 2.31 \begin{align*} \frac{a^{3} x^{4}}{4} + \frac{3 a^{2} b x^{8}}{8} + \frac{a b^{2} x^{12}}{4} + \frac{b^{3} x^{16}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11926, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{4} + a\right )}^{4}}{16 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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