Optimal. Leaf size=16 \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
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Rubi [A] time = 0.0023568, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {261} \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^3 \, dx &=\frac{\left (a+b x^2\right )^4}{8 b}\\ \end{align*}
Mathematica [A] time = 0.0018186, size = 16, normalized size = 1. \[ \frac{\left (a+b x^2\right )^4}{8 b} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.001, size = 36, normalized size = 2.3 \begin{align*}{\frac{{b}^{3}{x}^{8}}{8}}+{\frac{a{b}^{2}{x}^{6}}{2}}+{\frac{3\,{a}^{2}b{x}^{4}}{4}}+{\frac{{a}^{3}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.78371, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{4}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.81334, size = 80, normalized size = 5. \begin{align*} \frac{1}{8} x^{8} b^{3} + \frac{1}{2} x^{6} b^{2} a + \frac{3}{4} x^{4} b a^{2} + \frac{1}{2} x^{2} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.06199, size = 37, normalized size = 2.31 \begin{align*} \frac{a^{3} x^{2}}{2} + \frac{3 a^{2} b x^{4}}{4} + \frac{a b^{2} x^{6}}{2} + \frac{b^{3} x^{8}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.70175, size = 19, normalized size = 1.19 \begin{align*} \frac{{\left (b x^{2} + a\right )}^{4}}{8 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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