Optimal. Leaf size=13 \[ -\frac{1}{8 \left (a^4+x^4\right )^2} \]
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Rubi [A] time = 0.0023815, antiderivative size = 13, 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} \[ -\frac{1}{8 \left (a^4+x^4\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (a^4+x^4\right )^3} \, dx &=-\frac{1}{8 \left (a^4+x^4\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0034365, size = 13, normalized size = 1. \[ -\frac{1}{8 \left (a^4+x^4\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 12, normalized size = 0.9 \begin{align*} -{\frac{1}{8\, \left ({a}^{4}+{x}^{4} \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.921507, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{8 \,{\left (a^{4} + x^{4}\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.87433, size = 41, normalized size = 3.15 \begin{align*} -\frac{1}{8 \,{\left (a^{8} + 2 \, a^{4} x^{4} + x^{8}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.795548, size = 20, normalized size = 1.54 \begin{align*} - \frac{1}{8 a^{8} + 16 a^{4} x^{4} + 8 x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0583, size = 15, normalized size = 1.15 \begin{align*} -\frac{1}{8 \,{\left (a^{4} + x^{4}\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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