Optimal. Leaf size=16 \[ -\frac{1}{8 c \left (a+c x^4\right )^2} \]
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Rubi [A] time = 0.0032871, 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} \[ -\frac{1}{8 c \left (a+c x^4\right )^2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{\left (a+c x^4\right )^3} \, dx &=-\frac{1}{8 c \left (a+c x^4\right )^2}\\ \end{align*}
Mathematica [A] time = 0.0037017, size = 16, normalized size = 1. \[ -\frac{1}{8 c \left (a+c x^4\right )^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 15, normalized size = 0.9 \begin{align*} -{\frac{1}{8\,c \left ( c{x}^{4}+a \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.955873, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{8 \,{\left (c x^{4} + a\right )}^{2} c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59647, size = 51, normalized size = 3.19 \begin{align*} -\frac{1}{8 \,{\left (c^{3} x^{8} + 2 \, a c^{2} x^{4} + a^{2} c\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.36612, size = 27, normalized size = 1.69 \begin{align*} - \frac{1}{8 a^{2} c + 16 a c^{2} x^{4} + 8 c^{3} x^{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13548, size = 19, normalized size = 1.19 \begin{align*} -\frac{1}{8 \,{\left (c x^{4} + a\right )}^{2} c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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