Optimal. Leaf size=13 \[ \frac{1}{4 \left (1-x^4\right )} \]
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Rubi [A] time = 0.0025553, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {28, 261} \[ \frac{1}{4 \left (1-x^4\right )} \]
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin{align*} \int \frac{x^3}{1-2 x^4+x^8} \, dx &=\int \frac{x^3}{\left (-1+x^4\right )^2} \, dx\\ &=\frac{1}{4 \left (1-x^4\right )}\\ \end{align*}
Mathematica [A] time = 0.0026446, size = 11, normalized size = 0.85 \[ -\frac{1}{4 \left (x^4-1\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{4}-4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00088, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{4 \,{\left (x^{4} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.67114, size = 22, normalized size = 1.69 \begin{align*} -\frac{1}{4 \,{\left (x^{4} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.101148, size = 8, normalized size = 0.62 \begin{align*} - \frac{1}{4 x^{4} - 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09683, size = 12, normalized size = 0.92 \begin{align*} -\frac{1}{4 \,{\left (x^{4} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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