Optimal. Leaf size=11 \[ \frac{1}{2 (1-x)^2} \]
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Rubi [A] time = 0.0181356, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.095, Rules used = {1586, 32} \[ \frac{1}{2 (1-x)^2} \]
Antiderivative was successfully verified.
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Rule 1586
Rule 32
Rubi steps
\begin{align*} \int \frac{\left (1+x+x^2+x^3\right )^3}{\left (1-x^4\right )^3} \, dx &=\int \frac{1}{(1-x)^3} \, dx\\ &=\frac{1}{2 (1-x)^2}\\ \end{align*}
Mathematica [A] time = 0.0013108, size = 9, normalized size = 0.82 \[ \frac{1}{2 (x-1)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 8, normalized size = 0.7 \begin{align*}{\frac{1}{2\, \left ( -1+x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.936703, size = 16, normalized size = 1.45 \begin{align*} \frac{1}{2 \,{\left (x^{2} - 2 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66084, size = 28, normalized size = 2.55 \begin{align*} \frac{1}{2 \,{\left (x^{2} - 2 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096645, size = 10, normalized size = 0.91 \begin{align*} \frac{1}{2 x^{2} - 4 x + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06814, size = 9, normalized size = 0.82 \begin{align*} \frac{1}{2 \,{\left (x - 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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