Optimal. Leaf size=11 \[ \frac{1}{3 (1-x)^3} \]
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Rubi [A] time = 0.0193226, 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} \[ \frac{1}{3 (1-x)^3} \]
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 )^4}{\left (1-x^4\right )^4} \, dx &=\int \frac{1}{(1-x)^4} \, dx\\ &=\frac{1}{3 (1-x)^3}\\ \end{align*}
Mathematica [A] time = 0.0010176, size = 9, normalized size = 0.82 \[ -\frac{1}{3 (x-1)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 8, normalized size = 0.7 \begin{align*} -{\frac{1}{3\, \left ( -1+x \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.941818, size = 23, normalized size = 2.09 \begin{align*} -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.69488, size = 41, normalized size = 3.73 \begin{align*} -\frac{1}{3 \,{\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.102664, size = 17, normalized size = 1.55 \begin{align*} - \frac{1}{3 x^{3} - 9 x^{2} + 9 x - 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05314, size = 9, normalized size = 0.82 \begin{align*} -\frac{1}{3 \,{\left (x - 1\right )}^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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