Optimal. Leaf size=11 \[ \frac {1}{3 (1-x)^3} \]
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Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, 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 32
Rule 1586
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*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.82 \[ -\frac {1}{3 (x-1)^3} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.39, size = 17, normalized size = 1.55 \[ -\frac {1}{3 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 7, normalized size = 0.64 \[ -\frac {1}{3 \, {\left (x - 1\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 8, normalized size = 0.73 \[ -\frac {1}{3 \left (x -1\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.32, size = 17, normalized size = 1.55 \[ -\frac {1}{3 \, {\left (x^{3} - 3 \, x^{2} + 3 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.81, size = 7, normalized size = 0.64 \[ -\frac {1}{3\,{\left (x-1\right )}^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.15, size = 17, normalized size = 1.55 \[ - \frac {1}{3 x^{3} - 9 x^{2} + 9 x - 3} \]
Verification of antiderivative is not currently implemented for this CAS.
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