Optimal. Leaf size=7 \[ \frac {1}{1-x} \]
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Rubi [A] time = 0.02, antiderivative size = 7, 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} \[ \frac {1}{1-x} \]
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 )^2}{\left (1-x^4\right )^2} \, dx &=\int \frac {1}{(1-x)^2} \, dx\\ &=\frac {1}{1-x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 7, normalized size = 1.00 \[ -\frac {1}{x-1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 7, normalized size = 1.00 \[ -\frac {1}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 7, normalized size = 1.00 \[ -\frac {1}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 8, normalized size = 1.14 \[ -\frac {1}{x -1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 7, normalized size = 1.00 \[ -\frac {1}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 7, normalized size = 1.00 \[ -\frac {1}{x-1} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 5, normalized size = 0.71 \[ - \frac {1}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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