Optimal. Leaf size=11 \[ -\frac {1}{3} (1-x)^3 \]
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Rubi [A] time = 0.01, 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^4\right )^2}{\left (1+x+x^2+x^3\right )^2} \, dx &=\int (1-x)^2 \, dx\\ &=-\frac {1}{3} (1-x)^3\\ \end {align*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 1.27 \[ \frac {x^3}{3}-x^2+x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 12, normalized size = 1.09 \[ \frac {1}{3} \, x^{3} - x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 12, normalized size = 1.09 \[ \frac {1}{3} \, x^{3} - x^{2} + x \]
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 \[ \frac {\left (x -1\right )^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 12, normalized size = 1.09 \[ \frac {1}{3} \, x^{3} - x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 1.00 \[ \frac {x\,\left (x^2-3\,x+3\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.73 \[ \frac {x^{3}}{3} - x^{2} + x \]
Verification of antiderivative is not currently implemented for this CAS.
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