Optimal. Leaf size=11 \[ -\frac{1}{3} (1-x)^3 \]
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Rubi [A] time = 0.0122637, 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^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*}
Mathematica [A] time = 0.0005153, size = 14, normalized size = 1.27 \[ \frac{x^3}{3}-x^2+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 8, normalized size = 0.7 \begin{align*}{\frac{ \left ( -1+x \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.939669, size = 16, normalized size = 1.45 \begin{align*} \frac{1}{3} \, x^{3} - x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68165, size = 26, normalized size = 2.36 \begin{align*} \frac{1}{3} \, x^{3} - x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.066356, size = 8, normalized size = 0.73 \begin{align*} \frac{x^{3}}{3} - x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06477, size = 16, normalized size = 1.45 \begin{align*} \frac{1}{3} \, x^{3} - x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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