Optimal. Leaf size=11 \[ -\frac{1}{4} (1-x)^4 \]
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Rubi [A] time = 0.0125012, 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} \[ -\frac{1}{4} (1-x)^4 \]
Antiderivative was successfully verified.
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Rule 1586
Rule 32
Rubi steps
\begin{align*} \int \frac{\left (1-x^4\right )^3}{\left (1+x+x^2+x^3\right )^3} \, dx &=\int (1-x)^3 \, dx\\ &=-\frac{1}{4} (1-x)^4\\ \end{align*}
Mathematica [A] time = 0.0013102, size = 9, normalized size = 0.82 \[ -\frac{1}{4} (x-1)^4 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 8, normalized size = 0.7 \begin{align*} -{\frac{ \left ( -1+x \right ) ^{4}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 0.964346, size = 20, normalized size = 1.82 \begin{align*} -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.72758, size = 41, normalized size = 3.73 \begin{align*} -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.075679, size = 15, normalized size = 1.36 \begin{align*} - \frac{x^{4}}{4} + x^{3} - \frac{3 x^{2}}{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.10327, size = 20, normalized size = 1.82 \begin{align*} -\frac{1}{4} \, x^{4} + x^{3} - \frac{3}{2} \, x^{2} + x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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