Optimal. Leaf size=14 \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
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Rubi [A] time = 0.0075984, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {1588} \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin{align*} \int \frac{2-x^2}{\left (1-6 x+x^3\right )^5} \, dx &=\frac{1}{12 \left (1-6 x+x^3\right )^4}\\ \end{align*}
Mathematica [A] time = 0.0052907, size = 14, normalized size = 1. \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.9 \begin{align*}{\frac{1}{12\, \left ({x}^{3}-6\,x+1 \right ) ^{4}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02059, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.30672, size = 151, normalized size = 10.79 \begin{align*} \frac{1}{12 \,{\left (x^{12} - 24 \, x^{10} + 4 \, x^{9} + 216 \, x^{8} - 72 \, x^{7} - 858 \, x^{6} + 432 \, x^{5} + 1224 \, x^{4} - 860 \, x^{3} + 216 \, x^{2} - 24 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.208288, size = 56, normalized size = 4. \begin{align*} \frac{1}{12 x^{12} - 288 x^{10} + 48 x^{9} + 2592 x^{8} - 864 x^{7} - 10296 x^{6} + 5184 x^{5} + 14688 x^{4} - 10320 x^{3} + 2592 x^{2} - 288 x + 12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23666, size = 16, normalized size = 1.14 \begin{align*} \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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