Optimal. Leaf size=14 \[ \frac {1}{12 \left (x^3-6 x+1\right )^4} \]
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Rubi [A] time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \[ \frac {1}{12 \left (x^3-6 x+1\right )^4} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.83, size = 57, normalized size = 4.07 \[ \frac {1}{12 \, {\left (x^{12} - 24 \, x^{10} + 4 \, x^{9} + 216 \, x^{8} - 72 \, x^{7} - 858 \, x^{6} + 432 \, x^{5} + 1224 \, x^{4} - 860 \, x^{3} + 216 \, x^{2} - 24 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 12, normalized size = 0.86 \[ \frac {1}{12 \, {\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.93 \[ \frac {1}{12 \left (x^{3}-6 x +1\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 12, normalized size = 0.86 \[ \frac {1}{12 \, {\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.10, size = 12, normalized size = 0.86 \[ \frac {1}{12\,{\left (x^3-6\,x+1\right )}^4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.19, size = 56, normalized size = 4.00 \[ \frac {1}{12 x^{12} - 288 x^{10} + 48 x^{9} + 2592 x^{8} - 864 x^{7} - 10296 x^{6} + 5184 x^{5} + 14688 x^{4} - 10320 x^{3} + 2592 x^{2} - 288 x + 12} \]
Verification of antiderivative is not currently implemented for this CAS.
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