Optimal. Leaf size=14 \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
[Out]
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Rubi [A] time = 0.00863122, 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 \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
Antiderivative was successfully verified.
[In] Int[(2 - x^2)/(1 - 6*x + x^3)^5,x]
[Out]
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Rubi in Sympy [A] time = 2.93853, 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.
[In] rubi_integrate((-x**2+2)/(x**3-6*x+1)**5,x)
[Out]
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Mathematica [A] time = 0.00842163, size = 14, normalized size = 1. \[ \frac{1}{12 \left (x^3-6 x+1\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[(2 - x^2)/(1 - 6*x + x^3)^5,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 0.9 \[{\frac{1}{12\, \left ({x}^{3}-6\,x+1 \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+2)/(x^3-6*x+1)^5,x)
[Out]
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Maxima [A] time = 0.810874, size = 16, normalized size = 1.14 \[ \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244749, size = 77, normalized size = 5.5 \[ \frac{1}{12 \,{\left (x^{12} - 24 \, x^{10} + 4 \, x^{9} + 216 \, x^{8} - 72 \, x^{7} - 858 \, x^{6} + 432 \, x^{5} + 1224 \, x^{4} - 860 \, x^{3} + 216 \, x^{2} - 24 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.666687, size = 56, normalized size = 4. \[ \frac{1}{12 x^{12} - 288 x^{10} + 48 x^{9} + 2592 x^{8} - 864 x^{7} - 10296 x^{6} + 5184 x^{5} + 14688 x^{4} - 10320 x^{3} + 2592 x^{2} - 288 x + 12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+2)/(x**3-6*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.259587, size = 16, normalized size = 1.14 \[ \frac{1}{12 \,{\left (x^{3} - 6 \, x + 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 - 2)/(x^3 - 6*x + 1)^5,x, algorithm="giac")
[Out]