Optimal. Leaf size=13 \[ \frac{1}{8 \left (1-x^2\right )^4} \]
[Out]
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Rubi [A] time = 0.0078271, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{1}{8 \left (1-x^2\right )^4} \]
Antiderivative was successfully verified.
[In] Int[x/(1 - x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 1.92051, size = 8, normalized size = 0.62 \[ \frac{1}{8 \left (- x^{2} + 1\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**2+1)**5,x)
[Out]
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Mathematica [A] time = 0.0037918, size = 11, normalized size = 0.85 \[ \frac{1}{8 \left (x^2-1\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 - x^2)^5,x]
[Out]
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Maple [A] time = 0.001, size = 10, normalized size = 0.8 \[{\frac{1}{8\, \left ({x}^{2}-1 \right ) ^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^2+1)^5,x)
[Out]
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Maxima [A] time = 0.782708, size = 12, normalized size = 0.92 \[ \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^2 - 1)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263157, size = 32, normalized size = 2.46 \[ \frac{1}{8 \,{\left (x^{8} - 4 \, x^{6} + 6 \, x^{4} - 4 \, x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^2 - 1)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.320626, size = 22, normalized size = 1.69 \[ \frac{1}{8 x^{8} - 32 x^{6} + 48 x^{4} - 32 x^{2} + 8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**2+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.25912, size = 12, normalized size = 0.92 \[ \frac{1}{8 \,{\left (x^{2} - 1\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-x/(x^2 - 1)^5,x, algorithm="giac")
[Out]