3.119 \(\int \frac{\left (1-x^2\right )^2}{\left (-1+x^2\right )^2} \, dx\)

Optimal. Leaf size=1 \[ x \]

[Out]

x

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Rubi [A]  time = 0.00318223, antiderivative size = 1, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ x \]

Antiderivative was successfully verified.

[In]  Int[(1 - x^2)^2/(-1 + x^2)^2,x]

[Out]

x

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Rubi in Sympy [A]  time = 0.041971, size = 0, normalized size = 0. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-x**2+1)**2/(x**2-1)**2,x)

[Out]

x

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Mathematica [A]  time = 0.000409258, size = 1, normalized size = 1. \[ x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - x^2)^2/(-1 + x^2)^2,x]

[Out]

x

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Maple [A]  time = 0., size = 2, normalized size = 2. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-x^2+1)^2/(x^2-1)^2,x)

[Out]

x

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Maxima [A]  time = 1.34069, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1,x, algorithm="maxima")

[Out]

x

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Fricas [A]  time = 0.202327, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1,x, algorithm="fricas")

[Out]

x

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Sympy [A]  time = 0.071556, size = 0, normalized size = 0. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-x**2+1)**2/(x**2-1)**2,x)

[Out]

x

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GIAC/XCAS [A]  time = 0.21752, size = 1, normalized size = 1. \[ x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1,x, algorithm="giac")

[Out]

x