Optimal. Leaf size=11 \[ \frac{x}{1-x^2} \]
[Out]
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Rubi [A] time = 0.00728537, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{x}{1-x^2} \]
Antiderivative was successfully verified.
[In] Int[(1 + x^2)/(-1 + x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.67251, size = 5, normalized size = 0.45 \[ \frac{x}{- x^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+1)/(x**2-1)**2,x)
[Out]
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Mathematica [A] time = 0.00643358, size = 10, normalized size = 0.91 \[ -\frac{x}{x^2-1} \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^2)/(-1 + x^2)^2,x]
[Out]
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Maple [A] time = 0.008, size = 16, normalized size = 1.5 \[ -{\frac{1}{-2+2\,x}}-{\frac{1}{2+2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+1)/(x^2-1)^2,x)
[Out]
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Maxima [A] time = 1.33919, size = 14, normalized size = 1.27 \[ -\frac{x}{x^{2} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^2 - 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230401, size = 14, normalized size = 1.27 \[ -\frac{x}{x^{2} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^2 - 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.166185, size = 7, normalized size = 0.64 \[ - \frac{x}{x^{2} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+1)/(x**2-1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.218714, size = 15, normalized size = 1.36 \[ -\frac{1}{x - \frac{1}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^2 - 1)^2,x, algorithm="giac")
[Out]