Optimal. Leaf size=9 \[ \frac{x}{x^2+1} \]
[Out]
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Rubi [A] time = 0.0071113, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{x}{x^2+1} \]
Antiderivative was successfully verified.
[In] Int[(1 - x^2)/(1 + x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 4.16044, size = 5, normalized size = 0.56 \[ \frac{x}{x^{2} + 1} \]
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 = 0.00642078, size = 9, normalized size = 1. \[ \frac{x}{x^2+1} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x^2)/(1 + x^2)^2,x]
[Out]
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Maple [A] time = 0.009, size = 10, normalized size = 1.1 \[{\frac{x}{{x}^{2}+1}} \]
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 = 1.33772, size = 12, normalized size = 1.33 \[ \frac{x}{x^{2} + 1} \]
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 = 0.218094, size = 12, normalized size = 1.33 \[ \frac{x}{x^{2} + 1} \]
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 = 0.175413, size = 5, normalized size = 0.56 \[ \frac{x}{x^{2} + 1} \]
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 = 0.240044, size = 9, normalized size = 1. \[ \frac{1}{x + \frac{1}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^2 - 1)/(x^2 + 1)^2,x, algorithm="giac")
[Out]