Optimal. Leaf size=6 \[ x-2 \tan ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.0150226, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ x-2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[(-1 + x^2)/(1 + x^2),x]
[Out]
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Rubi in Sympy [A] time = 4.39052, size = 5, normalized size = 0.83 \[ x - 2 \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-1)/(x**2+1),x)
[Out]
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Mathematica [A] time = 0.00666589, size = 6, normalized size = 1. \[ x-2 \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + x^2)/(1 + x^2),x]
[Out]
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Maple [A] time = 0.003, size = 7, normalized size = 1.2 \[ x-2\,\arctan \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-1)/(x^2+1),x)
[Out]
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Maxima [A] time = 1.50244, size = 8, normalized size = 1.33 \[ x - 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.228536, size = 8, normalized size = 1.33 \[ x - 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.07292, size = 5, normalized size = 0.83 \[ x - 2 \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-1)/(x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.209032, size = 8, normalized size = 1.33 \[ x - 2 \, \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 1)/(x^2 + 1),x, algorithm="giac")
[Out]