Optimal. Leaf size=2 \[ \tan ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.00498854, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^2)/(1 + 2*x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.76924, size = 2, normalized size = 1. \[ \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+1)/(x**4+2*x**2+1),x)
[Out]
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Mathematica [A] time = 0.00360941, size = 2, normalized size = 1. \[ \tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^2)/(1 + 2*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.002, size = 3, normalized size = 1.5 \[ \arctan \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+1)/(x^4+2*x^2+1),x)
[Out]
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Maxima [A] time = 0.836428, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^4 + 2*x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.283217, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^4 + 2*x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.151909, size = 2, normalized size = 1. \[ \operatorname{atan}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+1)/(x**4+2*x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.268526, size = 3, normalized size = 1.5 \[ \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 1)/(x^4 + 2*x^2 + 1),x, algorithm="giac")
[Out]