Optimal. Leaf size=9 \[ \tan ^{-1}(2 x)-\tan ^{-1}(x) \]
[Out]
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Rubi [A] time = 0.0225844, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \tan ^{-1}(2 x)-\tan ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x^2)/(1 + 5*x^2 + 4*x^4),x]
[Out]
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Rubi in Sympy [A] time = 7.9074, size = 7, normalized size = 0.78 \[ - \operatorname{atan}{\left (x \right )} + \operatorname{atan}{\left (2 x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-2*x**2+1)/(4*x**4+5*x**2+1),x)
[Out]
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Mathematica [A] time = 0.0114487, size = 12, normalized size = 1.33 \[ \tan ^{-1}\left (\frac{x}{2 x^2+1}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x^2)/(1 + 5*x^2 + 4*x^4),x]
[Out]
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Maple [A] time = 0.009, size = 10, normalized size = 1.1 \[ -\arctan \left ( x \right ) +\arctan \left ( 2\,x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-2*x^2+1)/(4*x^4+5*x^2+1),x)
[Out]
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Maxima [A] time = 0.840871, size = 12, normalized size = 1.33 \[ \arctan \left (2 \, x\right ) - \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x^2 - 1)/(4*x^4 + 5*x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.31455, size = 23, normalized size = 2.56 \[ \arctan \left (4 \, x^{3} + 3 \, x\right ) - \arctan \left (2 \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x^2 - 1)/(4*x^4 + 5*x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.214699, size = 14, normalized size = 1.56 \[ - \operatorname{atan}{\left (2 x \right )} + \operatorname{atan}{\left (4 x^{3} + 3 x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x**2+1)/(4*x**4+5*x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.268504, size = 12, normalized size = 1.33 \[ \arctan \left (2 \, x\right ) - \arctan \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x^2 - 1)/(4*x^4 + 5*x^2 + 1),x, algorithm="giac")
[Out]