Optimal. Leaf size=11 \[ -\frac{1}{2 \left (x^2+1\right )} \]
[Out]
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Rubi [A] time = 0.00759608, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{1}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
[In] Int[x/(1 + 2*x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.74399, size = 8, normalized size = 0.73 \[ - \frac{1}{2 \left (x^{2} + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**4+2*x**2+1),x)
[Out]
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Mathematica [A] time = 0.00225236, size = 11, normalized size = 1. \[ -\frac{1}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x/(1 + 2*x^2 + x^4),x]
[Out]
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Maple [A] time = 0.004, size = 10, normalized size = 0.9 \[ -{\frac{1}{2\,{x}^{2}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^4+2*x^2+1),x)
[Out]
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Maxima [A] time = 0.697025, size = 12, normalized size = 1.09 \[ -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248907, size = 12, normalized size = 1.09 \[ -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.140513, size = 8, normalized size = 0.73 \[ - \frac{1}{2 x^{2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**4+2*x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.26804, size = 12, normalized size = 1.09 \[ -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^4 + 2*x^2 + 1),x, algorithm="giac")
[Out]