Optimal. Leaf size=16 \[ -\frac{1}{2 b \left (a+b x^2\right )} \]
[Out]
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Rubi [A] time = 0.0153704, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{1}{2 b \left (a+b x^2\right )} \]
Antiderivative was successfully verified.
[In] Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4),x]
[Out]
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Rubi in Sympy [A] time = 6.74245, size = 12, normalized size = 0.75 \[ - \frac{1}{2 b \left (a + b x^{2}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b**2*x**4+2*a*b*x**2+a**2),x)
[Out]
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Mathematica [A] time = 0.00470919, size = 16, normalized size = 1. \[ -\frac{1}{2 b \left (a+b x^2\right )} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a^2 + 2*a*b*x^2 + b^2*x^4),x]
[Out]
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Maple [A] time = 0.005, size = 15, normalized size = 0.9 \[ -{\frac{1}{2\,b \left ( b{x}^{2}+a \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b^2*x^4+2*a*b*x^2+a^2),x)
[Out]
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Maxima [A] time = 0.696605, size = 20, normalized size = 1.25 \[ -\frac{1}{2 \,{\left (b^{2} x^{2} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.246033, size = 20, normalized size = 1.25 \[ -\frac{1}{2 \,{\left (b^{2} x^{2} + a b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.15025, size = 15, normalized size = 0.94 \[ - \frac{1}{2 a b + 2 b^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b**2*x**4+2*a*b*x**2+a**2),x)
[Out]
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GIAC/XCAS [A] time = 0.270046, size = 19, normalized size = 1.19 \[ -\frac{1}{2 \,{\left (b x^{2} + a\right )} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2),x, algorithm="giac")
[Out]