Optimal. Leaf size=16 \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
[Out]
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Rubi [A] time = 0.0142325, 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 \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
[In] Int[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 6.31496, size = 14, normalized size = 0.88 \[ - \frac{1}{10 b \left (a + b x^{2}\right )^{5}} \]
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)**3,x)
[Out]
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Mathematica [A] time = 0.00526628, size = 16, normalized size = 1. \[ -\frac{1}{10 b \left (a+b x^2\right )^5} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a^2 + 2*a*b*x^2 + b^2*x^4)^3,x]
[Out]
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Maple [A] time = 0.006, size = 15, normalized size = 0.9 \[ -{\frac{1}{10\,b \left ( b{x}^{2}+a \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b^2*x^4+2*a*b*x^2+a^2)^3,x)
[Out]
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Maxima [A] time = 0.689691, size = 80, normalized size = 5. \[ -\frac{1}{10 \,{\left (b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248255, size = 80, normalized size = 5. \[ -\frac{1}{10 \,{\left (b^{6} x^{10} + 5 \, a b^{5} x^{8} + 10 \, a^{2} b^{4} x^{6} + 10 \, a^{3} b^{3} x^{4} + 5 \, a^{4} b^{2} x^{2} + a^{5} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.64774, size = 63, normalized size = 3.94 \[ - \frac{1}{10 a^{5} b + 50 a^{4} b^{2} x^{2} + 100 a^{3} b^{3} x^{4} + 100 a^{2} b^{4} x^{6} + 50 a b^{5} x^{8} + 10 b^{6} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b**2*x**4+2*a*b*x**2+a**2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.269741, size = 19, normalized size = 1.19 \[ -\frac{1}{10 \,{\left (b x^{2} + a\right )}^{5} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b^2*x^4 + 2*a*b*x^2 + a^2)^3,x, algorithm="giac")
[Out]