Optimal. Leaf size=16 \[ -\frac{1}{4 b \left (a+b x^2\right )^2} \]
[Out]
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Rubi [A] time = 0.0109076, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{1}{4 b \left (a+b x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x^2)^3,x]
[Out]
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Rubi in Sympy [A] time = 2.2242, size = 14, normalized size = 0.88 \[ - \frac{1}{4 b \left (a + b x^{2}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**2+a)**3,x)
[Out]
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Mathematica [A] time = 0.00447464, size = 16, normalized size = 1. \[ -\frac{1}{4 b \left (a+b x^2\right )^2} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x^2)^3,x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 0.9 \[ -{\frac{1}{4\,b \left ( b{x}^{2}+a \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^2+a)^3,x)
[Out]
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Maxima [A] time = 1.34332, size = 19, normalized size = 1.19 \[ -\frac{1}{4 \,{\left (b x^{2} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222624, size = 35, normalized size = 2.19 \[ -\frac{1}{4 \,{\left (b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.52871, size = 27, normalized size = 1.69 \[ - \frac{1}{4 a^{2} b + 8 a b^{2} x^{2} + 4 b^{3} x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x**2+a)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.210801, size = 19, normalized size = 1.19 \[ -\frac{1}{4 \,{\left (b x^{2} + a\right )}^{2} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^3,x, algorithm="giac")
[Out]