Optimal. Leaf size=30 \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]
[Out]
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Rubi [A] time = 0.0519524, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2/x^5,x]
[Out]
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Rubi in Sympy [A] time = 8.19193, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{4 x^{4}} - \frac{a b}{3 x^{6}} - \frac{b^{2}}{8 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2/x**5,x)
[Out]
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Mathematica [A] time = 0.00162967, size = 30, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2/x^5,x]
[Out]
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Maple [A] time = 0.01, size = 25, normalized size = 0.8 \[ -{\frac{{b}^{2}}{8\,{x}^{8}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{a}^{2}}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2/x^5,x)
[Out]
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Maxima [A] time = 1.43831, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215899, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.42908, size = 27, normalized size = 0.9 \[ - \frac{6 a^{2} x^{4} + 8 a b x^{2} + 3 b^{2}}{24 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.231567, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^5,x, algorithm="giac")
[Out]