Optimal. Leaf size=16 \[ -\frac{\left (a+\frac{b}{x^2}\right )^3}{6 b} \]
[Out]
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Rubi [A] time = 0.0188534, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{\left (a+\frac{b}{x^2}\right )^3}{6 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)^2/x^3,x]
[Out]
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Rubi in Sympy [A] time = 2.13121, size = 12, normalized size = 0.75 \[ - \frac{\left (a + \frac{b}{x^{2}}\right )^{3}}{6 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)**2/x**3,x)
[Out]
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Mathematica [A] time = 0.00160343, size = 30, normalized size = 1.88 \[ -\frac{a^2}{2 x^2}-\frac{a b}{2 x^4}-\frac{b^2}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)^2/x^3,x]
[Out]
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Maple [A] time = 0.007, size = 25, normalized size = 1.6 \[ -{\frac{{b}^{2}}{6\,{x}^{6}}}-{\frac{ab}{2\,{x}^{4}}}-{\frac{{a}^{2}}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)^2/x^3,x)
[Out]
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Maxima [A] time = 1.4382, size = 19, normalized size = 1.19 \[ -\frac{{\left (a + \frac{b}{x^{2}}\right )}^{3}}{6 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219369, size = 32, normalized size = 2. \[ -\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.33933, size = 26, normalized size = 1.62 \[ - \frac{3 a^{2} x^{4} + 3 a b x^{2} + b^{2}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)**2/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.226394, size = 32, normalized size = 2. \[ -\frac{3 \, a^{2} x^{4} + 3 \, a b x^{2} + b^{2}}{6 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)^2/x^3,x, algorithm="giac")
[Out]