Optimal. Leaf size=17 \[ -\frac{a}{2 x^2}-\frac{b}{4 x^4} \]
[Out]
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Rubi [A] time = 0.0150459, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{a}{2 x^2}-\frac{b}{4 x^4} \]
Antiderivative was successfully verified.
[In] Int[(a + b/x^2)/x^3,x]
[Out]
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Rubi in Sympy [A] time = 2.87073, size = 14, normalized size = 0.82 \[ - \frac{a}{2 x^{2}} - \frac{b}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**2)/x**3,x)
[Out]
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Mathematica [A] time = 0.00383628, size = 17, normalized size = 1. \[ -\frac{a}{2 x^2}-\frac{b}{4 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b/x^2)/x^3,x]
[Out]
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Maple [A] time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{4\,{x}^{4}}}-{\frac{a}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^2)/x^3,x)
[Out]
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Maxima [A] time = 1.44467, size = 19, normalized size = 1.12 \[ -\frac{{\left (a + \frac{b}{x^{2}}\right )}^{2}}{4 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)/x^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218902, size = 18, normalized size = 1.06 \[ -\frac{2 \, a x^{2} + b}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)/x^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.12329, size = 14, normalized size = 0.82 \[ - \frac{2 a x^{2} + b}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**2)/x**3,x)
[Out]
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GIAC/XCAS [A] time = 0.22647, size = 18, normalized size = 1.06 \[ -\frac{2 \, a x^{2} + b}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a + b/x^2)/x^3,x, algorithm="giac")
[Out]