3.1808 \(\int \left (a+\frac{b}{x^2}\right ) \, dx\)

Optimal. Leaf size=10 \[ a x-\frac{b}{x} \]

[Out]

-(b/x) + a*x

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Rubi [A]  time = 0.0094699, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a x-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Int[a + b/x^2,x]

[Out]

-(b/x) + a*x

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{b}{x} + \int a\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(a+b/x**2,x)

[Out]

-b/x + Integral(a, x)

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Mathematica [A]  time = 0.000349421, size = 10, normalized size = 1. \[ a x-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[a + b/x^2,x]

[Out]

-(b/x) + a*x

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Maple [A]  time = 0.002, size = 11, normalized size = 1.1 \[ -{\frac{b}{x}}+ax \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(a+b/x^2,x)

[Out]

-b/x+a*x

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Maxima [A]  time = 1.43336, size = 14, normalized size = 1.4 \[ a x - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x^2,x, algorithm="maxima")

[Out]

a*x - b/x

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Fricas [A]  time = 0.216677, size = 18, normalized size = 1.8 \[ \frac{a x^{2} - b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x^2,x, algorithm="fricas")

[Out]

(a*x^2 - b)/x

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Sympy [A]  time = 0.970894, size = 5, normalized size = 0.5 \[ a x - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a+b/x**2,x)

[Out]

a*x - b/x

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GIAC/XCAS [A]  time = 0.22677, size = 14, normalized size = 1.4 \[ a x - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(a + b/x^2,x, algorithm="giac")

[Out]

a*x - b/x