3.1810 \(\int \frac{a+\frac{b}{x^2}}{x^2} \, dx\)

Optimal. Leaf size=15 \[ -\frac{a}{x}-\frac{b}{3 x^3} \]

[Out]

-b/(3*x^3) - a/x

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Rubi [A]  time = 0.0164766, antiderivative size = 15, 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 \[ -\frac{a}{x}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)/x^2,x]

[Out]

-b/(3*x^3) - a/x

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Rubi in Sympy [A]  time = 3.04694, size = 10, normalized size = 0.67 \[ - \frac{a}{x} - \frac{b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)/x**2,x)

[Out]

-a/x - b/(3*x**3)

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Mathematica [A]  time = 0.00379276, size = 15, normalized size = 1. \[ -\frac{a}{x}-\frac{b}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)/x^2,x]

[Out]

-b/(3*x^3) - a/x

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Maple [A]  time = 0.008, size = 14, normalized size = 0.9 \[ -{\frac{b}{3\,{x}^{3}}}-{\frac{a}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)/x^2,x)

[Out]

-1/3*b/x^3-a/x

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Maxima [A]  time = 1.53122, size = 18, normalized size = 1.2 \[ -\frac{3 \, a x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3*(3*a*x^2 + b)/x^3

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Fricas [A]  time = 0.218322, size = 18, normalized size = 1.2 \[ -\frac{3 \, a x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3*(3*a*x^2 + b)/x^3

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Sympy [A]  time = 1.09921, size = 14, normalized size = 0.93 \[ - \frac{3 a x^{2} + b}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)/x**2,x)

[Out]

-(3*a*x**2 + b)/(3*x**3)

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GIAC/XCAS [A]  time = 0.224691, size = 18, normalized size = 1.2 \[ -\frac{3 \, a x^{2} + b}{3 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/3*(3*a*x^2 + b)/x^3