3.1813 \(\int \frac{a+\frac{b}{x^2}}{x^5} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{6 x^6} \]

[Out]

-b/(6*x^6) - a/(4*x^4)

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Rubi [A]  time = 0.0160299, 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 \[ -\frac{a}{4 x^4}-\frac{b}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)/x^5,x]

[Out]

-b/(6*x^6) - a/(4*x^4)

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Rubi in Sympy [A]  time = 2.87779, size = 14, normalized size = 0.82 \[ - \frac{a}{4 x^{4}} - \frac{b}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)/x**5,x)

[Out]

-a/(4*x**4) - b/(6*x**6)

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Mathematica [A]  time = 0.00361709, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)/x^5,x]

[Out]

-b/(6*x^6) - a/(4*x^4)

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Maple [A]  time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{b}{6\,{x}^{6}}}-{\frac{a}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)/x^5,x)

[Out]

-1/6*b/x^6-1/4*a/x^4

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Maxima [A]  time = 1.44189, size = 20, normalized size = 1.18 \[ -\frac{3 \, a x^{2} + 2 \, b}{12 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^5,x, algorithm="maxima")

[Out]

-1/12*(3*a*x^2 + 2*b)/x^6

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Fricas [A]  time = 0.215956, size = 20, normalized size = 1.18 \[ -\frac{3 \, a x^{2} + 2 \, b}{12 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^5,x, algorithm="fricas")

[Out]

-1/12*(3*a*x^2 + 2*b)/x^6

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Sympy [A]  time = 1.16136, size = 15, normalized size = 0.88 \[ - \frac{3 a x^{2} + 2 b}{12 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)/x**5,x)

[Out]

-(3*a*x**2 + 2*b)/(12*x**6)

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GIAC/XCAS [A]  time = 0.223297, size = 20, normalized size = 1.18 \[ -\frac{3 \, a x^{2} + 2 \, b}{12 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^5,x, algorithm="giac")

[Out]

-1/12*(3*a*x^2 + 2*b)/x^6