3.1814 \(\int \frac{a+\frac{b}{x^2}}{x^6} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{5 x^5}-\frac{b}{7 x^7} \]

[Out]

-b/(7*x^7) - a/(5*x^5)

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Rubi [A]  time = 0.0156606, 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 \[ -\frac{a}{5 x^5}-\frac{b}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)/x^6,x]

[Out]

-b/(7*x^7) - a/(5*x^5)

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Rubi in Sympy [A]  time = 2.93819, size = 14, normalized size = 0.82 \[ - \frac{a}{5 x^{5}} - \frac{b}{7 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x**2)/x**6,x)

[Out]

-a/(5*x**5) - b/(7*x**7)

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Mathematica [A]  time = 0.00339726, size = 17, normalized size = 1. \[ -\frac{a}{5 x^5}-\frac{b}{7 x^7} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)/x^6,x]

[Out]

-b/(7*x^7) - a/(5*x^5)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{7\,{x}^{7}}}-{\frac{a}{5\,{x}^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)/x^6,x)

[Out]

-1/7*b/x^7-1/5*a/x^5

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Maxima [A]  time = 1.44, size = 20, normalized size = 1.18 \[ -\frac{7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^6,x, algorithm="maxima")

[Out]

-1/35*(7*a*x^2 + 5*b)/x^7

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Fricas [A]  time = 0.215507, size = 20, normalized size = 1.18 \[ -\frac{7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^6,x, algorithm="fricas")

[Out]

-1/35*(7*a*x^2 + 5*b)/x^7

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Sympy [A]  time = 1.21881, size = 15, normalized size = 0.88 \[ - \frac{7 a x^{2} + 5 b}{35 x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)/x**6,x)

[Out]

-(7*a*x**2 + 5*b)/(35*x**7)

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GIAC/XCAS [A]  time = 0.229471, size = 20, normalized size = 1.18 \[ -\frac{7 \, a x^{2} + 5 \, b}{35 \, x^{7}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a + b/x^2)/x^6,x, algorithm="giac")

[Out]

-1/35*(7*a*x^2 + 5*b)/x^7