3.1556 \(\int \frac{a+\frac{b}{x}}{x^6} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]

[Out]

-b/(6*x^6) - a/(5*x^5)

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Rubi [A]  time = 0.0145442, 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 \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)/x^6,x]

[Out]

-b/(6*x^6) - a/(5*x^5)

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Rubi in Sympy [A]  time = 3.05298, size = 14, normalized size = 0.82 \[ - \frac{a}{5 x^{5}} - \frac{b}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)/x**6,x)

[Out]

-a/(5*x**5) - b/(6*x**6)

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Mathematica [A]  time = 0.00272178, size = 17, normalized size = 1. \[ -\frac{a}{5 x^5}-\frac{b}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)/x^6,x]

[Out]

-b/(6*x^6) - a/(5*x^5)

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Maple [A]  time = 0.007, size = 14, normalized size = 0.8 \[ -{\frac{b}{6\,{x}^{6}}}-{\frac{a}{5\,{x}^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)/x^6,x)

[Out]

-1/6*b/x^6-1/5*a/x^5

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Maxima [A]  time = 1.44016, size = 18, normalized size = 1.06 \[ -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30*(6*a*x + 5*b)/x^6

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Fricas [A]  time = 0.216651, size = 18, normalized size = 1.06 \[ -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30*(6*a*x + 5*b)/x^6

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Sympy [A]  time = 1.17681, size = 14, normalized size = 0.82 \[ - \frac{6 a x + 5 b}{30 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)/x**6,x)

[Out]

-(6*a*x + 5*b)/(30*x**6)

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GIAC/XCAS [A]  time = 0.223869, size = 18, normalized size = 1.06 \[ -\frac{6 \, a x + 5 \, b}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/30*(6*a*x + 5*b)/x^6