3.1555 \(\int \frac{a+\frac{b}{x}}{x^5} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]

[Out]

-b/(5*x^5) - a/(4*x^4)

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Rubi [A]  time = 0.0159841, 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 \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)/x^5,x]

[Out]

-b/(5*x^5) - a/(4*x^4)

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Rubi in Sympy [A]  time = 2.97283, size = 14, normalized size = 0.82 \[ - \frac{a}{4 x^{4}} - \frac{b}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((a+b/x)/x**5,x)

[Out]

-a/(4*x**4) - b/(5*x**5)

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Mathematica [A]  time = 0.00352973, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)/x^5,x]

[Out]

-b/(5*x^5) - a/(4*x^4)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{5\,{x}^{5}}}-{\frac{a}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)/x^5,x)

[Out]

-1/5*b/x^5-1/4*a/x^4

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Maxima [A]  time = 1.51146, size = 18, normalized size = 1.06 \[ -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/20*(5*a*x + 4*b)/x^5

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Fricas [A]  time = 0.215329, size = 18, normalized size = 1.06 \[ -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/20*(5*a*x + 4*b)/x^5

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Sympy [A]  time = 1.12534, size = 14, normalized size = 0.82 \[ - \frac{5 a x + 4 b}{20 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)/x**5,x)

[Out]

-(5*a*x + 4*b)/(20*x**5)

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GIAC/XCAS [A]  time = 0.224858, size = 18, normalized size = 1.06 \[ -\frac{5 \, a x + 4 \, b}{20 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/20*(5*a*x + 4*b)/x^5