3.613 \(\int \frac{a+b x^4}{x^6} \, dx\)

Optimal. Leaf size=15 \[ -\frac{a}{5 x^5}-\frac{b}{x} \]

[Out]

-a/(5*x^5) - b/x

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Rubi [A]  time = 0.013574, 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 \[ -\frac{a}{5 x^5}-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^6,x]

[Out]

-a/(5*x^5) - b/x

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Rubi in Sympy [A]  time = 2.90562, size = 10, normalized size = 0.67 \[ - \frac{a}{5 x^{5}} - \frac{b}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**4+a)/x**6,x)

[Out]

-a/(5*x**5) - b/x

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Mathematica [A]  time = 0.00366381, size = 15, normalized size = 1. \[ -\frac{a}{5 x^5}-\frac{b}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^6,x]

[Out]

-a/(5*x^5) - b/x

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Maple [A]  time = 0.008, size = 14, normalized size = 0.9 \[ -{\frac{a}{5\,{x}^{5}}}-{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^6,x)

[Out]

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

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Maxima [A]  time = 1.43862, size = 18, normalized size = 1.2 \[ -\frac{5 \, b x^{4} + a}{5 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^6,x, algorithm="maxima")

[Out]

-1/5*(5*b*x^4 + a)/x^5

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Fricas [A]  time = 0.219469, size = 18, normalized size = 1.2 \[ -\frac{5 \, b x^{4} + a}{5 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^6,x, algorithm="fricas")

[Out]

-1/5*(5*b*x^4 + a)/x^5

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Sympy [A]  time = 1.12274, size = 14, normalized size = 0.93 \[ - \frac{a + 5 b x^{4}}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**6,x)

[Out]

-(a + 5*b*x**4)/(5*x**5)

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GIAC/XCAS [A]  time = 0.217971, size = 18, normalized size = 1.2 \[ -\frac{5 \, b x^{4} + a}{5 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^6,x, algorithm="giac")

[Out]

-1/5*(5*b*x^4 + a)/x^5