3.616 \(\int \frac{a+b x^4}{x^9} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{8 x^8}-\frac{b}{4 x^4} \]

[Out]

-a/(8*x^8) - b/(4*x^4)

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Rubi [A]  time = 0.0128003, 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 \[ -\frac{a}{8 x^8}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^9,x]

[Out]

-a/(8*x^8) - b/(4*x^4)

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Rubi in Sympy [A]  time = 2.95685, size = 14, normalized size = 0.82 \[ - \frac{a}{8 x^{8}} - \frac{b}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**4+a)/x**9,x)

[Out]

-a/(8*x**8) - b/(4*x**4)

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Mathematica [A]  time = 0.00360173, size = 17, normalized size = 1. \[ -\frac{a}{8 x^8}-\frac{b}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^9,x]

[Out]

-a/(8*x^8) - b/(4*x^4)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{a}{8\,{x}^{8}}}-{\frac{b}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^9,x)

[Out]

-1/8*a/x^8-1/4*b/x^4

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Maxima [A]  time = 1.44623, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{4} + a}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^9,x, algorithm="maxima")

[Out]

-1/8*(2*b*x^4 + a)/x^8

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Fricas [A]  time = 0.219109, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{4} + a}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^9,x, algorithm="fricas")

[Out]

-1/8*(2*b*x^4 + a)/x^8

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Sympy [A]  time = 1.19651, size = 14, normalized size = 0.82 \[ - \frac{a + 2 b x^{4}}{8 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**9,x)

[Out]

-(a + 2*b*x**4)/(8*x**8)

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GIAC/XCAS [A]  time = 0.219892, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{4} + a}{8 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^9,x, algorithm="giac")

[Out]

-1/8*(2*b*x^4 + a)/x^8