3.617 \(\int \frac{a+b x^4}{x^{10}} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{9 x^9}-\frac{b}{5 x^5} \]

[Out]

-a/(9*x^9) - b/(5*x^5)

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Rubi [A]  time = 0.013565, 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 \[ -\frac{a}{9 x^9}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^4)/x^10,x]

[Out]

-a/(9*x^9) - b/(5*x^5)

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Rubi in Sympy [A]  time = 2.97977, size = 14, normalized size = 0.82 \[ - \frac{a}{9 x^{9}} - \frac{b}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**4+a)/x**10,x)

[Out]

-a/(9*x**9) - b/(5*x**5)

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Mathematica [A]  time = 0.00354381, size = 17, normalized size = 1. \[ -\frac{a}{9 x^9}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^4)/x^10,x]

[Out]

-a/(9*x^9) - b/(5*x^5)

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Maple [A]  time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{a}{9\,{x}^{9}}}-{\frac{b}{5\,{x}^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^4+a)/x^10,x)

[Out]

-1/9*a/x^9-1/5*b/x^5

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Maxima [A]  time = 1.44104, size = 20, normalized size = 1.18 \[ -\frac{9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^10,x, algorithm="maxima")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9

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Fricas [A]  time = 0.219002, size = 20, normalized size = 1.18 \[ -\frac{9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^10,x, algorithm="fricas")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9

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Sympy [A]  time = 1.25559, size = 15, normalized size = 0.88 \[ - \frac{5 a + 9 b x^{4}}{45 x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**4+a)/x**10,x)

[Out]

-(5*a + 9*b*x**4)/(45*x**9)

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GIAC/XCAS [A]  time = 0.23623, size = 20, normalized size = 1.18 \[ -\frac{9 \, b x^{4} + 5 \, a}{45 \, x^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^4 + a)/x^10,x, algorithm="giac")

[Out]

-1/45*(9*b*x^4 + 5*a)/x^9