3.144 \(\int \frac{b x^2+c x^4}{x^8} \, dx\)

Optimal. Leaf size=17 \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]

[Out]

-b/(5*x^5) - c/(3*x^3)

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Rubi [A]  time = 0.0147413, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2 + c*x^4)/x^8,x]

[Out]

-b/(5*x^5) - c/(3*x^3)

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Rubi in Sympy [A]  time = 4.65891, size = 14, normalized size = 0.82 \[ - \frac{b}{5 x^{5}} - \frac{c}{3 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((c*x**4+b*x**2)/x**8,x)

[Out]

-b/(5*x**5) - c/(3*x**3)

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Mathematica [A]  time = 0.00361293, size = 17, normalized size = 1. \[ -\frac{b}{5 x^5}-\frac{c}{3 x^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2 + c*x^4)/x^8,x]

[Out]

-b/(5*x^5) - c/(3*x^3)

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Maple [A]  time = 0.006, size = 14, normalized size = 0.8 \[ -{\frac{b}{5\,{x}^{5}}}-{\frac{c}{3\,{x}^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((c*x^4+b*x^2)/x^8,x)

[Out]

-1/5*b/x^5-1/3*c/x^3

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Maxima [A]  time = 0.686661, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^8,x, algorithm="maxima")

[Out]

-1/15*(5*c*x^2 + 3*b)/x^5

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Fricas [A]  time = 0.246537, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^8,x, algorithm="fricas")

[Out]

-1/15*(5*c*x^2 + 3*b)/x^5

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Sympy [A]  time = 1.14532, size = 15, normalized size = 0.88 \[ - \frac{3 b + 5 c x^{2}}{15 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x**4+b*x**2)/x**8,x)

[Out]

-(3*b + 5*c*x**2)/(15*x**5)

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GIAC/XCAS [A]  time = 0.268346, size = 20, normalized size = 1.18 \[ -\frac{5 \, c x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2)/x^8,x, algorithm="giac")

[Out]

-1/15*(5*c*x^2 + 3*b)/x^5