3.10 \(\int \frac{a+b x^2}{x^5} \, dx\)

Optimal. Leaf size=17 \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]

[Out]

-a/(4*x^4) - b/(2*x^2)

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Rubi [A]  time = 0.015626, 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 \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x^2)/x^5,x]

[Out]

-a/(4*x^4) - b/(2*x^2)

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Rubi in Sympy [A]  time = 3.1161, size = 14, normalized size = 0.82 \[ - \frac{a}{4 x^{4}} - \frac{b}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2+a)/x**5,x)

[Out]

-a/(4*x**4) - b/(2*x**2)

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Mathematica [A]  time = 0.00351693, size = 17, normalized size = 1. \[ -\frac{a}{4 x^4}-\frac{b}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x^2)/x^5,x]

[Out]

-a/(4*x^4) - b/(2*x^2)

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Maple [A]  time = 0.008, size = 14, normalized size = 0.8 \[ -{\frac{a}{4\,{x}^{4}}}-{\frac{b}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2+a)/x^5,x)

[Out]

-1/4*a/x^4-1/2*b/x^2

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Maxima [A]  time = 1.37844, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)/x^5,x, algorithm="maxima")

[Out]

-1/4*(2*b*x^2 + a)/x^4

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Fricas [A]  time = 0.225828, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)/x^5,x, algorithm="fricas")

[Out]

-1/4*(2*b*x^2 + a)/x^4

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Sympy [A]  time = 1.0974, size = 14, normalized size = 0.82 \[ - \frac{a + 2 b x^{2}}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2+a)/x**5,x)

[Out]

-(a + 2*b*x**2)/(4*x**4)

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GIAC/XCAS [A]  time = 0.210825, size = 18, normalized size = 1.06 \[ -\frac{2 \, b x^{2} + a}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2 + a)/x^5,x, algorithm="giac")

[Out]

-1/4*(2*b*x^2 + a)/x^4