3.1812 \(\int \frac{a+\frac{b}{x^2}}{x^4} \, dx\)

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

[Out]

-b/(5*x^5) - a/(3*x^3)

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Rubi [A]  time = 0.0159713, 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 \[ -\frac{a}{3 x^3}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)/x^4,x]

[Out]

-b/(5*x^5) - a/(3*x^3)

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Rubi in Sympy [A]  time = 2.86867, size = 14, normalized size = 0.82 \[ - \frac{a}{3 x^{3}} - \frac{b}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a/(3*x**3) - b/(5*x**5)

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Mathematica [A]  time = 0.00380172, size = 17, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{b}{5 x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)/x^4,x]

[Out]

-b/(5*x^5) - a/(3*x^3)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)/x^4,x)

[Out]

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

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Maxima [A]  time = 1.43559, size = 20, normalized size = 1.18 \[ -\frac{5 \, a x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15*(5*a*x^2 + 3*b)/x^5

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Fricas [A]  time = 0.21962, size = 20, normalized size = 1.18 \[ -\frac{5 \, a x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15*(5*a*x^2 + 3*b)/x^5

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Sympy [A]  time = 1.16954, size = 15, normalized size = 0.88 \[ - \frac{5 a x^{2} + 3 b}{15 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)/x**4,x)

[Out]

-(5*a*x**2 + 3*b)/(15*x**5)

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GIAC/XCAS [A]  time = 0.227119, size = 20, normalized size = 1.18 \[ -\frac{5 \, a x^{2} + 3 \, b}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/15*(5*a*x^2 + 3*b)/x^5