3.1826 \(\int \frac{\left (a+\frac{b}{x^2}\right )^2}{x^5} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]

[Out]

-b^2/(8*x^8) - (a*b)/(3*x^6) - a^2/(4*x^4)

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Rubi [A]  time = 0.0519524, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x^2)^2/x^5,x]

[Out]

-b^2/(8*x^8) - (a*b)/(3*x^6) - a^2/(4*x^4)

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Rubi in Sympy [A]  time = 8.19193, size = 26, normalized size = 0.87 \[ - \frac{a^{2}}{4 x^{4}} - \frac{a b}{3 x^{6}} - \frac{b^{2}}{8 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a**2/(4*x**4) - a*b/(3*x**6) - b**2/(8*x**8)

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Mathematica [A]  time = 0.00162967, size = 30, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{a b}{3 x^6}-\frac{b^2}{8 x^8} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x^2)^2/x^5,x]

[Out]

-b^2/(8*x^8) - (a*b)/(3*x^6) - a^2/(4*x^4)

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Maple [A]  time = 0.01, size = 25, normalized size = 0.8 \[ -{\frac{{b}^{2}}{8\,{x}^{8}}}-{\frac{ab}{3\,{x}^{6}}}-{\frac{{a}^{2}}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x^2)^2/x^5,x)

[Out]

-1/8*b^2/x^8-1/3*a*b/x^6-1/4*a^2/x^4

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Maxima [A]  time = 1.43831, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/24*(6*a^2*x^4 + 8*a*b*x^2 + 3*b^2)/x^8

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Fricas [A]  time = 0.215899, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/24*(6*a^2*x^4 + 8*a*b*x^2 + 3*b^2)/x^8

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Sympy [A]  time = 1.42908, size = 27, normalized size = 0.9 \[ - \frac{6 a^{2} x^{4} + 8 a b x^{2} + 3 b^{2}}{24 x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x**2)**2/x**5,x)

[Out]

-(6*a**2*x**4 + 8*a*b*x**2 + 3*b**2)/(24*x**8)

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GIAC/XCAS [A]  time = 0.231567, size = 35, normalized size = 1.17 \[ -\frac{6 \, a^{2} x^{4} + 8 \, a b x^{2} + 3 \, b^{2}}{24 \, x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/24*(6*a^2*x^4 + 8*a*b*x^2 + 3*b^2)/x^8