3.1567 \(\int \frac{\left (a+\frac{b}{x}\right )^2}{x^5} \, dx\)

Optimal. Leaf size=30 \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6} \]

[Out]

-b^2/(6*x^6) - (2*a*b)/(5*x^5) - a^2/(4*x^4)

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Rubi [A]  time = 0.0363635, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Int[(a + b/x)^2/x^5,x]

[Out]

-b^2/(6*x^6) - (2*a*b)/(5*x^5) - a^2/(4*x^4)

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Rubi in Sympy [A]  time = 6.193, size = 27, normalized size = 0.9 \[ - \frac{a^{2}}{4 x^{4}} - \frac{2 a b}{5 x^{5}} - \frac{b^{2}}{6 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-a**2/(4*x**4) - 2*a*b/(5*x**5) - b**2/(6*x**6)

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Mathematica [A]  time = 0.0052618, size = 30, normalized size = 1. \[ -\frac{a^2}{4 x^4}-\frac{2 a b}{5 x^5}-\frac{b^2}{6 x^6} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b/x)^2/x^5,x]

[Out]

-b^2/(6*x^6) - (2*a*b)/(5*x^5) - a^2/(4*x^4)

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Maple [A]  time = 0.007, size = 25, normalized size = 0.8 \[ -{\frac{{b}^{2}}{6\,{x}^{6}}}-{\frac{2\,ab}{5\,{x}^{5}}}-{\frac{{a}^{2}}{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((a+b/x)^2/x^5,x)

[Out]

-1/6*b^2/x^6-2/5*a*b/x^5-1/4*a^2/x^4

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Maxima [A]  time = 1.4444, size = 32, normalized size = 1.07 \[ -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/60*(15*a^2*x^2 + 24*a*b*x + 10*b^2)/x^6

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Fricas [A]  time = 0.21379, size = 32, normalized size = 1.07 \[ -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/60*(15*a^2*x^2 + 24*a*b*x + 10*b^2)/x^6

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Sympy [A]  time = 1.33422, size = 26, normalized size = 0.87 \[ - \frac{15 a^{2} x^{2} + 24 a b x + 10 b^{2}}{60 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((a+b/x)**2/x**5,x)

[Out]

-(15*a**2*x**2 + 24*a*b*x + 10*b**2)/(60*x**6)

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GIAC/XCAS [A]  time = 0.225218, size = 32, normalized size = 1.07 \[ -\frac{15 \, a^{2} x^{2} + 24 \, a b x + 10 \, b^{2}}{60 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/60*(15*a^2*x^2 + 24*a*b*x + 10*b^2)/x^6