3.2162 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^6} \, dx\)

Optimal. Leaf size=30 \[ -\frac{9}{5 x^5}+\frac{6}{x^4}-\frac{22}{3 x^3}+\frac{4}{x^2}-\frac{1}{x} \]

[Out]

-9/(5*x^5) + 6/x^4 - 22/(3*x^3) + 4/x^2 - x^(-1)

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Rubi [A]  time = 0.0330635, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ -\frac{9}{5 x^5}+\frac{6}{x^4}-\frac{22}{3 x^3}+\frac{4}{x^2}-\frac{1}{x} \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^6,x]

[Out]

-9/(5*x^5) + 6/x^4 - 22/(3*x^3) + 4/x^2 - x^(-1)

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Rubi in Sympy [A]  time = 5.40079, size = 26, normalized size = 0.87 \[ - \frac{1}{x} + \frac{4}{x^{2}} - \frac{22}{3 x^{3}} + \frac{6}{x^{4}} - \frac{9}{5 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2-4*x+3)**2/x**6,x)

[Out]

-1/x + 4/x**2 - 22/(3*x**3) + 6/x**4 - 9/(5*x**5)

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Mathematica [A]  time = 0.00157144, size = 30, normalized size = 1. \[ -\frac{9}{5 x^5}+\frac{6}{x^4}-\frac{22}{3 x^3}+\frac{4}{x^2}-\frac{1}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - 4*x + x^2)^2/x^6,x]

[Out]

-9/(5*x^5) + 6/x^4 - 22/(3*x^3) + 4/x^2 - x^(-1)

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Maple [A]  time = 0.007, size = 27, normalized size = 0.9 \[ -{\frac{9}{5\,{x}^{5}}}+6\,{x}^{-4}-{\frac{22}{3\,{x}^{3}}}+4\,{x}^{-2}-{x}^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^6,x)

[Out]

-9/5/x^5+6/x^4-22/3/x^3+4/x^2-1/x

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Maxima [A]  time = 0.795154, size = 34, normalized size = 1.13 \[ -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^6,x, algorithm="maxima")

[Out]

-1/15*(15*x^4 - 60*x^3 + 110*x^2 - 90*x + 27)/x^5

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Fricas [A]  time = 0.192559, size = 34, normalized size = 1.13 \[ -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^6,x, algorithm="fricas")

[Out]

-1/15*(15*x^4 - 60*x^3 + 110*x^2 - 90*x + 27)/x^5

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Sympy [A]  time = 0.237971, size = 26, normalized size = 0.87 \[ - \frac{15 x^{4} - 60 x^{3} + 110 x^{2} - 90 x + 27}{15 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2-4*x+3)**2/x**6,x)

[Out]

-(15*x**4 - 60*x**3 + 110*x**2 - 90*x + 27)/(15*x**5)

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GIAC/XCAS [A]  time = 0.203456, size = 34, normalized size = 1.13 \[ -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^6,x, algorithm="giac")

[Out]

-1/15*(15*x^4 - 60*x^3 + 110*x^2 - 90*x + 27)/x^5