3.2163 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^7} \, dx\)

Optimal. Leaf size=36 \[ -\frac{3}{2 x^6}+\frac{24}{5 x^5}-\frac{11}{2 x^4}+\frac{8}{3 x^3}-\frac{1}{2 x^2} \]

[Out]

-3/(2*x^6) + 24/(5*x^5) - 11/(2*x^4) + 8/(3*x^3) - 1/(2*x^2)

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Rubi [A]  time = 0.0340478, antiderivative size = 36, 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 \[ -\frac{3}{2 x^6}+\frac{24}{5 x^5}-\frac{11}{2 x^4}+\frac{8}{3 x^3}-\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^7,x]

[Out]

-3/(2*x^6) + 24/(5*x^5) - 11/(2*x^4) + 8/(3*x^3) - 1/(2*x^2)

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Rubi in Sympy [A]  time = 5.39574, size = 32, normalized size = 0.89 \[ - \frac{1}{2 x^{2}} + \frac{8}{3 x^{3}} - \frac{11}{2 x^{4}} + \frac{24}{5 x^{5}} - \frac{3}{2 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2-4*x+3)**2/x**7,x)

[Out]

-1/(2*x**2) + 8/(3*x**3) - 11/(2*x**4) + 24/(5*x**5) - 3/(2*x**6)

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Mathematica [A]  time = 0.00130969, size = 36, normalized size = 1. \[ -\frac{3}{2 x^6}+\frac{24}{5 x^5}-\frac{11}{2 x^4}+\frac{8}{3 x^3}-\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - 4*x + x^2)^2/x^7,x]

[Out]

-3/(2*x^6) + 24/(5*x^5) - 11/(2*x^4) + 8/(3*x^3) - 1/(2*x^2)

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Maple [A]  time = 0.008, size = 27, normalized size = 0.8 \[ -{\frac{3}{2\,{x}^{6}}}+{\frac{24}{5\,{x}^{5}}}-{\frac{11}{2\,{x}^{4}}}+{\frac{8}{3\,{x}^{3}}}-{\frac{1}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^7,x)

[Out]

-3/2/x^6+24/5/x^5-11/2/x^4+8/3/x^3-1/2/x^2

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Maxima [A]  time = 0.805505, size = 34, normalized size = 0.94 \[ -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^7,x, algorithm="maxima")

[Out]

-1/30*(15*x^4 - 80*x^3 + 165*x^2 - 144*x + 45)/x^6

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Fricas [A]  time = 0.206271, size = 34, normalized size = 0.94 \[ -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^7,x, algorithm="fricas")

[Out]

-1/30*(15*x^4 - 80*x^3 + 165*x^2 - 144*x + 45)/x^6

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Sympy [A]  time = 0.255811, size = 26, normalized size = 0.72 \[ - \frac{15 x^{4} - 80 x^{3} + 165 x^{2} - 144 x + 45}{30 x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2-4*x+3)**2/x**7,x)

[Out]

-(15*x**4 - 80*x**3 + 165*x**2 - 144*x + 45)/(30*x**6)

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GIAC/XCAS [A]  time = 0.20158, size = 34, normalized size = 0.94 \[ -\frac{15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^7,x, algorithm="giac")

[Out]

-1/30*(15*x^4 - 80*x^3 + 165*x^2 - 144*x + 45)/x^6