3.2161 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^5} \, dx\)

Optimal. Leaf size=25 \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]

[Out]

-9/(4*x^4) + 8/x^3 - 11/x^2 + 8/x + Log[x]

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Rubi [A]  time = 0.0323637, antiderivative size = 25, 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 \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^5,x]

[Out]

-9/(4*x^4) + 8/x^3 - 11/x^2 + 8/x + Log[x]

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Rubi in Sympy [A]  time = 5.30136, size = 22, normalized size = 0.88 \[ \log{\left (x \right )} + \frac{8}{x} - \frac{11}{x^{2}} + \frac{8}{x^{3}} - \frac{9}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2-4*x+3)**2/x**5,x)

[Out]

log(x) + 8/x - 11/x**2 + 8/x**3 - 9/(4*x**4)

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Mathematica [A]  time = 0.00133561, size = 25, normalized size = 1. \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - 4*x + x^2)^2/x^5,x]

[Out]

-9/(4*x^4) + 8/x^3 - 11/x^2 + 8/x + Log[x]

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Maple [A]  time = 0.012, size = 24, normalized size = 1. \[ -{\frac{9}{4\,{x}^{4}}}+8\,{x}^{-3}-11\,{x}^{-2}+8\,{x}^{-1}+\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^5,x)

[Out]

-9/4/x^4+8/x^3-11/x^2+8/x+ln(x)

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Maxima [A]  time = 0.806906, size = 31, normalized size = 1.24 \[ \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="maxima")

[Out]

1/4*(32*x^3 - 44*x^2 + 32*x - 9)/x^4 + log(x)

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Fricas [A]  time = 0.199811, size = 36, normalized size = 1.44 \[ \frac{4 \, x^{4} \log \left (x\right ) + 32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="fricas")

[Out]

1/4*(4*x^4*log(x) + 32*x^3 - 44*x^2 + 32*x - 9)/x^4

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Sympy [A]  time = 0.238605, size = 22, normalized size = 0.88 \[ \log{\left (x \right )} + \frac{32 x^{3} - 44 x^{2} + 32 x - 9}{4 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2-4*x+3)**2/x**5,x)

[Out]

log(x) + (32*x**3 - 44*x**2 + 32*x - 9)/(4*x**4)

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GIAC/XCAS [A]  time = 0.203665, size = 32, normalized size = 1.28 \[ \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} +{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="giac")

[Out]

1/4*(32*x^3 - 44*x^2 + 32*x - 9)/x^4 + ln(abs(x))