3.2159 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^3} \, dx\)

Optimal. Leaf size=27 \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]

[Out]

-9/(2*x^2) + 24/x - 8*x + x^2/2 + 22*Log[x]

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Rubi [A]  time = 0.0335931, antiderivative size = 27, 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 \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^3,x]

[Out]

-9/(2*x^2) + 24/x - 8*x + x^2/2 + 22*Log[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - 8 x + 22 \log{\left (x \right )} + \int x\, dx + \frac{24}{x} - \frac{9}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x + 22*log(x) + Integral(x, x) + 24/x - 9/(2*x**2)

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Mathematica [A]  time = 0.00135001, size = 27, normalized size = 1. \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]

Antiderivative was successfully verified.

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

[Out]

-9/(2*x^2) + 24/x - 8*x + x^2/2 + 22*Log[x]

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Maple [A]  time = 0.008, size = 24, normalized size = 0.9 \[ -{\frac{9}{2\,{x}^{2}}}+24\,{x}^{-1}-8\,x+{\frac{{x}^{2}}{2}}+22\,\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^3,x)

[Out]

-9/2/x^2+24/x-8*x+1/2*x^2+22*ln(x)

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Maxima [A]  time = 0.801528, size = 31, normalized size = 1.15 \[ \frac{1}{2} \, x^{2} - 8 \, x + \frac{3 \,{\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2 - 8*x + 3/2*(16*x - 3)/x^2 + 22*log(x)

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Fricas [A]  time = 0.202769, size = 34, normalized size = 1.26 \[ \frac{x^{4} - 16 \, x^{3} + 44 \, x^{2} \log \left (x\right ) + 48 \, x - 9}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*(x^4 - 16*x^3 + 44*x^2*log(x) + 48*x - 9)/x^2

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Sympy [A]  time = 0.195879, size = 22, normalized size = 0.81 \[ \frac{x^{2}}{2} - 8 x + 22 \log{\left (x \right )} + \frac{48 x - 9}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**2/2 - 8*x + 22*log(x) + (48*x - 9)/(2*x**2)

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GIAC/XCAS [A]  time = 0.20426, size = 32, normalized size = 1.19 \[ \frac{1}{2} \, x^{2} - 8 \, x + \frac{3 \,{\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \,{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/2*x^2 - 8*x + 3/2*(16*x - 3)/x^2 + 22*ln(abs(x))