3.2157 \(\int \frac{\left (3-4 x+x^2\right )^2}{x} \, dx\)

Optimal. Leaf size=27 \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]

[Out]

-24*x + 11*x^2 - (8*x^3)/3 + x^4/4 + 9*Log[x]

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Rubi [A]  time = 0.0266818, 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 \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x,x]

[Out]

-24*x + 11*x^2 - (8*x^3)/3 + x^4/4 + 9*Log[x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{4}}{4} - \frac{8 x^{3}}{3} - 24 x + 9 \log{\left (x \right )} + 22 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**4/4 - 8*x**3/3 - 24*x + 9*log(x) + 22*Integral(x, x)

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Mathematica [A]  time = 0.00118554, size = 27, normalized size = 1. \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]

Antiderivative was successfully verified.

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

[Out]

-24*x + 11*x^2 - (8*x^3)/3 + x^4/4 + 9*Log[x]

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Maple [A]  time = 0.004, size = 24, normalized size = 0.9 \[ -24\,x+11\,{x}^{2}-{\frac{8\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+9\,\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x,x)

[Out]

-24*x+11*x^2-8/3*x^3+1/4*x^4+9*ln(x)

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Maxima [A]  time = 0.811556, size = 31, normalized size = 1.15 \[ \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4 - 8/3*x^3 + 11*x^2 - 24*x + 9*log(x)

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Fricas [A]  time = 0.200803, size = 31, normalized size = 1.15 \[ \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4 - 8/3*x^3 + 11*x^2 - 24*x + 9*log(x)

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Sympy [A]  time = 0.158093, size = 24, normalized size = 0.89 \[ \frac{x^{4}}{4} - \frac{8 x^{3}}{3} + 11 x^{2} - 24 x + 9 \log{\left (x \right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2-4*x+3)**2/x,x)

[Out]

x**4/4 - 8*x**3/3 + 11*x**2 - 24*x + 9*log(x)

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GIAC/XCAS [A]  time = 0.204488, size = 32, normalized size = 1.19 \[ \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \,{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/4*x^4 - 8/3*x^3 + 11*x^2 - 24*x + 9*ln(abs(x))