3.2158 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^2} \, dx\)

Optimal. Leaf size=25 \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]

[Out]

-9/x + 22*x - 4*x^2 + x^3/3 - 24*Log[x]

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Rubi [A]  time = 0.0339393, 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 \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^2,x]

[Out]

-9/x + 22*x - 4*x^2 + x^3/3 - 24*Log[x]

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00134521, size = 25, normalized size = 1. \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]

Antiderivative was successfully verified.

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

[Out]

-9/x + 22*x - 4*x^2 + x^3/3 - 24*Log[x]

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Maple [A]  time = 0.009, size = 24, normalized size = 1. \[ -9\,{x}^{-1}+22\,x-4\,{x}^{2}+{\frac{{x}^{3}}{3}}-24\,\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^2,x)

[Out]

-9/x+22*x-4*x^2+1/3*x^3-24*ln(x)

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Maxima [A]  time = 0.809384, size = 31, normalized size = 1.24 \[ \frac{1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac{9}{x} - 24 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3 - 4*x^2 + 22*x - 9/x - 24*log(x)

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Fricas [A]  time = 0.200729, size = 34, normalized size = 1.36 \[ \frac{x^{4} - 12 \, x^{3} + 66 \, x^{2} - 72 \, x \log \left (x\right ) - 27}{3 \, x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*(x^4 - 12*x^3 + 66*x^2 - 72*x*log(x) - 27)/x

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Sympy [A]  time = 0.169346, size = 20, normalized size = 0.8 \[ \frac{x^{3}}{3} - 4 x^{2} + 22 x - 24 \log{\left (x \right )} - \frac{9}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**3/3 - 4*x**2 + 22*x - 24*log(x) - 9/x

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GIAC/XCAS [A]  time = 0.204232, size = 32, normalized size = 1.28 \[ \frac{1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac{9}{x} - 24 \,{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/3*x^3 - 4*x^2 + 22*x - 9/x - 24*ln(abs(x))