3.2160 \(\int \frac{\left (3-4 x+x^2\right )^2}{x^4} \, dx\)

Optimal. Leaf size=21 \[ -\frac{3}{x^3}+\frac{12}{x^2}+x-\frac{22}{x}-8 \log (x) \]

[Out]

-3/x^3 + 12/x^2 - 22/x + x - 8*Log[x]

_______________________________________________________________________________________

Rubi [A]  time = 0.032949, antiderivative size = 21, 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 \[ -\frac{3}{x^3}+\frac{12}{x^2}+x-\frac{22}{x}-8 \log (x) \]

Antiderivative was successfully verified.

[In]  Int[(3 - 4*x + x^2)^2/x^4,x]

[Out]

-3/x^3 + 12/x^2 - 22/x + x - 8*Log[x]

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 5.01811, size = 19, normalized size = 0.9 \[ x - 8 \log{\left (x \right )} - \frac{22}{x} + \frac{12}{x^{2}} - \frac{3}{x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 8*log(x) - 22/x + 12/x**2 - 3/x**3

_______________________________________________________________________________________

Mathematica [A]  time = 0.00155864, size = 21, normalized size = 1. \[ -\frac{3}{x^3}+\frac{12}{x^2}+x-\frac{22}{x}-8 \log (x) \]

Antiderivative was successfully verified.

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

[Out]

-3/x^3 + 12/x^2 - 22/x + x - 8*Log[x]

_______________________________________________________________________________________

Maple [A]  time = 0.008, size = 22, normalized size = 1.1 \[ -3\,{x}^{-3}+12\,{x}^{-2}-22\,{x}^{-1}+x-8\,\ln \left ( x \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2-4*x+3)^2/x^4,x)

[Out]

-3/x^3+12/x^2-22/x+x-8*ln(x)

_______________________________________________________________________________________

Maxima [A]  time = 0.785809, size = 28, normalized size = 1.33 \[ x - \frac{22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \log \left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - (22*x^2 - 12*x + 3)/x^3 - 8*log(x)

_______________________________________________________________________________________

Fricas [A]  time = 0.201072, size = 32, normalized size = 1.52 \[ \frac{x^{4} - 8 \, x^{3} \log \left (x\right ) - 22 \, x^{2} + 12 \, x - 3}{x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

(x^4 - 8*x^3*log(x) - 22*x^2 + 12*x - 3)/x^3

_______________________________________________________________________________________

Sympy [A]  time = 0.217369, size = 19, normalized size = 0.9 \[ x - 8 \log{\left (x \right )} - \frac{22 x^{2} - 12 x + 3}{x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - 8*log(x) - (22*x**2 - 12*x + 3)/x**3

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.204798, size = 30, normalized size = 1.43 \[ x - \frac{22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \,{\rm ln}\left ({\left | x \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x - (22*x^2 - 12*x + 3)/x^3 - 8*ln(abs(x))