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