Optimal. Leaf size=25 \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]
[Out]
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Rubi [A] time = 0.0323637, 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 \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]
Antiderivative was successfully verified.
[In] Int[(3 - 4*x + x^2)^2/x^5,x]
[Out]
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Rubi in Sympy [A] time = 5.30136, size = 22, normalized size = 0.88 \[ \log{\left (x \right )} + \frac{8}{x} - \frac{11}{x^{2}} + \frac{8}{x^{3}} - \frac{9}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2-4*x+3)**2/x**5,x)
[Out]
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Mathematica [A] time = 0.00133561, size = 25, normalized size = 1. \[ -\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(3 - 4*x + x^2)^2/x^5,x]
[Out]
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Maple [A] time = 0.012, size = 24, normalized size = 1. \[ -{\frac{9}{4\,{x}^{4}}}+8\,{x}^{-3}-11\,{x}^{-2}+8\,{x}^{-1}+\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2-4*x+3)^2/x^5,x)
[Out]
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Maxima [A] time = 0.806906, size = 31, normalized size = 1.24 \[ \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199811, size = 36, normalized size = 1.44 \[ \frac{4 \, x^{4} \log \left (x\right ) + 32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.238605, size = 22, normalized size = 0.88 \[ \log{\left (x \right )} + \frac{32 x^{3} - 44 x^{2} + 32 x - 9}{4 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2-4*x+3)**2/x**5,x)
[Out]
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GIAC/XCAS [A] time = 0.203665, size = 32, normalized size = 1.28 \[ \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} +{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 - 4*x + 3)^2/x^5,x, algorithm="giac")
[Out]