Optimal. Leaf size=18 \[ \frac{x^2}{2}-3 x+\frac{1}{x}+3 \log (x) \]
[Out]
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Rubi [A] time = 0.016003, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{x^2}{2}-3 x+\frac{1}{x}+3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[(-1 + 3*x - 3*x^2 + x^3)/x^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{3} - 3 x^{2} + 3 x - 1}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**3-3*x**2+3*x-1)/x**2,x)
[Out]
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Mathematica [A] time = 0.00166039, size = 18, normalized size = 1. \[ \frac{x^2}{2}-3 x+\frac{1}{x}+3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(-1 + 3*x - 3*x^2 + x^3)/x^2,x]
[Out]
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Maple [A] time = 0.008, size = 17, normalized size = 0.9 \[{x}^{-1}-3\,x+{\frac{{x}^{2}}{2}}+3\,\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^3-3*x^2+3*x-1)/x^2,x)
[Out]
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Maxima [A] time = 0.781365, size = 22, normalized size = 1.22 \[ \frac{1}{2} \, x^{2} - 3 \, x + \frac{1}{x} + 3 \, \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249545, size = 27, normalized size = 1.5 \[ \frac{x^{3} - 6 \, x^{2} + 6 \, x \log \left (x\right ) + 2}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.129684, size = 15, normalized size = 0.83 \[ \frac{x^{2}}{2} - 3 x + 3 \log{\left (x \right )} + \frac{1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**3-3*x**2+3*x-1)/x**2,x)
[Out]
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GIAC/XCAS [A] time = 0.259882, size = 23, normalized size = 1.28 \[ \frac{1}{2} \, x^{2} - 3 \, x + \frac{1}{x} + 3 \,{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 3*x^2 + 3*x - 1)/x^2,x, algorithm="giac")
[Out]