Optimal. Leaf size=10 \[ x+\log \left ((x-1)^2+1\right ) \]
[Out]
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Rubi [A] time = 0.0287703, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ x+\log \left ((x-1)^2+1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/(1 + (-1 + x)^2),x]
[Out]
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Rubi in Sympy [A] time = 5.57177, size = 10, normalized size = 1. \[ x + \log{\left (\left (x - 1\right )^{2} + 1 \right )} - 1 \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(1+(-1+x)**2),x)
[Out]
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Mathematica [A] time = 0.0106058, size = 11, normalized size = 1.1 \[ \log \left (x^2-2 x+2\right )+x \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(1 + (-1 + x)^2),x]
[Out]
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Maple [A] time = 0.003, size = 12, normalized size = 1.2 \[ x+\ln \left ({x}^{2}-2\,x+2 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(1+(-1+x)^2),x)
[Out]
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Maxima [A] time = 0.801978, size = 15, normalized size = 1.5 \[ x + \log \left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x - 1)^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.289087, size = 15, normalized size = 1.5 \[ x + \log \left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x - 1)^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.147849, size = 10, normalized size = 1. \[ x + \log{\left (x^{2} - 2 x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(1+(-1+x)**2),x)
[Out]
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GIAC/XCAS [A] time = 0.265363, size = 15, normalized size = 1.5 \[ x +{\rm ln}\left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/((x - 1)^2 + 1),x, algorithm="giac")
[Out]