Optimal. Leaf size=22 \[ \frac{1}{2} \log \left (x^2-2 x+2\right )-\tan ^{-1}(1-x) \]
[Out]
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Rubi [A] time = 0.0184598, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{1}{2} \log \left (x^2-2 x+2\right )-\tan ^{-1}(1-x) \]
Antiderivative was successfully verified.
[In] Int[x/(2 - 2*x + x^2),x]
[Out]
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Rubi in Sympy [A] time = 2.01616, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x^{2} - 2 x + 2 \right )}}{2} + \operatorname{atan}{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**2-2*x+2),x)
[Out]
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Mathematica [A] time = 0.00538467, size = 22, normalized size = 1. \[ \frac{1}{2} \log \left (x^2-2 x+2\right )-\tan ^{-1}(1-x) \]
Antiderivative was successfully verified.
[In] Integrate[x/(2 - 2*x + x^2),x]
[Out]
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Maple [A] time = 0.006, size = 17, normalized size = 0.8 \[ \arctan \left ( -1+x \right ) +{\frac{\ln \left ({x}^{2}-2\,x+2 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^2-2*x+2),x)
[Out]
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Maxima [A] time = 1.51392, size = 22, normalized size = 1. \[ \arctan \left (x - 1\right ) + \frac{1}{2} \, \log \left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - 2*x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197379, size = 22, normalized size = 1. \[ \arctan \left (x - 1\right ) + \frac{1}{2} \, \log \left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - 2*x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.093142, size = 15, normalized size = 0.68 \[ \frac{\log{\left (x^{2} - 2 x + 2 \right )}}{2} + \operatorname{atan}{\left (x - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**2-2*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.222689, size = 22, normalized size = 1. \[ \arctan \left (x - 1\right ) + \frac{1}{2} \,{\rm ln}\left (x^{2} - 2 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 - 2*x + 2),x, algorithm="giac")
[Out]