Optimal. Leaf size=19 \[ -\frac{2 \tan ^{-1}\left (\frac{1-2 x}{\sqrt{7}}\right )}{\sqrt{7}} \]
[Out]
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Rubi [A] time = 0.0257762, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{2 \tan ^{-1}\left (\frac{1-2 x}{\sqrt{7}}\right )}{\sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[(2 - x + x^2)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 0.663014, size = 22, normalized size = 1.16 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\sqrt{7} \left (\frac{2 x}{7} - \frac{1}{7}\right ) \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2-x+2),x)
[Out]
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Mathematica [A] time = 0.00933582, size = 19, normalized size = 1. \[ \frac{2 \tan ^{-1}\left (\frac{2 x-1}{\sqrt{7}}\right )}{\sqrt{7}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 - x + x^2)^(-1),x]
[Out]
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Maple [A] time = 0.004, size = 17, normalized size = 0.9 \[{\frac{2\,\sqrt{7}}{7}\arctan \left ({\frac{ \left ( 2\,x-1 \right ) \sqrt{7}}{7}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2-x+2),x)
[Out]
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Maxima [A] time = 1.5319, size = 22, normalized size = 1.16 \[ \frac{2}{7} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^2 - x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194369, size = 22, normalized size = 1.16 \[ \frac{2}{7} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^2 - x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.093559, size = 26, normalized size = 1.37 \[ \frac{2 \sqrt{7} \operatorname{atan}{\left (\frac{2 \sqrt{7} x}{7} - \frac{\sqrt{7}}{7} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2-x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.224673, size = 22, normalized size = 1.16 \[ \frac{2}{7} \, \sqrt{7} \arctan \left (\frac{1}{7} \, \sqrt{7}{\left (2 \, x - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^2 - x + 2),x, algorithm="giac")
[Out]