Optimal. Leaf size=14 \[ \frac{1}{2-x}+\tan ^{-1}(2-x) \]
[Out]
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Rubi [A] time = 0.0239587, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.19 \[ \frac{1}{2-x}+\tan ^{-1}(2-x) \]
Antiderivative was successfully verified.
[In] Int[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]
[Out]
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Rubi in Sympy [A] time = 3.55335, size = 10, normalized size = 0.71 \[ - \operatorname{atan}{\left (x - 2 \right )} + \frac{2}{- 2 x + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2-4*x+4)/(x**2-4*x+5),x)
[Out]
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Mathematica [A] time = 0.0123414, size = 14, normalized size = 1. \[ \tan ^{-1}(2-x)-\frac{1}{x-2} \]
Antiderivative was successfully verified.
[In] Integrate[1/((4 - 4*x + x^2)*(5 - 4*x + x^2)),x]
[Out]
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Maple [A] time = 0.009, size = 15, normalized size = 1.1 \[ -\arctan \left ( -2+x \right ) - \left ( -2+x \right ) ^{-1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2-4*x+4)/(x^2-4*x+5),x)
[Out]
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Maxima [A] time = 1.48672, size = 19, normalized size = 1.36 \[ -\frac{1}{x - 2} - \arctan \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^2 - 4*x + 5)*(x^2 - 4*x + 4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.197063, size = 23, normalized size = 1.64 \[ -\frac{{\left (x - 2\right )} \arctan \left (x - 2\right ) + 1}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^2 - 4*x + 5)*(x^2 - 4*x + 4)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.140555, size = 10, normalized size = 0.71 \[ - \operatorname{atan}{\left (x - 2 \right )} - \frac{1}{x - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2-4*x+4)/(x**2-4*x+5),x)
[Out]
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GIAC/XCAS [A] time = 0.220908, size = 19, normalized size = 1.36 \[ -\frac{1}{x - 2} - \arctan \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^2 - 4*x + 5)*(x^2 - 4*x + 4)),x, algorithm="giac")
[Out]