Optimal. Leaf size=26 \[ -\frac{x+2}{2 \left (x^2+2 x+2\right )}-\frac{1}{2} \tan ^{-1}(x+1) \]
[Out]
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Rubi [A] time = 0.0232807, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{x+2}{2 \left (x^2+2 x+2\right )}-\frac{1}{2} \tan ^{-1}(x+1) \]
Antiderivative was successfully verified.
[In] Int[x/(2 + 2*x + x^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 3.72278, size = 22, normalized size = 0.85 \[ - \frac{2 x + 4}{4 \left (x^{2} + 2 x + 2\right )} - \frac{\operatorname{atan}{\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x**2+2*x+2)**2,x)
[Out]
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Mathematica [A] time = 0.0204332, size = 28, normalized size = 1.08 \[ \frac{-x-2}{2 \left (x^2+2 x+2\right )}-\frac{1}{2} \tan ^{-1}(x+1) \]
Antiderivative was successfully verified.
[In] Integrate[x/(2 + 2*x + x^2)^2,x]
[Out]
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Maple [A] time = 0.005, size = 25, normalized size = 1. \[{\frac{-2\,x-4}{4\,{x}^{2}+8\,x+8}}-{\frac{\arctan \left ( 1+x \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x^2+2*x+2)^2,x)
[Out]
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Maxima [A] time = 0.752572, size = 30, normalized size = 1.15 \[ -\frac{x + 2}{2 \,{\left (x^{2} + 2 \, x + 2\right )}} - \frac{1}{2} \, \arctan \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 + 2*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.202441, size = 38, normalized size = 1.46 \[ -\frac{{\left (x^{2} + 2 \, x + 2\right )} \arctan \left (x + 1\right ) + x + 2}{2 \,{\left (x^{2} + 2 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 + 2*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.249234, size = 20, normalized size = 0.77 \[ - \frac{x + 2}{2 x^{2} + 4 x + 4} - \frac{\operatorname{atan}{\left (x + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x**2+2*x+2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.2026, size = 30, normalized size = 1.15 \[ -\frac{x + 2}{2 \,{\left (x^{2} + 2 \, x + 2\right )}} - \frac{1}{2} \, \arctan \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x^2 + 2*x + 2)^2,x, algorithm="giac")
[Out]