Optimal. Leaf size=13 \[ -\frac{1}{2 \left ((x+2)^2+1\right )} \]
[Out]
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Rubi [A] time = 0.0085989, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{2 \left ((x+2)^2+1\right )} \]
Antiderivative was successfully verified.
[In] Int[(2 + x)/(1 + (2 + x)^2)^2,x]
[Out]
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Rubi in Sympy [A] time = 2.15877, size = 10, normalized size = 0.77 \[ - \frac{1}{2 \left (\left (x + 2\right )^{2} + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+x)/(1+(2+x)**2)**2,x)
[Out]
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Mathematica [A] time = 0.00420682, size = 13, normalized size = 1. \[ -\frac{1}{2 \left ((x+2)^2+1\right )} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + x)/(1 + (2 + x)^2)^2,x]
[Out]
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Maple [A] time = 0.002, size = 13, normalized size = 1. \[ -{\frac{1}{2\,{x}^{2}+8\,x+10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+x)/(1+(2+x)^2)^2,x)
[Out]
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Maxima [A] time = 1.37199, size = 15, normalized size = 1.15 \[ -\frac{1}{2 \,{\left ({\left (x + 2\right )}^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.201616, size = 16, normalized size = 1.23 \[ -\frac{1}{2 \,{\left (x^{2} + 4 \, x + 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.198018, size = 12, normalized size = 0.92 \[ - \frac{1}{2 x^{2} + 8 x + 10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+x)/(1+(2+x)**2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.214925, size = 16, normalized size = 1.23 \[ -\frac{1}{2 \,{\left (x^{2} + 4 \, x + 5\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x + 2)/((x + 2)^2 + 1)^2,x, algorithm="giac")
[Out]