Optimal. Leaf size=14 \[ \frac{x^2}{2}+2 \log (x+2) \]
[Out]
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Rubi [A] time = 0.0246137, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{x^2}{2}+2 \log (x+2) \]
Antiderivative was successfully verified.
[In] Int[(2 + 2*x + x^2)/(2 + x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 2 \log{\left (x + 2 \right )} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+2*x+2)/(2+x),x)
[Out]
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Mathematica [A] time = 0.00669884, size = 15, normalized size = 1.07 \[ \frac{1}{2} \left (x^2+4 \log (x+2)-4\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 2*x + x^2)/(2 + x),x]
[Out]
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Maple [A] time = 0.005, size = 13, normalized size = 0.9 \[{\frac{{x}^{2}}{2}}+2\,\ln \left ( 2+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+2*x+2)/(2+x),x)
[Out]
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Maxima [A] time = 0.805176, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, x^{2} + 2 \, \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 2)/(x + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214002, size = 16, normalized size = 1.14 \[ \frac{1}{2} \, x^{2} + 2 \, \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 2)/(x + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.125825, size = 10, normalized size = 0.71 \[ \frac{x^{2}}{2} + 2 \log{\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+2*x+2)/(2+x),x)
[Out]
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GIAC/XCAS [A] time = 0.203123, size = 18, normalized size = 1.29 \[ \frac{1}{2} \, x^{2} + 2 \,{\rm ln}\left ({\left | x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^2 + 2*x + 2)/(x + 2),x, algorithm="giac")
[Out]