Optimal. Leaf size=17 \[ \frac{\sqrt{x^2+2 x}}{x+2} \]
[Out]
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Rubi [A] time = 0.0236695, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{\sqrt{x^2+2 x}}{x+2} \]
Antiderivative was successfully verified.
[In] Int[1/((2 + x)*Sqrt[2*x + x^2]),x]
[Out]
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Rubi in Sympy [A] time = 4.16075, size = 12, normalized size = 0.71 \[ \frac{\sqrt{x^{2} + 2 x}}{x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2+x)/(x**2+2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.011474, size = 11, normalized size = 0.65 \[ \frac{x}{\sqrt{x (x+2)}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((2 + x)*Sqrt[2*x + x^2]),x]
[Out]
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Maple [A] time = 0.004, size = 12, normalized size = 0.7 \[{x{\frac{1}{\sqrt{{x}^{2}+2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2+x)/(x^2+2*x)^(1/2),x)
[Out]
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Maxima [A] time = 0.688519, size = 20, normalized size = 1.18 \[ \frac{\sqrt{x^{2} + 2 \, x}}{x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 2*x)*(x + 2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21037, size = 24, normalized size = 1.41 \[ \frac{2}{x - \sqrt{x^{2} + 2 \, x} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 2*x)*(x + 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x \left (x + 2\right )} \left (x + 2\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2+x)/(x**2+2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.206661, size = 24, normalized size = 1.41 \[ \frac{2}{x - \sqrt{x^{2} + 2 \, x} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^2 + 2*x)*(x + 2)),x, algorithm="giac")
[Out]