Optimal. Leaf size=13 \[ \frac{x}{\sqrt{x^2+2 x}} \]
[Out]
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Rubi [A] time = 0.0252502, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{x}{\sqrt{x^2+2 x}} \]
Antiderivative was successfully verified.
[In] Int[x/(x*(2 + x))^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 1.63904, size = 10, normalized size = 0.77 \[ \frac{x}{\sqrt{x^{2} + 2 x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(x*(2+x))**(3/2),x)
[Out]
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Mathematica [A] time = 0.00911312, size = 11, normalized size = 0.85 \[ \frac{x}{\sqrt{x (x+2)}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(x*(2 + x))^(3/2),x]
[Out]
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Maple [A] time = 0.006, size = 15, normalized size = 1.2 \[{{x}^{2} \left ( 2+x \right ) \left ( x \left ( 2+x \right ) \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(x*(2+x))^(3/2),x)
[Out]
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Maxima [A] time = 0.680424, size = 15, normalized size = 1.15 \[ \frac{x}{\sqrt{x^{2} + 2 \, x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 2)*x)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.266967, size = 24, normalized size = 1.85 \[ \frac{2}{x - \sqrt{x^{2} + 2 \, x} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 2)*x)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\left (x \left (x + 2\right )\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(x*(2+x))**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.261805, size = 22, normalized size = 1.69 \[ \frac{2}{x - \sqrt{{\left (x + 2\right )} x} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((x + 2)*x)^(3/2),x, algorithm="giac")
[Out]