Optimal. Leaf size=26 \[ \frac{4 \left (\sqrt{\frac{1}{x}}+\frac{1}{x}\right )^{3/2}}{3 \left (\frac{1}{x}\right )^{3/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0429081, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{4 \left (\sqrt{\frac{1}{x}}+\frac{1}{x}\right )^{3/2}}{3 \left (\frac{1}{x}\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[Sqrt[x^(-1)] + x^(-1)],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.27735, size = 22, normalized size = 0.85 \[ \frac{4 \left (\sqrt{\frac{1}{x}} + \frac{1}{x}\right )^{\frac{3}{2}}}{3 \left (\frac{1}{x}\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1/x+(1/x)**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0444018, size = 0, normalized size = 0. \[ \int \sqrt{\sqrt{\frac{1}{x}}+\frac{1}{x}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[Sqrt[x^(-1)] + x^(-1)],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.029, size = 32, normalized size = 1.2 \[{\frac{4}{3}\sqrt{{\frac{1}{x} \left ( \sqrt{{x}^{-1}}x+1 \right ) }} \left ( \sqrt{{x}^{-1}}x+1 \right ){\frac{1}{\sqrt{{x}^{-1}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1/x+(1/x)^(1/2))^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.37492, size = 12, normalized size = 0.46 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/sqrt(x) + 1/x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.243532, size = 28, normalized size = 1.08 \[ \frac{4 \,{\left (x^{\frac{3}{2}} + x\right )} \sqrt{\frac{x + \sqrt{x}}{x^{\frac{3}{2}}}}}{3 \, \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/sqrt(x) + 1/x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{\sqrt{\frac{1}{x}} + \frac{1}{x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x+(1/x)**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.213938, size = 15, normalized size = 0.58 \[ \frac{4}{3} \,{\left (\sqrt{x} + 1\right )}^{\frac{3}{2}} - \frac{4}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(1/sqrt(x) + 1/x),x, algorithm="giac")
[Out]