Optimal. Leaf size=31 \[ \frac{x^3 \sqrt{b-\frac{a}{x^2}}}{2 \sqrt{a-b x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.120606, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.107 \[ \frac{x^3 \sqrt{b-\frac{a}{x^2}}}{2 \sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Int[(Sqrt[b - a/x^2]*x^2)/Sqrt[a - b*x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{\sqrt{a - b x^{2}} \int x\, dx}{x \sqrt{- \frac{a}{x^{2}} + b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0156379, size = 31, normalized size = 1. \[ \frac{x^3 \sqrt{b-\frac{a}{x^2}}}{2 \sqrt{a-b x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[(Sqrt[b - a/x^2]*x^2)/Sqrt[a - b*x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 31, normalized size = 1. \[{\frac{{x}^{3}}{2}\sqrt{-{\frac{-b{x}^{2}+a}{{x}^{2}}}}{\frac{1}{\sqrt{-b{x}^{2}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.726032, size = 7, normalized size = 0.23 \[ -\frac{1}{2} i \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)*x^2/sqrt(-b*x^2 + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.274983, size = 55, normalized size = 1.77 \[ -\frac{\sqrt{-b x^{2} + a} x^{3} \sqrt{\frac{b x^{2} - a}{x^{2}}}}{2 \,{\left (b x^{2} - a\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)*x^2/sqrt(-b*x^2 + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2} \sqrt{- \frac{a}{x^{2}} + b}}{\sqrt{a - b x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b-a/x**2)**(1/2)/(-b*x**2+a)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.273877, size = 53, normalized size = 1.71 \[ -\frac{{\left (b x^{2} - a\right )} i{\rm sign}\left (b x^{2} - a\right ){\rm sign}\left (x\right )}{2 \, b} + \frac{a i{\rm sign}\left (a\right ){\rm sign}\left (x\right )}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b - a/x^2)*x^2/sqrt(-b*x^2 + a),x, algorithm="giac")
[Out]