Optimal. Leaf size=21 \[ -\frac{2 \sqrt{b x^n}}{(2-n) x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0153905, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{2 \sqrt{b x^n}}{(2-n) x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^n]/x^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.9047, size = 26, normalized size = 1.24 \[ - \frac{2 x^{- \frac{n}{2}} x^{\frac{n}{2} - 1} \sqrt{b x^{n}}}{- n + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(1/2)/x**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00386763, size = 19, normalized size = 0.9 \[ \frac{2 \sqrt{b x^n}}{(n-2) x} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^n]/x^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 18, normalized size = 0.9 \[ 2\,{\frac{\sqrt{b{x}^{n}}}{x \left ( -2+n \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(1/2)/x^2,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)/x^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)/x^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**n)**(1/2)/x**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{b x^{n}}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)/x^2,x, algorithm="giac")
[Out]