Optimal. Leaf size=21 \[ \frac{2 x^2}{(4-n) \sqrt{b x^n}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0134409, antiderivative size = 21, 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 \[ \frac{2 x^2}{(4-n) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[b*x^n],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.41738, size = 26, normalized size = 1.24 \[ \frac{2 x^{- \frac{n}{2}} x^{- \frac{n}{2} + 2} \sqrt{b x^{n}}}{b \left (- n + 4\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**n)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00654173, size = 19, normalized size = 0.9 \[ -\frac{2 x^2}{(n-4) \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[b*x^n],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 18, normalized size = 0.9 \[ -2\,{\frac{{x}^{2}}{ \left ( n-4 \right ) \sqrt{b{x}^{n}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^n)^(1/2),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(x/sqrt(b*x^n),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(x/sqrt(b*x^n),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(x/(b*x**n)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\sqrt{b x^{n}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(b*x^n),x, algorithm="giac")
[Out]