Optimal. Leaf size=14 \[ \frac{2 \sqrt{b x^n}}{n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00976556, antiderivative size = 14, 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 \[ \frac{2 \sqrt{b x^n}}{n} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^n]/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.7267, size = 10, normalized size = 0.71 \[ \frac{2 \sqrt{b x^{n}}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00293232, size = 14, normalized size = 1. \[ \frac{2 \sqrt{b x^n}}{n} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^n]/x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 13, normalized size = 0.9 \[ 2\,{\frac{\sqrt{b{x}^{n}}}{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(1/2)/x,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,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226632, size = 16, normalized size = 1.14 \[ \frac{2 \, \sqrt{b x^{n}}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.752516, size = 22, normalized size = 1.57 \[ \begin{cases} \frac{2 \sqrt{b} \sqrt{x^{n}}}{n} & \text{for}\: n \neq 0 \\\sqrt{b} \log{\left (x \right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**n)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{b x^{n}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)/x,x, algorithm="giac")
[Out]