Optimal. Leaf size=19 \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0093851, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 - n/2)*Sqrt[b*x^n],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.32132, size = 15, normalized size = 0.79 \[ x^{- \frac{n}{2}} \sqrt{b x^{n}} \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1-1/2*n)*(b*x**n)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00699099, size = 19, normalized size = 1. \[ x^{-n/2} \log (x) \sqrt{b x^n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 - n/2)*Sqrt[b*x^n],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.044, size = 22, normalized size = 1.2 \[{\ln \left ( x \right ) \sqrt{b \left ({x}^{{\frac{n}{2}}} \right ) ^{2}} \left ({x}^{{\frac{n}{2}}} \right ) ^{-1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1-1/2*n)*(b*x^n)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.51002, size = 8, normalized size = 0.42 \[ \sqrt{b} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)*x^(-1/2*n - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.226512, size = 36, normalized size = 1.89 \[ x x^{-\frac{1}{2} \, n - 1} \sqrt{\frac{b}{x^{2} x^{-n - 2}}} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)*x^(-1/2*n - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(-1-1/2*n)*(b*x**n)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.23396, size = 8, normalized size = 0.42 \[ \sqrt{b}{\rm ln}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^n)*x^(-1/2*n - 1),x, algorithm="giac")
[Out]