Optimal. Leaf size=22 \[ \frac{x^{n/2} \log (x)}{b \sqrt{b x^n}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00877873, antiderivative size = 22, 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 \[ \frac{x^{n/2} \log (x)}{b \sqrt{b x^n}} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + (3*n)/2)/(b*x^n)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.65139, size = 19, normalized size = 0.86 \[ \frac{x^{- \frac{n}{2}} \sqrt{b x^{n}} \log{\left (x \right )}}{b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+3/2*n)/(b*x**n)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00662045, size = 19, normalized size = 0.86 \[ \frac{x^{3 n/2} \log (x)}{\left (b x^n\right )^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + (3*n)/2)/(b*x^n)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.045, size = 23, normalized size = 1.1 \[{\frac{\ln \left ( x \right ) }{b}{x}^{{\frac{n}{2}}}{\frac{1}{\sqrt{b \left ({x}^{{\frac{n}{2}}} \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+3/2*n)/(b*x^n)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.53026, size = 8, normalized size = 0.36 \[ \frac{\log \left (x\right )}{b^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3/2*n - 1)/(b*x^n)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.237995, size = 27, normalized size = 1.23 \[ \frac{\sqrt{b x^{n}} \log \left (x\right )}{b^{2} x^{\frac{1}{2} \, n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3/2*n - 1)/(b*x^n)^(3/2),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+3/2*n)/(b*x**n)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{\frac{3}{2} \, n - 1}}{\left (b x^{n}\right )^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(3/2*n - 1)/(b*x^n)^(3/2),x, algorithm="giac")
[Out]