Optimal. Leaf size=24 \[ -\frac{2 b x^{n-2} \sqrt{b x^n}}{4-3 n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0189459, antiderivative size = 24, 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 \[ -\frac{2 b x^{n-2} \sqrt{b x^n}}{4-3 n} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(3/2)/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.28617, size = 31, normalized size = 1.29 \[ - \frac{2 b x^{- \frac{n}{2}} x^{\frac{3 n}{2} - 2} \sqrt{b x^{n}}}{- 3 n + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(3/2)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0109716, size = 22, normalized size = 0.92 \[ \frac{\left (b x^n\right )^{3/2}}{\left (\frac{3 n}{2}-2\right ) x^2} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(3/2)/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 20, normalized size = 0.8 \[ 2\,{\frac{ \left ( b{x}^{n} \right ) ^{3/2}}{{x}^{2} \left ( 3\,n-4 \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(3/2)/x^3,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((b*x^n)^(3/2)/x^3,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((b*x^n)^(3/2)/x^3,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((b*x**n)**(3/2)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (b x^{n}\right )^{\frac{3}{2}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(3/2)/x^3,x, algorithm="giac")
[Out]