Optimal. Leaf size=19 \[ \frac{3 x \left (b x^n\right )^{2/3}}{2 n+3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0150834, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{3 x \left (b x^n\right )^{2/3}}{2 n+3} \]
Antiderivative was successfully verified.
[In] Int[(b*x^n)^(2/3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.25012, size = 29, normalized size = 1.53 \[ \frac{3 x^{- \frac{2 n}{3}} x^{\frac{2 n}{3} + 1} \left (b x^{n}\right )^{\frac{2}{3}}}{2 n + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**n)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00462759, size = 20, normalized size = 1.05 \[ \frac{x \left (b x^n\right )^{2/3}}{\frac{2 n}{3}+1} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x^n)^(2/3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 18, normalized size = 1. \[ 3\,{\frac{x \left ( b{x}^{n} \right ) ^{2/3}}{3+2\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^n)^(2/3),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)^(2/3),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)^(2/3),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((b*x**n)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.247843, size = 26, normalized size = 1.37 \[ \frac{3 \, b^{\frac{2}{3}} x e^{\left (\frac{2}{3} \, n{\rm ln}\left (x\right )\right )}}{2 \, n + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^n)^(2/3),x, algorithm="giac")
[Out]