Optimal. Leaf size=16 \[ \frac{x \left (a x^m\right )^r}{m r+1} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0126771, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{x \left (a x^m\right )^r}{m r+1} \]
Antiderivative was successfully verified.
[In] Int[(a*x^m)^r,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.02921, size = 22, normalized size = 1.38 \[ \frac{x^{- m r} x^{m r + 1} \left (a x^{m}\right )^{r}}{m r + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*x**m)**r,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00507077, size = 16, normalized size = 1. \[ \frac{x \left (a x^m\right )^r}{m r+1} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^m)^r,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 17, normalized size = 1.1 \[{\frac{x \left ( a{x}^{m} \right ) ^{r}}{mr+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*x^m)^r,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.705845, size = 23, normalized size = 1.44 \[ \frac{a^{r} x{\left (x^{m}\right )}^{r}}{m r + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^m)^r,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.279681, size = 27, normalized size = 1.69 \[ \frac{x e^{\left (m r \log \left (x\right ) + r \log \left (a\right )\right )}}{m r + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^m)^r,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((a*x**m)**r,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.262485, size = 27, normalized size = 1.69 \[ \frac{x e^{\left (m r{\rm ln}\left (x\right ) + r{\rm ln}\left (a\right )\right )}}{m r + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x^m)^r,x, algorithm="giac")
[Out]