Optimal. Leaf size=20 \[ \frac{x^{m+1} \left (a x^n\right )^{-1/n}}{m} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0026378, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {15, 30} \[ \frac{x^{m+1} \left (a x^n\right )^{-1/n}}{m} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 15
Rule 30
Rubi steps
\begin{align*} \int x^m \left (a x^n\right )^{-1/n} \, dx &=\left (x \left (a x^n\right )^{-1/n}\right ) \int x^{-1+m} \, dx\\ &=\frac{x^{1+m} \left (a x^n\right )^{-1/n}}{m}\\ \end{align*}
Mathematica [A] time = 0.0041813, size = 20, normalized size = 1. \[ \frac{x^{m+1} \left (a x^n\right )^{-1/n}}{m} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 21, normalized size = 1.1 \begin{align*}{\frac{{x}^{1+m}}{m\sqrt [n]{a{x}^{n}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.01143, size = 36, normalized size = 1.8 \begin{align*} \frac{x e^{\left (m \log \left (x\right ) - \frac{\log \left (x^{n}\right )}{n}\right )}}{a^{\left (\frac{1}{n}\right )} m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.81443, size = 23, normalized size = 1.15 \begin{align*} \frac{x^{m}}{a^{\left (\frac{1}{n}\right )} m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.12959, size = 19, normalized size = 0.95 \begin{align*} \frac{x^{m}}{a^{\left (\frac{1}{n}\right )} m} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]