Optimal. Leaf size=28 \[ \frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+1}}{(n+1)^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0098877, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2304} \[ \frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+1}}{(n+1)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2304
Rubi steps
\begin{align*} \int x^n \log (a x) \, dx &=-\frac{x^{1+n}}{(1+n)^2}+\frac{x^{1+n} \log (a x)}{1+n}\\ \end{align*}
Mathematica [A] time = 0.0052956, size = 21, normalized size = 0.75 \[ \frac{x^{n+1} ((n+1) \log (a x)-1)}{(n+1)^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.013, size = 36, normalized size = 1.3 \begin{align*}{\frac{x\ln \left ( ax \right ){{\rm e}^{n\ln \left ( x \right ) }}}{1+n}}-{\frac{x{{\rm e}^{n\ln \left ( x \right ) }}}{{n}^{2}+2\,n+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0.519222, size = 85, normalized size = 3.04 \begin{align*} \frac{{\left ({\left (n + 1\right )} x \log \left (a\right ) +{\left (n + 1\right )} x \log \left (x\right ) - x\right )} x^{n}}{n^{2} + 2 \, n + 1} \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 [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{n} \log \left (a x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]