$\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots . .+a^{n-1}\right) d x=$ (where $C$ is a constant of integration)
$\int(x-a)\left(x^{n-1}+x^{n-2} a+\ldots . .+a^{n-1}\right) d x=$ (where $C$ is a constant of integration)
$\frac{x^{n+1}}{n+1}-a^n x+C$
$x^n-a^n+C$
$\frac{x^{n+1}}{n+1}-a^n+C$
$n a^{n-1}+C$
Solution
$\begin{aligned} & \int(x-a)\left(x^{n-1}+x^{n-2} \cdot a+\ldots \ldots+a^{n-1}\right) d x \\ & =\int\left(x^n-a^n\right) d x \\ & =\frac{x^{n+1}}{n+1}-a^n x+c\end{aligned}$