I need to solve following integral $$\int_u^{\infty}\left[1-\frac{1}{\left(1+\frac{a}{x^k}\right)^m}\right]xdx$$ by using substitution $v=\left(\frac{u}{x}\right)^k$ I need to show that $$\int_u^{\infty}\left[1-\frac{1}{\left(1+\frac{a}{x^k}\right)^m}\right]xdx=\int_0^1\left[1-\frac{1}{\left(1+\frac{av}{u^k}\right)^m}\right]\frac{u^2}{k}v^{\frac{2}{k}-1}dv$$ where $a,u,m$ are all positive and $k>2$. Please help me how to get this answer.
My Attempt:
In my attempt I get following answer $$\int_0^1\left[1-\frac{1}{\left(1+\frac{av}{u^k}\right)^m}\right]\frac{u^2}{k}v^{-\frac{2}{k}-1}dv$$ this answer does not allow me to solve the integration further. Please guide me where I am doing it wrong. Many thanks in advance.