Integral with several parameters 
Let $r>0$. Find $(p,q) \in \mathbb{R}^{2}$ such that the integral:
  $$\int_{1}^{\infty}{\frac{(x^{r}-1)^{p}}{x^{q}}} ~dx$$
  converges and for those values calculate it.

I've already calculated the values for which it is convergent. The integral above converges iff $rp-q <-1$ or equivalently when $p<\frac{q-1}{r}$.
I get stuck when trying to calculate it. I've derived the integrand with respect to every parameter and then tried to substitute the order of integration but in all cases I get a non-elementary integral. Any ideas how to calculate this? Any help would be appreciated.
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\begin{align}
&\bbox[5px,#ffd]{\large\int_{1}^{\infty}{\pars{x^{r} - 1}^{p} \over x^{q}}\,\dd x} =
\int_{1}^{0}{\pars{x^{-r} - 1}^{p} \over x^{-q}}\,\pars{-\,{\dd x \over x^{2}}}
\\[5mm] = &\
\int_{0}^{1}{\pars{1 - x^{r}}^{p} \over x^{pr - q + 2}}\,\dd x =
\int_{0}^{1}{\pars{1 - x}^{p} \over \pars{x^{1/r}}^{pr - q + 2}}
\,{1 \over r}\,x^{1/r - 1}\dd x
\\[5mm] = &\
{1 \over r}\int_{0}^{1}\pars{1 - x}^{p}x^{-p + \pars{q - 1}/r -1}\,\dd x
\\[3mm]&=\color{#00f}{\large{1 \over r}\,{\rm B}\pars{p + 1,-p + {q - 1 \over r}}}
\\[5mm]&\quad \Re\pars{{q - 1 \over r}} > \Re p > -1
\end{align}
where ${\rm B}\pars{x,y}$ is the Beta function.
A: Carry out the substitution $y=x^{1-q}$ and then use Newton's generalized binomial theorem.
