# how to solve the integral with terms involve exponentiation

I have problem of solving or approximating the following integral:

$$\int_{0}^{\infty} \frac{(1- (ax+1)^{(1-n)})^{(m-1)}}{(ax+1)^n} dx$$

I tried substitution or simplification, but it did not work. It was not successful.

Can anyone suggest any tips please?

Thank you.

I am assuming $$a>0,n>1$$.
Keep $$1-(ax+1)^{1-n}=u,du=a(n-1)dx/(ax+1)^n$$ which gives$$I=\int_{0}^1\frac{u^{m-1}}{a(n-1)} du=\begin{cases}\frac1{am(n-1)},&m>0\\\infty,&m\le0\end{cases}$$
For $$n=1$$ the integrand is $$0$$. For $$n<1$$ we get $$-\infty$$ for $$m\le0$$ but the same result as above for $$m>0$$.