Evaluation of the integral $\int^{\infty}_{0} \frac{dx}{(x+\sqrt{x^2+1})^n}$ $$
\mbox{If}\ n>1,\ \mbox{then prove that}\quad\int_{0}^{\infty}{\mathrm{d}x \over
\left(x + \,\sqrt{\, x^{2} + 1\,}\,\right)^{n}} = {n \over n^{2} - 1}
$$
Could someone give me little hint so that I could proceed in this question. I tried putting $x = \tan\left(A\right)$ but it did not work out.

You asked for a hint, so here is one:
Let
$$
u=x+\sqrt{1+x^2}.
$$
