Evaluate the following integral

\(\int {\sqrt{4+\sqrt{4+\sqrt{4+\dots +\sqrt{4+x}}}} dx} \)

Like so:

Oh, Thank you! but I think the sequence is finite, so we can't just say what you did with y(x).

The ellipsis (the ...) usually indicates continuation forever. If the sequence is finite then perhaps the number of levels should be specified.