<p>Can I integrate my exsisting C++ library in an iPhone application?</p>

Objective C++ is well defined and supported by Apple's gcc.
But you can't mix C++ and objective C classes, which makes this rather messy pretty fast. I don't think there are many projects in the wild which mix C++ and Objective C to any serious extent.
This highly depends on your library, but if (realistically) feasible I'd wrap the C++ inside a C library, using extern "C" entrypoints for all real functionality, and link with that from inside your objective C code for your iphone app.