I had the same problem. libcurl is really complete. There is a C++ wrapper curlpp that might interest you as you ask for a C++ library. neon is another interesting C library that also support WebDAV.
curlpp seems natural if you use C++. There are many examples provided in the source distribution.
To get the content of an URL you do something like that (extracted from examples) :
// Edit : rewritten for cURLpp 0.7.3
// Note : namespace changed, was cURLpp in 0.7.2 ...
#include <curlpp/cURLpp.hpp>
#include <curlpp/Options.hpp>
// RAII cleanup
curlpp::Cleanup myCleanup;
// Send request and get a result.
// Here I use a shortcut to get it in a string stream ...
std::ostringstream os;
os << curlpp::options::Url(std::string("http://www.wikipedia.org"));
string asAskedInQuestion = os.str();
See the examples
directory in curlpp source distribution, there is a lot of more complex cases, as well as a simple complete minimal one using curlpp.
my 2 cents ...
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