Can I use llvm in my commercial closed-source application without changing the source code of llvm?
Yes. LLVM uses the University of Illinois/NCSA Open Source License. It states:
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal with the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
* Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimers. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimers in the documentation and/or other materials provided with the distribution. * Neither the names of the LLVM Team, University of Illinois at Urbana-Champaign, nor the names of its contributors may be used to endorse or promote products derived from this Software without specific prior written permission.
For more details and some restrictions regarding the license see Copyright, License, and Patents