With multi body parts, Autodesk® Inventor® exports all bodies with the built in export > cad formats > STL.

Similarly, with Assemblies, Inventor exports all parts into one single STL.

For downstream work, if you require separate STL files for each body/parts, you can use this app to quickly export them individually. 

Select one or more solid bodies from the browser or graphics window> right-click> Export Bodies to STL.

Update (version 1.1.0): Adjust export settings from Addin > Export Individual STL > Settings. (Include Timestamp, Resolution, Units, ASCII/Binary)