An integrated single-piece exhaust system (SPEX) with modular construction that facilitates design changes for enhanced aerodynamics, structural integrity or serviceability. The SPEX defines splined or curved exhaust path surfaces, such as a series of cylindrical and frusto-conical sections that mimic curves. The constructed sections may include: (i) a tail cone assembly fabricated from conical sections that taper downstream to a reduced diameter; or (ii) an area-ruled cross section axially aligned with one or more rows of turbine struts; or both features. Modular inner and outer diameter inlet lips enhance transitional flow between the last row blades and the SPEX, as well as enhance structural integrity. Modular strut collars have large radius profiles between the SPEX annular inner diameter and outer diameter flow surfaces, for enhanced airflow and constant thickness walls for uniform heat transfer and thermal expansion. Scalloped mounting flanges enhance structural integrity and longevity.