Dave's Math Tables: Integral ex 
(Math | Calculus | Integrals | Table Of | ex)
 
Discussion of
(integral) ex dx = ex + C.
1. Proof
Since we know the derivative: (d/dx) ex = ex,
we can use the Fundamental Theorem of calculus:
(integral) ex dx = (integral) (d/dx) (ex) dx = ex + C
Q.E.D.

See also the proof that (d/dx) ex = exPROOF