To determine the antiderivative of the given function, we'll have to evaluate the indefinite integral.
We can use the substitution technique to evaluate the indefinite integral.
Let sin x be t.
sin x = t
We'll differentiate both sides and we'll get:
cos x*dx = dt
We'll re-write the integral, changing the x variable:
Int (e^sin x)*cos x dx = Int e^t*dt
Int e^t*dt = e^t + C
The requested antiderivative of the function y =(e^sin x)*cos x is: Y = [e^(sin x)] + C