What is the antiderivative of the function y=(e^sinx)*cosx?

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