need help integrating cos(x) e^sin(x)?

Answer 1

Let's see:

e^f(x) f'(x) -- does this remind you of the chain rule much? The antiderivative is simply e^f(x) + C in these cases -- in particular, ∫e^(sin x) cos x dx = e^(sin x) + C

Answer 2

use u-substitution:
u = sin(x), then du = cos(x)dx
so integrate du e^u
= e^u + C
resub in u
= e^sin(x) + C

Answer 3

integral of u.v = u (int v dx) - int [int v dx (du/dx)]
u = cosx
v = e^sinx
now solve the problem with this formula