# Trigonometric Integral

1. Sep 12, 2010

### psholtz

1. The problem statement, all variables and given/known data

I'm trying to integrate the following form:

$$y = \int e^{\sin x} dx$$

3. The attempt at a solution

I thought about trying to write something like:

$$y = \int e^{\frac{i}{2}e^{-ix} - \frac{i}{2}e^{ix}} dx$$

But this seems to lead down the road of trying to integrate the form

$$\int e^{e^x} dx$$

which seems similarly intractable.

Is there a way to reduce the expression to something simpler, or are you just left w/ leaving the expression in a form like:

$$y(x) = \int_{x_0}^x e^{\sin t} dt$$

2. Sep 12, 2010

### jgens

3. Sep 12, 2010

### psholtz

Yes, I tried Wolfram before posting as well and it came up empty for me too..

My guess is that the integral:

$$y = \int e^{\sin x + 2x} dx$$

is just as intractable as the first one, yes?