# Help With This Supposedly Easy Integration!

1. Sep 26, 2010

### NeedPhysHelp8

The problem statement, all variables and given/known data

Integrate: $$\exp(\sin(t)) / (1 + t^2)$$

The attempt at a solution
Ok so I tried substituting u=sin(t) du=cos(t)dt but I end up with (1 + arcsin^2(u)) on the bottom and I don't know how to integrate that.
I also tried letting t=cos(u) dt=-sin(u)du but then I end up with e^(sin(cos(t)) which I've never seen before!
If anyone knows how to do this please just give me a hint or the first step to take and I will try to do the rest! Thanks

2. Sep 26, 2010

### vela

Staff Emeritus
I don't think you can integrate that analytically. Is this integral part of a larger problem?

3. Sep 26, 2010

### NeedPhysHelp8

Ok well it was a differential equation problem that I reduced to that but here is the initial problem:

$$dy/dt + y\cos(t) = 1/ (1+t^2)$$

so I got an integrating factor of $$e^(sint)$$ which led to this integral! Hope this helps maybe I did something wrong in first part.

4. Sep 26, 2010

### vela

Staff Emeritus
Hmm, perhaps you're expected to leave the solution in terms of the integral.

5. Sep 26, 2010

### NeedPhysHelp8

I don't think so since the prof asked to solve it in terms of t explicitly. Maybe she made a mistake in writing the problem if this cannot be solved analytically.