Help With This Supposedly Easy Integration!

  • #1
Homework Statement

Integrate: [tex] \exp(\sin(t)) / (1 + t^2) [/tex]

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
 

Answers and Replies

  • #2
vela
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I don't think you can integrate that analytically. Is this integral part of a larger problem?
 
  • #3
Ok well it was a differential equation problem that I reduced to that but here is the initial problem:

[tex] dy/dt + y\cos(t) = 1/ (1+t^2) [/tex]

so I got an integrating factor of [tex] e^(sint) [/tex] which led to this integral! Hope this helps maybe I did something wrong in first part.
 
  • #4
vela
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Hmm, perhaps you're expected to leave the solution in terms of the integral.
 
  • #5
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.
 

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