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# integrating sinx /x

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1. I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
2. (Original post by StarvingAutist)
I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
Limits?
3. (Original post by StarvingAutist)
I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
You'll need limits, it doesn't have an antiderivative in terms of elementary functions (other than its trivial Si(x)).
4. (Original post by ODES_PDES)
Limits?
5. (Original post by StarvingAutist)
I have no idea how to go about this.. integrating by parts won't work and I can't think of a substitution.
It's a result in itself.

https://en.wikipedia.org/wiki/Trigonometric_integral
6. (Original post by StarvingAutist)
reverse the order of integration
7. (Original post by ODES_PDES)
reverse the order of integration
What should that look like?
8. (Original post by StarvingAutist)
What should that look like?
...
Attached Images

9. (Original post by TeeEm)
...
I didn't realise the sinx / x could go in the y integral; I put it as a limit which obviously didn't help
10. (Original post by StarvingAutist)
Start by doing the y integral and it becomes very simple. On another note I did just work out the exact solution to the integral of sinx/x - if someone fancies checking, that would be great.

11. (Original post by natninja)
Start by doing the y integral and it becomes very simple. On another note I did just work out the exact solution to the integral of sinx/x - if someone fancies checking, that would be great.

Looks like you've done far more work that needs to be.

Then divide that by and integrate term-by-term (skipping over some mild technical justifications).

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