# Thread: Integral of sech(x) between infinity and minus infinity

1. ## Integral of sech(x) between infinity and minus infinity

As the title says, I am trying to find the definite integral of sech(x) with limits of infinity and minus infinity.

I always get 2pi as my solution, but all calculators and integration applets give pi as the answer.

Below is my method so far:

Could someone please tell me where I have gone wrong?

EDIT: there is an error in line 6 of my method, that extra u is just a typo.

2. You didn't change your terminals when you substituted u. Also, your integrand should be 1/(u^2 + 1), not u/(u^2 + 1), but since you have integrated this correctly I suspect that is just a typo.

3. You didn't change your terminals when you substituted u.
I did, but e^infinity is just infinity.

Also, your integrand should be 1/(u^2 + 1), not u/(u^2 + 1), but since you have integrated this correctly I suspect that is just a typo.
Yes, that was a typo. I had mentioned it in an edit prior to your post.

Anyway, I still have the issue of 2pi versus pi.

4. Originally Posted by incblue
I did, but e^infinity is just infinity.
But $\displaystyle \lim_{x \to -\infty}e^x = 0$, not $\displaystyle -\infty$...

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# integration of sechx up-to limit 0 to infinity

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