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# Annoying trig integral watch

1. Hi

I have this integral , the answer to which is
Spoiler:
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I seem to be useless with the normal tangent half-angle substitution because I can't get my head around the fact that one of my limits becomes undefined. Is there a 'usual' way to deal with this? I have a method to do it by considering the function from 0 to and halving the result, but is there a better way?

(I also suspect the paper meant , any thoughts?

*****gr8wizard10*******
2. (Original post by klegend02)
Hi

I have this integral , the answer to which is
Spoiler:
Show
The t = tan(x/2) substitution should work fine - it transforms the integral into a standard inverse trigonometric one.

I seem to be useless with the normal tangent half-angle substitution because I can't get my head around the fact that one of my limits becomes undefined.
One of the limits becomes +infinity but that is not a problem ultimately, as its arc-tangent is defined.

Is there a 'usual' way to deal with this?
At a more elevated (university) level this is a standard integral to approach with residue theory/complex analysis.

(I also suspect the paper meant , any thoughts?
Yes, it should have stated that.

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Updated: September 6, 2015
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