Here's a fairly difficult integration problem. Show that ∫_{0,∞}(dx/(1+x^n))=π/(nsin(π/n)) for ∀n∈ℝ.

This is complex analysis, I think? Well, whatever. I don't know how to solve it. XD

Question

Here's a fairly difficult integration problem. Show that ∫_{0,∞}(dx/(1+x^n))=π/(nsin(π/n)) for ∀n∈ℝ.

This is complex analysis, I think? Well, whatever. I don't know how to solve it. XD

anonymous · Answer

Makes not sense :P

anonymous · Answer

Hmm? Did I typo?

dumbcow · Answer

i have no idea...most of the anti-derivatives of that form involve logs and arctan

dumbcow · Answer

it works though, but showing it ....

anonymous · Answer

I have "context" for this problem. It involves the residue theorem. Yeah, I'm not sure how to go about solving it the "classical" way using trigonometric derivatives and logarithms.

dumbcow · Answer

you might have to use graphing software and analyze it using numerical analysis to show the various areas match up with pi/nsin(pi/n)

anonymous · Answer

I somehow doubt the "software" part. The question giver is very strict about analog computation. XD

dumbcow · Answer

thats no fun :)