- #1
taylormade
- 4
- 0
Homework Statement
Calculate
[tex]\int_0^{+\infty}\frac{\x^2}{1+x^6}dx[/tex]
I found the poles/residues for this guy, and did the integral over the semicircular contour from -R to R, with R->infinity.
I get poles that contribute at:
[tex]\frac{1}{6}e^\frac{-4*pi*i}{6}[/tex].
[tex]\frac{1}{6}e^\frac{-12*pi*i}{6}[/tex].
[tex]\frac{1}{6}e^\frac{-20*pi*i}{6}[/tex].
Where I'm confused, it that when you sum the residues (I.e. 2*pi*i(Sum of Residues)), the sum of the residues is zero.
I also tried doing this integral over a smaller contour, from 0 to theta = 2pi/6 - and get similar weird answer.
My actual question is - What does this mean? I'm inclined to say that this integral equals zero - but looking at the function, that doesn't make sense to me.
Where have I gone off the rails?
I apologize - I'm still not very good with the Latex stuff.