I'm getting stuck while I'm trying to solve a integral.

What I've got so far:

Since the integer is even I get:

=

Using the complex plane. More precise, the area of a half circle in the upper part. of the plane.

;

So now I calculate the roots of the divisor.

;

This is where I get stuck. I can find out how many of the roots lies in the upper part of the complex plane.

As many as their imaginary part is positive:

So, ...and we get an easy inequality.

Tonio
Argument-variance to find roots.

= the arch going from +R to -R on the real axis.

is -R to +R on the real axis.

:

No roots on the real axis.

: R is chosen big enough to include any roots in the half circle. Along the rim?

- Wich means that there are

roots in my area.

This is about it, I don't know how to get further on this one. If anyone could wave their magic wand over it. That would really make my weekend.

Cheers!