How to do this kind of integral?

[nicksauce]

Homework Statement

I want to evaluate, using residue calculus, the following
\int_0^{\infty}\frac{xdx}{1+x^4}
I can't find any kind of formula for this kind of integral though. We just know \int_{-\infty}^{\infty}\frac{P(x)dx}{Q(x)}, however that would give 0 in this case as the function is odd. Any pointers?

Homework Equations

The Attempt at a Solution

 

[nicksauce]

Err... figured it out. Just have to use a the contour with a quarter-arc, then along the y-axis, then the x-axis...