Calculating Moment of Inertia of Long, Thin Rod w/ Varying Mass Density

[factor]

I've been trying to find the moment of inertia of a long thin rod of mass M and length L whose mass density increases as the square of the distance from the axis which is at one end of the rod and perpendicular to the rod. But so far, I'm pretty stumped on how to do it. My first instinct was using the geometry of the object but that didn't seem to work, now I'm trying to find the centroid of the object's mass distribution to see if that fits any better. Any help on this would be appreciated.

 

[Galileo]

The moment of inertia of a mass element of the rod is x^2dm, where dm is the mass and x the distance from the axis. Just add all the contributions up (i.e. integrate) and use dm=rho*dx, where rho is the mass density (mass/unit lenght).