Calculating Mss of a Rod using Integration

[mm391]

Homework Statement

Let a rod with length L and constant cross-sectional area A have the density
ρ(x) = ρ((3.x^2 + 2.x.L)/L^2)

0 ≤ x ≤ L

where x is the distance from one end of the rod and ρ0 is a real constant.
(a) Find the total mass M of the rod.
(b) Find the x-coordinate xc of the centre of mass of the rod.
(c) Find, in terms of M, the moment of inertia of the rod about the vertical axis through x = 0.

Homework Equations

M = ∫Aρ(x).dx

The Attempt at a Solution

M = ∫Aρ(x).dx

M= A.ρ∫((3.x^2 + 2.x.L)/L^2).dx

I am slightly confused where to go from here! Do I use integration by parts?

 

[HallsofIvy]

Why? That is just the integral of a polynomial. What is the integral of 3x^2 dx? What is the integral of 2x dx?