Answer
$$0$$
Work Step by Step
We are asked to evaluate the integral below using the properties of even and odd functions.
$$\int_{-2}^{2} x(x^2+1)^3 dx$$
By looking at a picture of the graph (enclosed below), we will see that the function is an odd function. By knowing the properties of odd functions with respect to integrals, we can say that the value of this integral is $0$.
