Techniques of Integration · Hard problem

A component's power dissipation is modeled by $P(x)=\dfrac{x^3}{x^2+1}$ watts for $0\le x\le1$ (with $x$ a dimensionless control setting). Find the total energy dissipated, $\displaystyle\int_0^1\frac{x^3}{x^2+1}\,dx$ (in joules).