I am trying to determine the volume of region bounded by y = $\frac{x}{x^4+x^2+1}$ ,$x=1$, $x = 0$ by disc method with y-axis. However, I have stuck at the beginning since I have found no way to find the inverse function of y = $\frac{x}{x^4+x^2+1}$ nor what to exactly do next given that the function is inversible. Based on what little I understand, I am thinking about subtracting the volume of the big cylinder bounded by Oy and x = 1 with the integral of the inverse function bounded by its intersection with Oy and x =1 (multiply by pi) .
Thanks