This integration seems easy!

Calculus Level 5

\[\large{ f(x) = \int \dfrac{dx}{(x+2)^4 + (x+4)^4 + 14} }\]

Let \(f(x)\) be a function defined as above such that \(f(-3) = 0\) holds true. Then find the value of \(f(0)\) upto three decimal places.