$\large \displaystyle \int_{\ln \lambda}^{\ln \left( {1}/{\lambda} \right)} {\dfrac{f \left( \dfrac{x^{2}}{4} \right) \big( f(x) - f(-x) \big)}{g \left( \dfrac{x^{2}}{4} \right) \big( g(x) + g(-x) \big)}} \,dx$

Given that $f(x)$ and $g(x)$ are both continuous functions. Does the value of the above anti-derivative depend on the value of $\lambda$?

**Notations:** $\ln(\cdot)$ denotes the natural logarithm function.