Let's do some calculus! (23)

Calculus Level 3

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

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.

Let's do some calculus! (23)

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