Assume that we have a function $f:\mathbb{R}^+\rightarrow\mathbb{R}^+$ and $D$ a constant. How can we solve the following equation for $f$:
$$ \int^{b}_{x_2=a} \int^{b}_{x_1=a} \frac{1}{(f(x_1)+f(x_2))^2}d x_1 d x_2 = D \log(\tfrac{b}{a})$$
where $0.
Thanks.