I have this integral and I sense it could somehow be simplified using per partes, but so far I had no luck.
$$ \int_{0}^{b}\left(\frac{dy}{dx}\right)^2\frac{dx}{x+a} $$
The neat thing is the boundary condition. Here, $a$ and $b$ are a real constants and $x>0$. We know that $\left(\frac{dy}{dx}\right)|_{0}=0$. Any ideas would be greatly appreciated.