Hi all, I have the following integral:

$\int _{0}^{\pi/2} \sqrt{ r \left( x \right) ^{2} + \left( {\frac {d}{dx}} r \left( x \right) \right) ^{2}}\ln \left( { \frac {\sin \left( x \right) }{1-\cos \left( x \right) }} \right) {dx}$

Note that the integrand shoots to infinity as x approaches 0. It's not too hard to establish that the integral will nonetheless always converge, regardless of the choice of r. My question is: will an extremizer satisfy the Euler-Lagrange Equation on the interval (0,Pi/2], and how can I tell? Sorry if this is trivial, I do not know much about the calculus of variations.