I'm having trouble with solving the following integral with Leibniz's rule.
$F\left(\alpha\right) = \int_{0}^{π}{\frac{\ln{\left(1+\sin{\alpha}\cos{\alpha}\right)}}{\cos{x}}\,\mathrm{d}x} $
The first thing I did was to find the derivative in respect to the parameter α and also taking care of the critical x=π/2 by splitting the integral in two parts with two limits.
My question is: is it even allowed to split the integral like that and also using Leibniz's formula, when we have a point where the integrand goes to infinity?
If not, then what's the best method to use here?