I am working on The Reynolds equation in the case of a long journal bearing with different conditions, and I got stuck on these mathematical calculus, so as seen in the images I know the value of Ws but I can't find it doing the integration, I am not so good at math so I think I did my calculus wrong, and I wanna know if it's possible to find the value of the angle φR, if it's possible how to do that? hopefully, everything needed and all the different equations are in the attached images. Ps: This is my very first time here so I really hope I haven't done anything wrong and everything is clear.
