Hello, I'm having trouble doing this one integration problem and it needs to be done using substitution and only substitution (no integration by parts). I can pretty much figure it out by looking at it that it needs to be arctan(cos x) + C, but I need to show my work and I can't figure out how to get that answer using substitution. I would think that it would make sense to make u = 1 + (cosx)^2, but when I do that it doesn't seem to work. Can anyone help? Thanks!
sin[x] / (1 + (cos[x])^2)
To be clearer, it's sine x over the quantity: one plus cosine squared x. Cosine is being squared, not the x inside of it, and not the entire quantity.