find the derivative of the function.

integral cos(x) to sin(x) ((ln(8+3v))dv)

If you want to find F'(x) where

F(x) = ∫[cosx,sinx] ln(8+3v) dv
then using Leibniz' Rule,
F'(x) = ln(8+3sinx)*cosx - ln(8+3cosx)(-sinx)