Answer
$${\text{False}}$$
Work Step by Step
$$\eqalign{
& {\text{False}}{\text{, the integral can be evaluated using the substitution method}} \cr
& \int {\frac{{\cos x}}{{5 + \sin x}}} dx \cr
& {\text{then let }}u = 5 + \sin x,\,\,\,\,\,\,du = \cos xdx \cr
& \int {\frac{{\cos x}}{{5 + \sin x}}} dx = \int {\frac{{du}}{u}} \cr
& = \ln \left| u \right| + C \cr
& = \ln \left| {5 + \sin x} \right| + C \cr} $$
