Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 272: 69

$-\cos \theta +\theta +C$

Given: $\int (\cos \theta \tan \theta) d\theta + \int (\cos \theta \sec \theta) d\theta $ Thus, $\int (\cos \theta \tan \theta) d\theta + \int (\cos \theta \sec \theta) d\theta=\int (\cos \theta (\dfrac{\sin \theta}{\cos \theta}) d\theta + \int \cos \theta (\dfrac{1}{\cos \theta}) d\theta=-\cos \theta +\theta +C$