Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 239: 55

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

Integrate. $\int (\cos \theta \tan \theta) d\theta + \int (\cos \theta \sec \theta) d\theta $ Thus, $\int (\cos \theta \tan \theta) d\theta + \int (\cos \theta \sec \theta) d\theta=\int [\cos \theta (\dfrac{\sin \theta}{\cos \theta}) d\theta + \int \cos \theta (\dfrac{1}{\cos \theta})] d\theta$ or, $=-\cos \theta +\theta +C$