Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 61

$$\int \frac{d\theta}{1+cos\theta}=-cot\theta+csc\theta+C$$

$$\int \frac{d\theta}{1+cos\theta}=\int \frac{(1-cos\theta)d\theta}{1-cos^{2}\theta}$$ $$=\int \frac{(1-cos\theta)d\theta}{sin^{2}\theta}=\int (csc^{2}\theta-cot\theta\,csc\theta)d\theta$$ $$=-cot\theta+csc\theta+C$$