Single Variable Calculus

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Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 70

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Evaluate the integral $\displaystyle \int \frac{\cos x}{2 + \sin x} dx$

$ \begin{equation} \begin{aligned} \text{Let } u =& 2 + \sin x \\ \\ du =& \cos x dx \\ \\ =& \int \frac{du}{u} \\ \\ =& \ln u + C \\ \\ =& ln (2 + \sin x) + C \end{aligned} \end{equation} $

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