# Find the integral. {eq}\displaystyle \int \frac{1}{(5 + 4\cos x)}\text{ d}x {/eq}

## Question:

Find the integral.

{eq}\displaystyle \int \frac{1}{(5 + 4\cos x)}\text{ d}x {/eq}

## Integration:

Being familiar with common forms of integral is vital to efficiently evaluate a complex integral. This is especially true for integral results involving trigonometric functions. For example, the integral {eq}\displaystyle \int {\dfrac{1}{{{a^2} + {x^2}}}\text{ d}x} {/eq} can be directly written as {eq}\displaystyle \int {\dfrac{1}{{{a^2} + {x^2}}}\text{ d}x = \dfrac{1}{a}} {\tan ^{ - 1}}\left( {\dfrac{x}{a}} \right) {/eq}.

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Given data

$$\int {\dfrac{1}{{5 + 4\cos x}}} \text{ d}x \\$$

Let {eq}I{/eq} represent the given integral.

I = \int {\dfrac{1}{{5 + 4\cos x}}}...