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## Homework Statement

I have the function below which i need to find the area under the graph.

## Homework Equations

[tex]\int_{ - \frac {\pi}{4}}^{\frac {\pi}{3}}\frac {2\sec x}{2 + \tan x}dx[/tex]

## The Attempt at a Solution

I can simplify it to

[tex]\int_{ - \frac {\pi}{4}}^{\frac {\pi}{3}}\frac {2}{2\cos x + \sin x}[/tex]

But I am at a loss as to where to go from here, I've tried all sorts of things. I have Mathcad which has given me the answer, but I want to be able to do it myself. I have been shown the Weierstrass substitution method which I can follow, but it is something that isn't covered by the course.

Thanks

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