## anonymous 4 years ago How do I integrate this?

1. anonymous

|dw:1326789570521:dw|

2. ash2326

could you draw the diagram again, it's not clear

3. anonymous

$\int\limits \cos(\frac{1}{1+\cos(x)})dx$

4. anonymous

Off the top of my head, I'd say that is transcendental and has no elementary antiderivative. Wolfram|Alpha backs me up on that.

5. anonymous

|dw:1326789627857:dw|

6. anonymous

|dw:1326790075583:dw|

7. anonymous

Perhaps just a rough area approximation near pi based on the width of the slice, something like the Taylor expansion around zero of the function given by: $F(\epsilon)=\int\limits_{\pi-\epsilon}^{\pi} \cos(\frac{1}{1+\cos(t)})dt$