# Simple cosine expression NOT so simple

• Mark Wood
In summary, the conversation is about a person who is trying to integrate a mathematical expression, but is struggling to find a solution. They have tried various methods, but have not been successful. The conversation also mentions the use of an integrator on Wolfram's website, which ultimately helps the person find the solution.

#### Mark Wood

:grumpy:

I am rediscovering my long lost "A" level maths and have been having lots of fun working on puzzles. Unfortunately, I seem to have hit something of a wall in the following simple expression that is repelling every attack I launch:

f(x)=$$Sqrt$$(1+kcos(x))

I have tried substituting x=arccos(w) and w=arccos(w/k), expressing things as logs, mungeing the equations I get, and a number of slightly more desperate attacks, but whatever I do to get rid of one term or provide something that can be canceled out, a new problem pops up.

I feel that there is a simple answer to this, but the more I look at it the less I can see the way forward.

Any suggestions anyone?

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What exactly do you want to do with f(x)?

Ah! So absorbed by it, I've missed the most important bit!

I'm trying to integrate it to get the area under the curve between x=0 and x=pi

Sorry, i couldn't get ur expression. is it (1+kcos(x))^(1/2)

Yes it is - the root of (1+kcos(x))

I don't think it has a solution made up entirely of elementary functions. Elliptic functions may be involved.

I too struggled for it for 6-8 months. Its a kind of elliptic integral(which i didn't knew). u might be knowing. u can check it on an integrator at www.wolfram.com

Gosh - what a great tip. I didn't know the integrator existed. Thank you.

Having got the answer from Wolfram I'm kind of pleased that I hadn't missed an obvious solution.

Thank you all.