# Math Help - Integration of roots...

1. ## Integration of roots...

Hi all.

My battle with calculus is forever ongoing, although I feel I've made lots of progress recently. However I am a bit unsure on how to go about the following:

$\int \sqrt{9 + cos x}$

I am aware that:

$\int \sqrt{9 + cos x}= \int (9 + cos x)^\frac{1}{2}$

but am still stumped.

Any pointers would be greatly appreciated.

Mav

2. First, you forgot dx....

Second, I don't think that there is analytic function for your integral...

3. In other words, don't be upset that you could not integrate it. If it were $\int \sqrt{1+ 9 cos^2(\theta)}d\theta$ then you could use the substitution $u= 3 cos(\theta)$ but as the integral is it cannot be integrated in terms of elementary functions- you must use the "elliptic integral of the second kind" which, itself, must be evaluated numerically.

4. O.K.

Would the same be true of:

$\int \sqrt{9 - sin x} dx$

I have the above as a denominator of a function and am using a separation of variables to find an implict solution.

So I have $\int \sqrt{9 - sin x} dx$ on one side of the equation because I multiplied through by it. So if I can't integrate it, what do I do?

Confused.