1. ## Integration Help

Hi

I am working on how to get the last closed field lines of a moving magnetic field (as a bit of background). Anyhow, as part of it, I have to integrate
$\frac{c\Omega \cos(K)+\sin(K)(c^2+\Omega^3K)}{2c^2\Omega(\cos(K) +K \sin(K)}dK$

Anybody have any ideas how I would go about doing this?

2. ## Re: Integration Help

c and $\Omega$ are assumed to be constants? or they are defined in terms of K?

3. ## Re: Integration Help

c and Omega are constants. Everything except K is a constant.

4. ## Re: Integration Help

The denominator is not clear, is it:
$2c^2\Omega[\cos(K)+K\cdot \sin(K)]$
Or
$2c^2\Omega[\cos(K)]+K\cdot \sin(K)$
?
Maybe it's useful to split the fraction in two fractions with the same denominator.

5. ## Re: Integration Help

Originally Posted by Siron
The denominator is not clear, is it:
$2c^2\Omega[\cos(K)+K\cdot \sin(K)]$
Or
$2c^2\Omega[\cos(K)]+K\cdot \sin(K)$
?
Maybe it's useful to split the fraction in two fractions with the same denominator.
The frightening capital letter, omega make the problem to look scary...

Prove that:

$\int x\sin{x}\;dx=\sin{x}-x\cos{x}+C$

6. ## Re: Integration Help

Originally Posted by Also sprach Zarathustra
The frightening capital letter, omega make the problem to look scary...

Prove that:

$\int x\sin{x}\;dx=\sin{x}-x\cos{x}+C$
That can be proved with integration by parts.

7. ## Re: Integration Help

Sorry, I left out a bracket in my original post . I have also changed it so that you no longer have to deal with Omega .

$\frac{cA \cos(K)+\sin(K)(c^2+A^3K)}{2c^2A(\cos(K) +K \sin(K))}dK$

Ok, so $\int x\sin{x}\;dx=\sin{x}-x\cos{x}+C$

Let x=u, dv=sin(x) then you have that v=-cos(x) and $\int x\sin{x}\;dx=-x \cos(x) -\int \cos(x) dx=\sin(x)-x\cos(x) +C$

Sop how does that help with my original equation?