# Hard Integral

#### roeb

Nevermind, I seem to have figured it out

1. The problem statement, all variables and given/known data
show that:
$$\int \frac{dN}{N} = \int_{0}^{\theta_max} \frac{dcos \theta}{2} \frac{1 + \frac{v^2}{v_0^2} cos(2 \theta ) }{ \sqrt{ 1 - \frac{v^2 sin^2 \theta}{v_0^2} } }$$

2. Relevant equations

3. The attempt at a solution
I'm having a lot of difficulty doing this...
Note that $$sin(\theta_{max} ) = \frac{v_0}{v}$$
so after a bunch of algebra I get:

$$\int \frac{dN}{N} = cot(\theta_{max} ) \int_{0}^{\theta_{max} } \frac{2y^2 - 1}{\sqrt{y^2 - 1} }$$
I am fairly confident that is correct because I keep on getting it.
Unfortunately, I can't seem to integrate this at all.

Last edited:

#### rootX

$$\int \frac{dN}{N} = cot(\theta_{max} ) \int_{0}^{\theta_{max} } \frac{2y^2 - 1}{\sqrt{y^2 - 1} }$$

If you are finding it hard to integrate the right side, try u = sqrt(y^2-1) .. fairly simple to integrate

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