Help Solving Integral Relevant to Sterman-Weinberg Jets in QFT

[eoghan]

Hi!
I'm studying Sterman-Weinberg Jets in QFT and I came about with this integral. Despite it is very simple, I can't solve it.
The integral is
$$\int_{\theta=\pi-\delta}^{\theta=\pi}\frac{d\cos (\theta)}{1-\cos^2(\theta)}$$
Solving it I get
$$\frac{1}{2}\left[\log\left(\frac{1+\cos\delta}{1-\cos\delta}\right)-\log\left(\frac{1-\cos\delta}{1+\cos\delta}\right)\right]$$
However, the text states that the result is proportional to
$$\log\delta^2$$

Any ideas?

 

[eoghan]

I get the correct result. $\log\delta^2$ follows from the approximation $\delta<<1$.