# Should I expand as a power series and then integrate or is there an elegant method?

$$\int_{0}^{\pi/2}(cos(\theta)*exp(-2[\pi(1-cos(\theta))]^2)/k^2)/erf(2\pi/k)$$

Where of course the error function erf is defined as:
$$erf(x)=2/\pi\int_{0}^{x}exp(-t^2)dt$$

Anyway... this is the problem I want to integrate. I am not looking for someone to post a solution. My question is simply what is the best way of tackling this monster. My first thought is to expand each of the functions into a power series and use the "crank the handle" method. Not very elegant. Can anyone see a better/quicker method?

Thanks

Harry

$$\int_{0}^{\pi \over 2} cos(\theta) \frac{\exp\left ( \frac{-2\pi(1-cos\theta)^2}{k^2}\right ) }{erf(\frac{2\pi}{k})}d\theta$$