# Math Help - Using Maclauriw series to find first 3 terms

1. ## Using Maclauriw series to find first 3 terms

Hello everyone, i need some help on this question :
By using the Maclauriw series, show that the first three terms of the expansion ln[sec(2x)+tan(2x)] in powers of x are 2x + [4(x^3)]/3 + [4(x^5)]/3.
Thanks!

2. ## Re: Using Maclauriw series to find first 3 terms

It will be easiest if you find the MacLaurin Series for \displaystyle \begin{align*} \sec{(2x)} \end{align*} and integrate it, since \displaystyle \begin{align*} \int{\sec{(2x)}\,dx} = \ln{\left[ \sec{(2x)} + \tan{(2x)} \right]} \end{align*}.