It is given that \(\mathrm{f}(x)=\frac{e^x}{1+2e^x}\).
Write down \(\int \mathrm{f}(x)\,dx\).[1]
Using standard series from the List of Formulae (MF27), find the Maclaurin series for \(\mathrm{f}(x)\), up to and including the term in \(x^2\).[4]
Hence, or otherwise, find the first four non-zero terms of the Maclaurin series for \(\ln(1+2e^x)\).[2]