Question 0814

Write down ${\displaystyle \int f(x) \; \mathrm{d}x.}$

Find the binomial expansion for ${f(x),}$ up to and including the term in ${x^6.}$ Give the coefficients as exact fractions in their simplest form.

Hence, or otherwise, find the first four non-zero terms of the Maclaurin series for ${\ln \left( \frac{9+x}{9-x} \right).}$ Give the coefficients as exact fractions in their simplest form.