Problem

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

(i) Determine

$$\int \frac{1}{4x^2 + 12x + 25}\,dx$$

(ii) Show that

$$\int_3^9 \frac{1}{\sqrt{x^2 + 4x - 17}}\,dx = \ln a$$

where $a$ is an integer to be determined.