Problem

(a) Determine

$$\int \frac{1}{\sqrt{9x^2+16}}\,dx$$

(b) Hence determine the exact value of

$$\int_{-2}^{2}\frac{1}{\sqrt{9x^2+16}}\,dx$$

Give your answer in the form $a\ln(b+c\sqrt{13})$, where $a$, $b$ and $c$ are rational numbers.