2024 VJC H1 Q4

The coefficients in the requested exact form are rational numbers.

1. Differentiate \(\frac{3}{(1 - 4x^2)^3}\) with respect to \(x\).[2]
2. Without using a calculator, find \(\displaystyle\int_3^7 \frac{3}{\sqrt{3x - 1}} \, \mathrm{d}x\). Give your answer in the form \(a\sqrt{5} + b\sqrt{2}\) where \(a\) and \(b\) are constants to be found.[4]