Question 7 - A-Level Maths

On separate diagrams:
1. sketch the curve with equation $y = | 3 x + 3 |$;
2. sketch the curve with equation $y = \left| x ^ { 2 } - 1 \right|$.
1. Solve the equation $| 3 x + 3 | = \left| x ^ { 2 } - 1 \right|$.
2. Hence solve the inequality $| 3 x + 3 | < \left| x ^ { 2 } - 1 \right|$.
  $8 \quad$ Use the substitution $u = 1 + 2 \tan x$ to find $$\int \frac { 1 } { ( 1 + 2 \tan x ) ^ { 2 } \cos ^ { 2 } x } d x$$