Question 4 - A-Level Maths

Given that $\cosh y = x$, show that $y = \pm \ln \left( x + \sqrt { x ^ { 2 } - 1 } \right)$ and that $\operatorname { arcosh } x = \ln \left( x + \sqrt { x ^ { 2 } - 1 } \right)$.
Find $\int _ { \frac { 4 } { 5 } } ^ { 1 } \frac { 1 } { \sqrt { 25 x ^ { 2 } - 16 } } \mathrm {~d} x$, expressing your answer in an exact logarithmic form.
Solve the equation $$5 \cosh x - \cosh 2 x = 3$$ giving your answers in an exact logarithmic form.