Find \(\int \left( 2 x ^ { 3 } + \frac { 8 } { x ^ { 2 } } \right) \mathrm { d } x\)
3
A curve has gradient function \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x ^ { 3 } + \frac { 8 } { x ^ { 2 } }\)
The \(x\)-intercept of the curve is at the point \(( 2,0 )\)
Find the equation of the curve.
Fully justify your answer.
\(4 \quad\) Find the exact solution of the equation \(\ln ( x + 1 ) + \ln ( x - 1 ) = \ln 15 - 2 \ln 7\)