\begin{enumerate}
  \setcounter{enumi}{4}
  \item (a) Show that the substitution $t = \tan \left( \frac { x } { 2 } \right)$ transforms the integral
\end{enumerate}

$$\int \frac { 1 } { 2 \sin x - \cos x + 5 } d x$$

into the integral

$$\int \frac { 1 } { 3 t ^ { 2 } + 2 t + 2 } \mathrm {~d} t$$

(b) Hence determine

$$\int \frac { 1 } { 2 \sin x - \cos x + 5 } d x$$

\hfill \mbox{\textit{Edexcel FP1 2023 Q5}}