11 Let \(\mathrm { f } ( x ) = \frac { 2 \mathrm { e } ^ { 2 x } } { \mathrm { e } ^ { 2 x } - 3 \mathrm { e } ^ { x } + 2 }\).
- Find \(\mathrm { f } ^ { \prime } ( x )\) and hence find the exact coordinates of the stationary point of the curve with equation \(y = \mathrm { f } ( x )\).
\includegraphics[max width=\textwidth, alt={}, center]{9da6c2ac-31aa-4063-88b9-e15e38bedd8a-16_2718_35_107_2012} - Use the substitution \(u = e ^ { x }\) and partial fractions to find the exact value of \(\int _ { \ln 3 } ^ { \ln 5 } \mathrm { f } ( x ) \mathrm { d } x\).
Give your answer in the form \(\ln a\), where \(a\) is a rational number in its simplest form.
If you use the following page to complete the answer to any question, the question number must be clearly shown.
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