15. In this question you must use detailed reasoning.
- Show that \(\int _ { \frac { \pi } { 3 } } ^ { \frac { \pi } { 2 } } \frac { 1 + \sin 2 x } { - \cos 2 x } d x = \ln ( \sqrt { a } + b )\), where \(a\) and \(b\) are integers to be determined.
- Show that \(\frac { \pi } { \frac { \pi } { 4 } } \frac { 1 + \sin 2 x } { - \cos 2 x } d x\) is undefined, explaining your reasoning clearly.
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