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Calculus Level pending

The value of \[I\quad =\quad \int _{ 0 }^{ \cfrac { \pi }{ 4 } }{ { tan }^{ n+1 }x\quad dx\quad +\quad \cfrac { 1 }{ 2 } \int _{ 0 }^{ \cfrac { \pi }{ 2 } }{ { tan }^{ n-1 }(\cfrac { x }{ 2 } } )\quad dx } \] is equal to

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