Since `1/(sec\ x)=cos\ x`, we can re-write the question as:

`int(4\ cos\ x\ dx)/(e^(sin\ x)`

Put `u = sin\ x` then `du = cos\ x\ dx`

`int(4\ cos\ x\ dx)/(e^(sin\ x))=4int(du)/e^u`

`=4int e^-u\ du`

`=-4e^-u+K`

`=-4e^(-sin\ x)+K`

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