Evaluate : `int sec x tan x sqrt(4 sec^(2) x- 1 dx)`

Explanation

`int sec x tan x sqrt((2 sec x)^(2) -1^(2)) dx`
` =int sec x tan x sqrt((2 sec x)^(2) -1^(2)) dx`
`=int sqrt(t^(2) -1^(2)) (dt)/(2)" ""Let2 sec "x=t`
` rArr 2sec x tan x= (dt)/(dx)`
` rArr sec x tan x dx = (dt)/(2)`
`=1/2[t/2sqrt(t^(2) -1)-1/2 log |t+sqrt(t^(2)-1)|]+c`
`=1/4 [2 sec x sqrt(4 sec ^(2) x-1)`
` =log |2sec x+ sqrt(4sec^(2) x-1) |]+c`