`int secx tanx sqrt(4 sec^(2)x-1)dx` का मान ज्ञात कीजिए ।

Explanation

`int sec x tan x sqrt(4 sec^(2)x-1)dx`
`=int sec x tanx sqrt((2secx)^(2)-1^(2))dx`
`=intsqrt(t^(2)-1^(2))(dt)/(2)" "{:(" माना "2sec x=t),(therefore" "2 sec x tanx=(dt)/(dx)),(therefore" "sec x tanx dx =(dt)/(2)):}`
`=(1)/(2)[(t)/(2)sqrt(t^(2)-1)-(1)/(2)log|t+sqrt(t^(2)-1)|]+c`
`=(1)/(4)[2 secxsqrt(4 sec^(2)x-1)-log|2secx+sqrt(4sec^(2)x-1)|]+c`