" (i) "int sqrt(1+2tan x(tan x+sec x))dx...

" (i) "int sqrt(1+2tan x(tan x+sec x))dx

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int sqrt(1+2tan x(tan x+sec x))dx is equal to

int{1+2tan x(tan x+sec x)}^((1)/(2))dx

int (1+2) tan x(tan x+ sec x)}^(1//2) dx=

int {(1+2 tan x(tan x + sec x))^(1//2) dx is equal to

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int(tan x+sec x-1)/(tan x-sec x+1)dx

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int sec x tan x sqrt(sec^(2) x+1)dx

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