It's on Indefinite Integrals int sqrt(1+2 tan x (tan x + sec x )) dx Please tell me the way of solving such questions. like what could i assume sec x or sec x tan x to be equal to?

Wevybrearttexcl 2022-09-17 Answered
It's on Indefinite Integrals
1 + 2 tan x ( tan x + sec x ) d x
Please tell me the way of solving such questions. like what could i assume sec x or sec x tan x to be equal to?
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Answers (1)

Willie Sharp
Answered 2022-09-18 Author has 8 answers
M y S o l u t i o n :: Let
I = 1 + 2 tan x ( tan x + sec x ) d x = 1 + 2 tan 2 ( x ) + 2 tan x sec x d x
So I = 1 + tan 2 x + tan 2 x + 2 tan x sec x d x = ( tan x + sec x ) 2 d x
So I = tan x d x + sec x d x = ln | sec x | + ln | sec x + tan x | + C = ln | sec x ( sec x + tan x ) | + C

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