Indefinite IntegrationHard

Question

Primitive of w.r.t.x is -

Options

A.ln | sec x| - ln | sec x - tan x | + c
B.ln | sec x + tan x| + ln | sec x | + c
C.2 ln + c
D.ln |1 + tan x (sec x + tan x) | + c

Solution

= | sec x + tanx |
∴  ∫|sec x + tan x | dx = I
I = ln | sec x + tan x | + ln | sec x | + c    ......(i)
I = ln | sec2 x + sec x tan x | + c
I = - ln | sec x - tan x | + ln | sec x | + c
I = ln | 1 + tan x (sec x + tan x) | + c

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