Indefinite IntegrationHard

Question

The value of ∫{1 + 2tan x(tan x + sec x)}1/2 dx is equal to

Options

A.ln |sec x (sec x - tan x)| + C
B.ln |cosec x (sec x + tan x)| + C
C.ln |sec x (sec x + tan x)| + C
D.ln |(sec x + tan x)|+ C

Solution

∫{sec2x + tan2x + 2tanx sec x}1/2 dx
= ∫(sec x + tan x)dx
= ln |(sec x + tan x)|+ ln |sec x| + C
= ln |sec x (sec x + tan x)| + C

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