Question

integration of sec X upon sec 2x DX​

Answer 1

Strategy: The strategy is not obvious. Multiply and divide by (sec x + tan x); use Substitution.

(integral) sec x dx = (integral) sec x sec x + tan x

sec x + tan x dx

set

u = sec x + tan x

then we find

du = (sec x tan x + sec2 x) dx

substitute du = (sec x tan x + sec2 x) dx, u = sec x + tan x

(integral) sec x sec x + tan x

sec x + tan x dx = (integral)

(sec2 x + sec x tan x) dx

sec x + tan x

= (integral)

du

u

solve integral

= ln |u| + C

substitute back u=sec x + tan x

= ln |sec x + tan x| + C

Q.E.D.

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