Question

intregation of ,secx.dx=​

Answer 1

GOOD MORNING!!!

integration of sec x dx

MULTIPLY NR AND DN BY Sec x + Tan x

=>

integration of

Sec x { Sec x + Tan x }
_________________ dx
{ Sec x + Tan x }

Now, put Sec x + Tan x = z

dz = {Sec x × Tan x + Sec² x }dx

dz = Secx { Tan x + Sec x }dx

=>

So, integration of Sec x dx is

integration of 1/z dz

=>

log ( z ) + c

=>

log ( Sec x + Tan x ) + c

where c is called constant of integration.

Answer 2

∫ secx dx = log | secx + tanx | +c

= log | tan {(π/4)+(x/2)} | + c