Question

Evaluate : `int  (sec^2 x)/(tan^2 x + 4)` dx

Answer 1

Let I = `int  (sec^2 x)/(tan^2 x + 4)` dx

Put tan x = t
      `sec^2 x dx = dt`

       I = `int dt/[ t^2 + 2^2 ]`

      I = `1/2 tan^-1 (t/2) + c`

            `( ∴ int 1/[ x^2 + a^2] dx = 1/a tan^-1 x/a + c)`

     I = `1/2 tan^-1(tan x/2) + c`