Question

integral of (1+tan^2x)/2tan x​

Answer 1

Answer:

1/2 * Log [ Sec 2x ]  + integration constant.

Step-by-step explanation:

Integrand function =  (1 + tan^2 x ) / [2 Tan x ]

           =  1 / tan 2x

           = cot 2x   = Cot y     , where y = 2x   and  dy = 2 * dx

So the integral becomes

   integral  1/2 * Cot y * dy

 = 1/2 * [ Log Sec y ] + K    using the simple formula for integral of Cot y.

 = 1/2 * Log Sec 2x +  K

Answer 2

Answer:

Question solved with explanation⤴️