∫sec^2 x / √ tan x +1 dx

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∫sec^2 x / √ tan x +1 dx
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∫sec^2 x / √ tan x +1 dx
∫sec^2 x / √ tan x +1 dx

∫sec^2 x / √ tan x +1 dx
∫sec^2 x / √ (tan x +1 )dx
=∫1 / √ (tan x +1 )d(tan x)
=2√ (tan x +1 )+C

∫sec^2 x / √ tan x +1 dx
=∫1 / √ tan x +1 dtanx
=21√ (tan x +1)+C