evaluate the integral of e^tanx dx/cos^2 x

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Use the substitution tan x = p.

Differentiating, the result will be: `dx/(cos^2 x) = dp`

Integrate:

`int e^(tan x)dx/(cos^2 x) = int e^p dp = e^p + c`

Substitute back p = tan x

`int e^(tan x)dx/cos^2 x = e^(tan x) + c`

ANSWER: The result of integration is

`int e^(tan x)dx/(cos^2 x) = e^(tan x) + c`

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