e x sec x ? ( 1 + tan x ) ? d x equals:

Question

$\int e^{x} \sec x (1 + \tan x) d x$ equals:

Smart Achievers · Accepted Answer

(1)

Ans. $e^{x} \sec x + c$

Explanation :

$Let$ $I = \int e^{x} \sec x (1 + \tan x) d x$

$= \int e^{x} \sec x d x + \int e^{x} . \sec x . \tan x d x$

It is in the form

$\int e^{x} [f (x) + f' (x)] d x = e^{x} f (x) + c$

$f (x) = \sec x$

$f' (x) = \sec x - \tan x$

$\int e^{x} (\sec x + \sec x . \tan x) d x = e^{x} \sec x + c$

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