tan x ( sec x - tan x ) ? d x =

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Solution

Q.
$\int \tan x (\sec x - \tan x) d x =$

1 $\sec x - \tan x + x - C$

2 $\sec x - \tan^{2} x + C$

3 $\sec x + \tan x + x + C$

4 $\sec x - \tan x + C$

Ans.
(1)

Ans. $\sec x - \tan x + x - C$

Explanation :

$I = \int (\tan x \cdot \sec x - \tan^{2} x) d x$

$= \int \tan x \cdot \sec x d x - \int \tan^{2} x d x$

$= \sec x + x - \tan x + C$

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