If $I = \int (sec x - sin x tan x) d x,$ then the value of $I$ is
(where $C$ is constant of integration)

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Solution

$I = \int (sec x - sin x tan x) d x$
$\Rightarrow I = \int (\frac{1}{cos x} - \frac{{sin}^{2} x}{cos x})$
$\Rightarrow I = \int \frac{{cos}^{2} x}{cos x} d x$
$\Rightarrow I = \int cos x d x = sin x + C$

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