Integrate the function: $x \sec^{2} x$

(N/A) Let $I = \int x \sec^{2} x \, dx$.
Using the integration by parts formula $\int u \cdot v \, dx = u \int v \, dx - \int \left( \frac{du}{dx} \int v \, dx \right) dx$,where $u = x$ and $v = \sec^{2} x$:
$I = x \int \sec^{2} x \, dx - \int \left( \frac{d}{dx}(x) \int \sec^{2} x \, dx \right) dx$
$I = x \tan x - \int (1 \cdot \tan x) \, dx$
$I = x \tan x - \int \tan x \, dx$
Since $\int \tan x \, dx = \ln |\sec x| + C$ or $-\ln |\cos x| + C$,we have:
$I = x \tan x + \ln |\cos x| + C$,where $C$ is an arbitrary constant.