Integrate integral of x sec^(2) x dx.

\(I=\int x \cdot \sec ^{2} x d x \\ \int u . v d x=u \int v d x-\int\left(\frac{d u}{d x} \int v d x\right) d x \\ \int x \cdot \sec ^{2} x d x=x \int \sec ^{2} x d x-\int\left(\frac{d x}{d x} \int \sec ^{2} x\right) d x \\ =x \tan x-\int 1 \cdot \tan x d x \\ =x \tan x-\log \sec x+C \)

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