## Thomas' Calculus 13th Edition

$x\tan x+\ln|\cos x|+C$
We use the formula $\int udv=uv-\int vdu$ with $u=x$, $dv=\sec^{2}xdx$ $du=dx$, $v=\tan x$ Then $\int x\sec^{2}xdx=x\times \tan x-\int \tan xdx$ $=x\tan x+\ln|\cos x|+C$