Question

$\int\limits^a_b {2xtanxsecx} \, dx$

Answer 1

u = x . dv = sec x tanx dx.
v = sec x.
$\int {u dv } = u v - \int {du* v } \\\\ answer = 2 x sec x - 2 \int {sec x } dx \\\\ = 2 x sec x - 2 Ln (sec x + tan x)$

It is Integration by parts.