Evaluate the following integrals:
∫ sec x log (sec x + tan x) dx
Assume log(secx + tanx) = t
d(log(secx + tanx)) = dt
(use chain rule to differentiate first differentiate log(secx + tanx) then (secx + tanx)
⇒ = dt
⇒
⇒ secx dx = dt
Put t and dt in given equation we get
Substituting the values oft and dt we get
⇒
⇒
But t = log(secx + tanx)
⇒ .