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)

⇒ .