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