Evaluate the following integrals : ∫cotx/(log sinx) dx ​

Question

Evaluate the following integrals :

\(\int\frac{cot\,x}{log\,sin\,x}\)dx

Answer 1

Assume,

log(sinx) = t 

d(log(sinx)) = dt 

⇒ dx = dt 

⇒ cotx dx = dt 

Put t and dt in given equation we get

 ⇒ ∫\(\frac{dt}{t}\) 

= ln|t| + c.

But, 

t = log(sinx) 

= ln| log(sinx) | + c