Evaluate the following integrals : ∫(secx cosecx)/log(tanx) dx ​

Question

Evaluate the following integrals :

\(\int\)\(\frac{sec\,x\,cosec\,x}{log(tan\,x)}\)dx

Answer 1

Assume,

log(tanx) = t 

d(log(tanx)) = dt 

⇒ \(\frac{sec^2x}{tanx}\)dx = dt

⇒ secx.cosecx.dx = dt 

Put t and dt in given equation we get,

⇒ ∫\(\frac{dt}{t}\) 

= ln|t| + c. 

But, 

t = log(tanx) 

= ln|log(tanx)| + c.