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

Question

Evaluate the following integrals :

\(\int\)\(\frac{secx}{log(secx+tanx)}\)dx

Answer 1

Assume,

log(secx + tanx) = t 

d(log(secx + tanx)) = dt 

(use chain rule to differentiate) 

First differentiate, 

log(secx + tanx) 

Then, 

(secx + tanx)

⇒ secx dx = dt 

Put t and dt in the given equation we get,

⇒ ∫\(\frac{dt}{t}\)

=ln |t| + c.

But,

t = log(secx + tanx) 

= ln |log(secx + tanx)| + c.