Evaluate the following integrals : ∫1/(cosx-sinx) dx ​

Question

Evaluate the following integrals :

\(\int\frac{1}{cosx-sinx}\)dx

Answer 1

Given,

I =  \(\int\frac{1}{cosx-sinx}\)dx

We know that,

Replacing 1 + tan²x/2 in numerator by sec²x/2 and putting tan x/2 = t and sec² x/2 dx = 2dt,