Evaluate the following integrals : ∫(1-cotx)/(1+cotx) dx ​

Question

Evaluate the following integrals :

\(\int\frac{1-cot\,x}{1+cot\,x}\)dx

Answer 1

Convert cotx in form of sinx and cosx.

⇒ cot x = \(\frac{cos\,x}{sin\,x}\)

∴ The equation now becomes,

Assume,

cosx + sinx = t 

∴ d(cosx + sinx) = dt 

= cosx - sinx 

∴ dt = cosx – sinx 

⇒ \(\int\frac{dt}{t}\)

= ln|t| + c 

But,

t = cosx + sinx 

∴ ln|cosx + sinx| + c.