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

Question

Evaluate the following integrals :

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

Answer 1

We know,

d(sinx) = cosx, and cot can be written in terms of cos and sin

∴ cot x = \(\frac{cos\,x}{sin\,x}\)

∴ The given equation can be written as

Now assume,

sinx = t 

d(sinx) = dt 

cosx dx = dt 

Substitute values of t and dt in above equation