Question

What's the integral of (√cosec x) ?

Answer 1

Answer:

Step-by-step explanation:

∫ √(1 + cosecx) dx

= ∫ √[(1 + cosecx)*(cosecx - 1)] / √(cosecx - 1) dx

= ∫ cotx / √(cosecx - 1) dx

= ∫ cosecx cotx dx / [cosecx √(cosecx - 1)]

Let cosecx - 1 = u^2

=> - cosecx cotx dx = 2udu

=> integral

= - 2 ∫ u du / [(u^2 + 1) * u]

= - 2 arctanu + c

= - 2arctan(√(cosecx - 1) + c.

hope it will help u