Evaluate the integral

Question

Evaluate  

Answer 1

Perform the substitution u = 1 + sin(x)

Then du = cos(x)dx and the integral is ∫u^-1/2du = 2u^1/2 + C = √(1+sin(x)) + C

Answer 2

Make the substitution u=sin x which will convert the integrand to (1+u)^-1/2.