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

Question

Evaluate the following integrals :

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

Answer 1

Assume,

x - cosx = t 

⇒ d(x - cosx) = dt 

⇒ (1 + sinx )dx = dt 

∴ Substituting t and dt in given equation we get

But,

t = x – cosx. 

⇒ 2(x - cosx)^1/2 + c.