Evaluate the following integrals : ∫sinx/√(4cos^x-1) dx ​

Question

Evaluate the following integrals:

\(\int\frac{sin\,x}{\sqrt{4cos^2x-1}}\)dx

Answer 1

Let,

2cosx = t

Then,

dt = -2sinx dx

Or, sinx dx = \(-\frac{dt}{2}\)

Therefore,

 \(\int\frac{sin\,x}{\sqrt{4cos^2x-1}}\)dx

=  \(\int-\frac{dt}{2\sqrt{(t^2-1^2)}}\)

Since,