Evaluate: ∫ sin x/√(4+cos^2x)dx

Question

Evaluate: \(\int\cfrac{sinx}{\sqrt{4+cos^2x}}dx\)

∫ sin x/√(4+cos²x)dx

Answer 1

Tip – d(cosx) = - sinxdx i.e. sinxdx = - d(cosx)

Formula to be used - \(\int\cfrac{dx}{\sqrt{x^2\pm a^2}}=log(x+\sqrt{x^2\pm a^2})+c\) where c is the integrating constant

\(=-log|cosx+\sqrt{4+cos^2x}|+c\), c being the integrating constant