Evaluate: ∫ ((e^cos^-1 x)(sin^-1 x))/√(1-x^2), x ∈ [1/√2,1]

Question

Evaluate:

\(\int_{1/\sqrt{2}}^1 \cfrac{(e^{cos^{-1}})(sin^{-1}x)}{\sqrt{1-x^2}}.dx\)

∫ ((e ^{cos^-1 x})(sin^-1 x))/√(1-x²), x ∈ [1/√2,1]

Answer 1

Let \(I\) = \(\int_{1/\sqrt{2}}^1 \cfrac{(e^{cos^{-1}})(sin^{-1}x)}{\sqrt{1-x^2}}.dx\)