Evaluate : ∫ [1+√(|x|-x)]e^x + (√(|x|-x))e^x / e^x+e^(-x) dx x ∈ to (-1, 1)

Question

Evaluate : \(\int_\limits{-1}^1 \frac{[1+\sqrt{|x|-x}] e^x + (\sqrt{|x|-x})e^{-x}}{e^x+e^{-x}} dx\) 

Answer 1

Answer is:   \(1+\frac{2\sqrt2}{3}\) 

Apply king property

\(I = 1+\frac{2\sqrt2}{3}\)