If \( \displaystyle \int e^x \left( \frac{x\sin^{-1}x}{\sqrt{1-x^2}} + \frac{\sin^{-1}x}{(1-x^2)^{3/2}} + \frac{x}{1-x^2} \right) dx = g(x) + C \), where \( C \) is the constant of integration, then \(\displaystyle g\left(\frac{1}{2}\right) \) equals:
