$\int e^x(x+1)^2 dx=$

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

$\int e^{\cos ^{-1} x} \left[ \frac{x-\sqrt{1-x^{2}}}{\sqrt{1-x^{2}}} \right] dx =$

$\int {{e^{2x}}\left( {\frac{{\sin 4x - 2}}{{1 - \cos 4x}}} \right)\;dx = } $

$\int \frac{e^{\sqrt{x}}}{\sqrt{x}} (x + \sqrt{x}) \, dx$

$\int {{e^x}\left( {\frac{{1 - \sin x}}{{1 - \cos x}}} \right)dx}$ is equal to