Variance of first $$2 n$$ natural numbers is

$$\int \frac{x-3}{(x-1)^3} e^x d x=$$

If $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ are non-coplanar unit vectors such that $$\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\frac{\mathbf{b}+\mathbf{c}}{\sqrt{2}}$$, then the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$ is

$$\int \frac{2+\cos \frac{x}{2}}{x+\sin \frac{x}{2}} d x=$$