The integral $\int \frac{2 x^3-1}{x^4+x} \mathrm{~d} x$ is equal to

If $\int \frac{\log \left(t+\sqrt{1+t^2}\right)}{\sqrt{1+t^2}} d t=\frac{1}{2}(g(t))^2+c$ where c is a constant of integration, then $\mathrm{g}(2)$ is equal to

$$\int \operatorname{cosec}(x-a) \cdot \operatorname{cosec} x d x=$$

$\int\left(1+x-\frac{1}{x}\right) \mathrm{e}^{x+\frac{1}{x}} \mathrm{~d} x$ is equal to