The value of $\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{~d} x$ is equal to

If $\int \frac{x+1}{\sqrt{2 x-1}} \mathrm{~d} x=\mathrm{f}(x) \sqrt{2 x-1}+\mathrm{c}$, (where c is a constant of integration), then $\mathrm{f}(x)$ is equal to

The value of $\mathrm{I}=\int \frac{\mathrm{d} x}{x^2\left(x^4+1\right)^{\frac{3}{4}}}$ is

$\int\left(\mathrm{f}(x) \mathrm{g}^{\prime \prime}(x)-\mathrm{f}^{\prime \prime}(x) \mathrm{g}(x)\right) \mathrm{d} x$ is equal to