If $\int \mathrm{f}(x) \mathrm{d} x=\psi(x)$, then $\int x^5 \mathrm{f}\left(x^3\right) \mathrm{d} x$ is equal to

If $\int \frac{d x}{\sqrt[3]{\sin ^{11} x \cos x}}=-\left(\frac{3}{8} f(x)+\frac{3}{2} g(x)\right)+c$ then

$\int \frac{x^4+x^2+1}{x^2-x+1} d x$ is equal to

The value of $I=\int \frac{(x-1) \mathrm{e}^x}{(x+1)^3} \mathrm{dx}$ is