How do I Calculate, if possible, in terms of well-known constants the integral :

$\int_{0}^{1}x^{k}\psi(x)dx$ , where $k\geq 3$ is an integer ?

note: $\psi(x)$ is digamma function.

Any help is very welcom .

How do I Calculate, if possible, in terms of well-known constants the integral :

$\int_{0}^{1}x^{k}\psi(x)dx$ , where $k\geq 3$ is an integer ?

note: $\psi(x)$ is digamma function.

Any help would be greatly appreciated.