Why this indefinite integral cannot be solved ?$\int\ln(x)\sqrt{x^{2 }+ ax + b}\, dx$

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I am trying to find a solution to this integral. However I have found nothing that helps, even wolfram alpha can not solve this integral. What would be the secret about it, since it looks so simple ?

indefinite integral:

$\int \ln(x)\sqrt{x^{2 }+ ax + b}\, dx$

Anyone has a guess ?