All seven variables are real numbers. Is it possible to obtain an analytical solution?

Analytical no posssible .

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

The rules explain how to format your code properly. Posting code Images doesn’t help other members to copy your code. Please next time make sure code blocks start on a new paragraph and look framed and colored like this.

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

You can also embed notebook or attach notebook.