Hello! I was very tormented with this Lebesgue-related problem. I searched the whole Internet, but I didn't find a solution (maybe I was looking in the wrong places). The task looks like this: Is the function integrable by Lebesgue on a ray (-∞,-1)? [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-3-13-png.4063/[/IMG] if it is, then find its value. I've tried to find Riemann improper integral [CENTER][IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-8-56-png.4064/[/IMG] [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-9-5-png.4065/[/IMG] [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-9-14-png.4066/[/IMG] [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-9-20-png.4067/[/IMG] [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-9-27-png.4068/[/IMG] [IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-9-50-png.4069/[/IMG][/CENTER] But in the end, there happens division by zero (in first addendum) [CENTER][IMG]https://www.math-forums.com/attachments/upload_2023-1-13_10-10-56-png.4070/[/IMG][/CENTER] I'm not asking for a complete solution, but at least a hint in which direction to move, which theorems to use, otherwise I'm completely desperate. Thanks! PS I'm sorry if there is some wrong terminology - I'm not native english speaker