How do I solve integrals like these ones?

[lasvegas666]

I know that directly asking someone else for an answer is not the way to solve these questions.

I want to be able to solve logarithmic integrals like these ten on my own, and I would like help with at least one of the questions and also with the general methodology for solving these integrals because it's confusing.

 

[mario99]

Use integration by parts.

hint: [imath]\displaystyle \int u \ dv = uv - \int v \ du[/imath]

 

[khansaheb]

I know that directly asking someone else for an answer is not the way to solve these questions.

I want to be able to solve logarithmic integrals like these ten on my own, and I would like help with at least one of the questions and also with the general methodology for solving these integrals because it's confusing.

View attachment 37647

Please use the hints supplied with your problems and show us your progress.