How do I choose which term do I differentiate/integrate when I am integrating by parts

What you would do in this scenario is consider all the terms in the expression you are integrating. You then want to go through the acronym LATE to choose which term you should differentiate.L stands for Logs (including Ln)A stands for Algebra (regular terms such as x, x^2 etc)T stands for Trig (sin,cos,tan etc)E stands for e^x (Euler's number)Once you have decided which of the terms rank higher in this list, that will be the term you differentiate meanwhile the other term you will integrate.