So, I have got another problem and can't figure out where is my mistake,

I have the following integral

, I considered

and proceeded as follows:

here, I considered that I can do some simplifications and

obtained that

,

but by evaluating it further and doing all the math I don't get the correct answer,

I saw that and thought that I can't do the simplifications since they are still

and

,

so, I considered them separately, even though it seems wrong for me

, but this also, as I expected, wrong,

please, can someone show me the mistake(s)?