If no one does this by night time and I can remember, I will look at it around 1 am or 2 am

For the second part, write x - 1 as x + 1 - 2 so that x + 1 divided by the fraction leads to cancellation of the numerator and the denominator while the -2 divided by the denominator can be obtained by multiplying the first part show results by -2.

For the resulting integral in variable u, we can also do partial fractions before integrating the result as well, since

2 / (x² - 1)

decomposes into

1 / (x - 1) minus 1 / (x + 1).