13: If you decided on differentiation, you should get
This series has
Partial fractions go
These are again series leading to a logarithmic expansion, but the second series has to be adjusted first similarly to the first approach.
If you tried the third approach, you should get
Now it is time to integrate, it is necessary to use
integration by parts.
After integration there will be constant C, typically we would
determine its value by substituting 0 into the series and the resulting
expression on the right, but that is not possible here, since the
calculation above only works for non-zero x. To circumvent it, apply
limit for x going to 0 in that expression on the right to confirm
that