What did you get for your partial-fraction decomposition? Because I got
but it doesn't look like it would lead to your final step.
Partial Fractions yields
The second integral can be evaluated as follows,
Now let's look at
What happens when we try to make this look like the inverse tan integral?
If you expand inside the integral (to check that we have done this correctly) we will see that
It should be obvious then that,
I leave you to consider