I miscopied the signs on the last term the final answer when I combined both parts of the integral. The computations of the two integrals is correct, so please refer to those! The final term should go: +,- on numerator and +,+ on denominator. Annotations have been added to show these corrections.
This is the most difficult integral that I have solved so far. If you can think of harder one, let me know! Remember to submit any questions / requests that you may have to get your own solution video like this one! Enjoy.