There was an error on this week's homework set, fixed now. The integrand in the second integral in question 1 should have had a 1 - x^2 + x^4 in the denominator, rather than 1 + x^2 + x^4. If you have already solved the problem with the original integral you may submit what you have for full marks, there is no need to rewrite it (just please make sure your paper indicates clearly which integrand you were using!). I apologise for that!
The solutions to the make-up term test are now available here; they may be useful for the current homework set.
I think I am almost caught up in replying to your e-mails, and will do my best to finish entirely soon. If I have not responded to an urgent query, please feel free to write me again.
Please let me know if you have any questions!
Nathan