What is the Integral of Y=1/(1+x^4)?

Answer 1

This is not easy to compute!
However I will give you a hint:
x^4 + 1 = (x²+√2x + 1)(x²-√2x+1).
Now use partial fractions on the denominator.
You will get 2 log terms and 2 arctan terms in your
final answer.
Good luck!