This antiderivative has arguable the highest ratio of “really hard to compute” to “really easy to write”:
So far, I’ve shown that the denominator can be factored over the real numbers:
To evaluate the remaining two integrals, I’ll use the antiderivative
.
To begin, I’ll complete the squares:
Applying the substitutions and
, I can continue:
Combining, I finally arrive at the answer for :
Naturally, this can be checked by differentiation, but I’m not going type that out.
One thought on “The antiderivative of 1/(x^4+1): Part 6”