4:30 AM
@Fundamental Resolved.
After a question merge, this is now the parent question of the whole group.

4 hours later…
8:30 AM
@anorton That one was waiting in the starboard for a long time.
@anorton Reopened and unpinned.
@anorton After this reopening, should we choose one of these two questions and to be left open and close the other one as a duplicate? Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$ and How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
Oh I see. I should have noticed your comment.
Related problem (definite integral): math.stackexchange.com/q/43457/23353 (but not duplicate!) — anorton 4 hours ago
Well probably we could find several other questions about indefinite intergral closed as a duplicate of definite integral. But reopening and reclosing is probably too much fuss.