I am reading "Inside Interesting Integrals" by Paul Nahin. Around pg. 59, he goes through a lengthy explanation of how to do the definite integral from 0 to infinity of ∫1/(x4+1)dx. However, he then simply writes down that this integral is equal to ∫x2/(x4+1)dx with the same limits. Now, it's easy to pop these into an integral calculator and see that they are in fact both equal to 1.1107... = (π√2)/4, but how can I see that they should be equal to each other without actually calculating the value for each? In other words, if you just showed me ∫1/(x4+1)dx = ∫x2/(x4+1)dx , I would be suspicious because of the different numerators but apparently I would be wrong. Why?