#### SamRoss

Gold Member

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- 11

^{4}+1)dx. However, he then simply writes down that this integral is equal to ∫x

^{2}/(x

^{4}+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/(x

^{4}+1)dx = ∫x

^{2}/(x

^{4}+1)dx , I would be suspicious because of the different numerators but apparently I would be wrong. Why?