>>367
∫dx/(x^4+1) = (1/4)∫{(√2)x+2}/{x^2+(√2)x+1} + {2-(√2)x}/{x^2-(√2)x+1} dx
= (1/4)∫{(√2)x+1}/{x^2+(√2)x+1} + 1/{x^2+(√2)x+1}
+ {1-(√2)x}/{x^2-(√2)x+1} + 1/{x^2-(√2)x+1} dx
= (√2/4)*{(1/2)*log|{x^2+(√2)x+1}/{x^2-(√2)x+1}| + arctan((√2)x/(1-x^2))} + C