>>5

1/(x^4 +a^4) =
　　= 1/{[x^2 -(√2)ax +a^2][x^2 +(√2)ax +a^2]}
　　= {1/(2√2)a^3}{[-x+(√2)a]/[x^2 -(√2)ax +a^2] + [x+(√2)a]/[x^2 +(√2)ax +a^2]}