[理工] [工數] 複數積分
∞ 1 1 ∞ 1
∫─── dx = ─∫ ─── dx
0 x^3+1 2 -∞ x^3+1
1
令 f(z)= ─── 單極點 e^ iπ/3, e^ iπ, e^ i2π/3
z^3+1
e^ -i2π/3 1 2 2 1 2^0.5
Res(e^ iπ/3)= ────── = ─ (cos─π ─ isin─π)= ─ ─ ─ ───i
3 3 3 3 6 6
1
Res(e^ iπ) = ─
3
1 3^0.5
─ { 2πi[Res(e^ iπ/3]+ πi[Res(e^ iπ)]}= ─── π
2 6 .
2π
請問我哪邊算錯了? 為啥解答本是用多值函數路徑求法來算 答案為 ────
3x(3^0.5)
感謝
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