[分析] 初微(4)

[plover (>//////<)]

Let a and b be positive. Show that

    +∞   -a(x^2) - (b/x^2)
    ∫  e                   dx = (1/2)√(π/a) e^( -2√(ab) ).
     0

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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 219.68.227.219
※ 編輯: plover          來自: 219.68.227.219       (07/01 22:25)
→ akrsw:z = x - sqrt(b/a)/x and
→ akrsw:x = z/2 + sqrt(z^2/4 + sqrt(b/a))
→ akrsw:變數變換