由分部积分法得
∫du/(u^2+a^2) = u/(u^2+a^2) + ∫2u^2du/(u^2+a^2)^2
= u/(u^2+a^2) + ∫2(u^2+a^2-a^2)du/(u^2+a^2)^2
= u/(u^2+a^2) + 2 ∫du/(u^2+a^2) -2a^2 ∫du/(u^2+a^2)^2
则 2a^2 ∫du/(u^2+a^2)^2 = u/(u^2+a^2) + ∫du/(u^2+a^2),
∫du/(u^2+a^2)^2 = (1/2a^2)[u/(u^2+a^2) + ∫du/(u^2+a^2)]
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