讨论了一类特殊的反常积分，称为反常Frullani 积分，它们形似Frullani 积分，然而不满足Frullani 积分存在条件.从两个基本的反常Frullani 积分出发，导出了一系列的方程Frullani 积分.

A series of improper integrals，anomaly Frullani integrals，are discussed. They cannot be ascribed to the famous Frullani integrals，although they are in the form similar to the Frullani integrals，but fail to meet the requirements for the latter. Many anomaly Frullani integrals are deduced from two typical ones.