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In this work, we investigate one class of Volterra type
integral equation, in model case, when kernels have first order fixed
singularity and logarithmic singularity. In detail study the case, when n = 3. In depend of the signs parameters solution to this integral
equation can contain three arbitrary constants, two arbitrary constants, one
constant and may have unique solution. In the case when general solution of integral equation
contains arbitrary constants, we stand and investigate
different boundary value problems, when conditions are given in singular point.
Besides for considered integral equation, the solution found cane represented
in generalized power series. Some results obtained in the general model case.