![]() Since the Cauchy principal value has a precise mathematical definition, Mathematica should give the same result or decline to answer. Which is also clearly not defined at x=1. EDIT: The two expressions above should calculate the same result, the first by calculating a general form of the integral and evaluating it at x01, the second by performing the integral with x0 set to 1. When you solve the indefinite integral: Integrate) - 1/Sqrt, x] You can also see that when you plot the integrand for some values a and b: Plot) - (1/Sqrt) /. When x equals a the denominators become zero. The problem might be the singularity at the lower integration boundary.
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