An automatic quadrature is presented for computing Cauchy principal value integrals
Q
(
f
;
c
)
=
₯
a
b
f
(
t
)
/
(
t
−
c
)
d
t
,
a
>
c
>
b
Q(f;c) = \fint _a^bf(t)/(t-c)\,dt, a > c > b
, for smooth functions
f
(
t
)
f(t)
. After subtracting out the singularity, we approximate the function
f
(
t
)
f(t)
by a sum of Chebyshev polynomials whose coefficients are computed using the FFT. The evaluations of
Q
(
f
;
c
)
Q(f;c)
for a set of values of c in (a, b) are efficiently accomplished with the same number of function evaluations. Numerical examples are also given.