I have an integral of the form:

```
I = \int\limits_{-1}^{1} f(x)*w(x) dx,
```

The function `f(x)`

has a singularity of the form `1/(x-a)`

inside the interval [-1, 1], so that the integral `I`

exists only as a cauchy principal value. The weight function `w(x)`

also has a singularity of the form `log|x-b|`

at some point `b`

which may be different from the point `a`

.

Could anyone advise a good quadrature rule to deal with the cauchy principal value integral?

Is such a quadrature rule sensitive to the presence of other integrable singularities?

Maybe this rule is implemented in some Julia package?

Thank you in advance.