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Function: quad_qawc (<f(x)>, <x>, <c>, <a>, <b>, [<epsrel>, <epsabs>, <limit>])

Function: quad_qawc (<f>, <x>, <c>, <a>, <b>, [<epsrel>, <epsabs>, <limit>]) Computes the Cauchy principal value of f(x)/(x - c) over a finite interval. The strategy is globally adaptive, and modified Clenshaw-Curtis integration is used on the subranges which contain the point x = c.

`quad_qawc` computes the Cauchy principal value of

integrate (f(x)/(x - c), x, a, b)

using the Quadpack QAWC routine. The function to be integrated is `<f(x)>/(<x> - <c>)`, with dependent variable <x>, and the function is to be integrated over the interval <a> to <b>.

The integrand may be specified as the name of a Maxima or Lisp function or operator, a Maxima lambda expression, or a general Maxima expression.

The keyword arguments are optional and may be specified in any order. They all take the form `key=val`. The keyword arguments are:

<epsrel> Desired relative error of approximation. Default is 1d-8.

<epsabs> Desired absolute error of approximation. Default is 0.

<limit> Size of internal work array. <limit> is the maximum number of subintervals to use. Default is 200.

`quad_qawc` returns a list of four elements:

* an approximation to the integral,

* the estimated absolute error of the approximation,

* the number integrand evaluations,

* an error code.

The error code (fourth element of the return value) can have the values:

`0` no problems were encountered;

`1` too many sub-intervals were done;

`2` excessive roundoff error is detected;

`3` extremely bad integrand behavior occurs;

`6` if the input is invalid.

Examples:

```          (%i1) quad_qawc (2^(-5)*((x-1)^2+4^(-5))^(-1), x, 2, 0, 5,
epsrel=1d-7);
(%o1)    [- 3.130120337415925, 1.306830140249558E-8, 495, 0]
(%i2) integrate (2^(-alpha)*(((x-1)^2 + 4^(-alpha))*(x-2))^(-1),
x, 0, 5);
Principal Value
alpha
alpha       9 4                 9
4      log(------------- + -------------)
alpha           alpha
64 4      + 4   64 4      + 4
(%o2) (-----------------------------------------
alpha
2 4      + 2```

3 alpha 3 alpha ------- ------- 2 alpha/2 2 alpha/2 2 4 atan(4 4 ) 2 4 atan(4 ) alpha - --------------------------- - -------------------------)/2 alpha alpha 2 4 + 2 2 4 + 2

`          (%i3) ev (%, alpha=5, numer);`
`          (%o3)                    - 3.130120337415917`

```(%o1)                                true
(%i2) ```

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