### The Maxima on-line user's manual

Algebra Calculator

#### Integrate_use_rootsof

-- Option variable: integrate_use_rootsof Default value: `false`

When `integrate_use_rootsof` is `true` and the denominator of a rational function cannot be factored, `integrate` returns the integral in a form which is a sum over the roots (not yet known) of the denominator.

For example, with `integrate_use_rootsof` set to `false`, `integrate` returns an unsolved integral of a rational function in noun form:

```          (%i1) integrate_use_rootsof: false\$
(%i2) integrate (1/(1+x+x^5), x);
/  2
[ x  - 4 x + 5
I ------------ dx                            2 x + 1
]  3    2                2            5 atan(-------)
/ x  - x  + 1       log(x  + x + 1)          sqrt(3)
(%o2)   ----------------- - --------------- + ---------------
7                 14             7 sqrt(3)```

Now we set the flag to be true and the unsolved part of the integral will be expressed as a summation over the roots of the denominator of the rational function:

```          (%i3) integrate_use_rootsof: true\$
(%i4) integrate (1/(1+x+x^5), x);
====        2
\       (%r4  - 4 %r4 + 5) log(x - %r4)
>      -------------------------------
/                    2
====            3 %r4  - 2 %r4
3    2
%r4 in rootsof(x  - x  + 1)
(%o4) ----------------------------------------------------------
7```

2 x + 1 2 5 atan(-------) log(x + x + 1) sqrt(3) - --------------- + --------------- 14 7 sqrt(3)

Alternatively the user may compute the roots of the denominator separately, and then express the integrand in terms of these roots, e.g., `1/((x - a)*(x - b)*(x - c))` or `1/((x^2 - (a+b)*x + a*b)*(x - c))` if the denominator is a cubic polynomial. Sometimes this will help Maxima obtain a more useful result.

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

### Related Examples

##### integrate_use_rootsof

? integrate_use_rootsof;

Calculate

##### integrate_use_rootsof-true

integrate_use_rootsof...

integrate (1/(1+x+x^5...

Calculate

##### integrate_use_rootsof

? integrate_use_rootsof;

Calculate

##### integrate_use_rootsof-true

integrate_use_rootsof...

integrate (1/(1+x+x^5...

Calculate