[Maxima-bugs] [maxima:bugs] #5711 integrate() reads c^3 as c+3 in (c-c*x)^3/((1-x)^3*sqrt(1-x^2))

[David S. <tom...@us...>]

- **status**: open --> closed
- **Comment**:

Fixed by commit [8f787d].



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**[bugs:#5711] integrate\(\) reads c^3 as c+3 in \(c-c\*x\)^3/\(\(1-x\)^3\*sqrt\(1-x^2\)\)**

**Status:** closed
**Group:** None
**Labels:** integrate 
**Created:** Sat Oct 24, 2026 10:42 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:42 AM UTC
**Owner:** nobody


By Claude:

`integrate` gives a wrong result for a product of a polynomial and a square root:

```
(%i1) integrate((c-c*x)^3/((1-x)^3*sqrt(1-x^2)), x);
(%o1) c*asin(x)+3*asin(x)
```

The integrand is `c^3/sqrt(1-x^2)`, so the result should be `c^3*asin(x)`. It is as if `c^3` were read as `c+3`. A similar integrand ends in a Lisp error:

```
(%i2) integrate(sqrt(1+x)/sqrt(1-x)*(c-c*x), x);
Maxima encountered a Lisp error:
 The value
   $C
 is not of type
   LIST
```

Here the integrand is `c*sqrt(1-x^2)`, and the result should be `c*asin(x)/2+c*x*sqrt(1-x^2)/2`.


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