[Maxima-bugs] [maxima:bugs] #5712 integrate(%e^atanh(x), x) returns a noun form

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

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**[bugs:#5712] integrate\(%e^atanh\(x\), x\) returns a noun form**

**Status:** open
**Group:** None
**Labels:** integrate 
**Created:** Sat Oct 24, 2026 10:44 AM UTC by David Scherfgen
**Last Updated:** Sat Oct 24, 2026 10:44 AM UTC
**Owner:** nobody


By Claude:

`integrate` cannot integrate `%e^atanh(x)`:

```
(%i1) integrate(%e^atanh(x), x);
(%o1) 'integrate(%e^atanh(x),x)
```

But `%e^atanh(x) = sqrt(1+x)/sqrt(1-x)`, since `atanh(x) = (log(1+x)-log(1-x))/2`, as `logarc` writes it, and `integrate` finds the integral of that form:

```
(%i2) integrate(sqrt(1+x)/sqrt(1-x), x);
(%o2) asin(x)-sqrt(1-x^2)
```

The same holds for other powers of `%e^atanh(u)` and `%e^acoth(u)` times algebraic functions, such as `x^4*%e^atanh(a*x)`.


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