# integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer

HI everybody,

```
var('x u m')
assume(x>0)
assume(m>0)
assume(m<1)
integral(rho*sqrt(1/(-m*sin(u)^2 +1)),(u,0,x))
```

returns

```
2*rho*x/m
```

Expected answer is

```
elliptic_f(x,m)
```

Does anyone know how to fix this ?

Thank you.

What is

`rho`

!?rho is a constant

returns

Seems a (Maxima) bug.

`giac`

and`fricas`

explicitely fail to integrate (retun the unevaluated integral and`"failed"`

respectively`mathematica`

returns the expected result (along with (reasonable) conditions.`maple`

return a suspiciously complicated expression involving`elliptic_f`

, which I was unable to simplify`sympy`

does not returnWorth a ticket (+ upstream bug report) ?