# an integral with arccos wrong

The value of the integral `integrate(exp(arccos(x)),x,0,1)`

is badly return by
Sage. However, `sympy_integrator`

or `giac_integrator`

give the exact value
(and also the primitive), maxima giving the same wrong value than Sage (the both unable to give a primitive)

```
sage: integrate(exp(arccos(x)),x,0,1)
-1/2*e^(-1/2*pi) + 1/2
```

Calculus gives through the change of variable x=cos t the equality

```
sage: integrate(exp(t)*sin(t),t,0,pi/2)
1/2*e^(1/2*pi) + 1/2
from sage.symbolic.integration.external import sympy_integrator
sympy_integrator(exp(arccos(x)), x, 0, 1)
1/2*e^(1/2*pi) + 1/2
# GOOD
from sage.symbolic.integration.external import maxima_integrator
maxima_integrator(exp(arccos(x)), x, 0, 1)
-1/2*e^(-1/2*pi) + 1/2
# BAD
from sage.symbolic.integration.external import giac_integrator
giac_integrator(exp(arccos(x)), x, 0, 1)
1/2*e^(1/2*pi) + 1/2
# GOOD
```