# problems with symbolic integration and then numerical evaluating

can anyone explain this:

```
sage: integrate(legendre_P(64,x)*sin((1+x)*pi/2),x,-1,1).n()
1.16508247725542e79
```

from approximation one know's that the legendre coefficients converge exponentially to zero and not to infinity!

and indeed with mpmath I get a better answer:

```
sage: import sage.libs.mpmath.all as mpmath
sage: mpmath.call(mpmath.quad,lambda x: mpmath.legendre(64,x)*mpmath.sin(pi/2*(x+1)),[-1,1])
-5.04684703543649e-25
```

Is there an overhead happening, when I numerically evaluate large rationals or something???

Thanks in advance, maldun