I am trying to numerically solve an integral in a specific region and then visualize it as follows.

```
RegionPlot3D(
NIntegrate(1/Sqrt(r) - 1/Sqrt(l + r Sin(t)), {r, l, t} ∈
ImplicitRegion(r + l Sin(t) > 0 && l > 0 && r > 0, {r, l, t})), {r,
0, 5}, {l, 0, 10}, {t, 0, pi/4})
```

However, Mathematica complains that

`NIntegrate::slwcon`

: Numerical integration that converges very slowly; suspect

of the following: singularity, the value of integration is 0, highly

integrating oscillatory, or WorkingPrecision too small.

Basically I tried to get rid of the potential singularities considering that region of specific integration. However, I have no idea about the slow convergence of highly oscillatory integrating.

**Edit 1:** There is also another warning that says

NIntegrate :: ncvb: NIntegrate could not converge to the prescribed accuracy

after 27 recursive bisections in l near {r, l, t} =

{0.184661,1.641681647898248 * 10 ^ 690538901,0.184661}. NIntegrate

obtained 8.935806122974667 * 10 ^ 22717757165 + 31581.2 I and

2.096578395728379`15.954589770191005 * ^ 22717757166 for comprehensive and error estimates.

How can I solve these problems?

**Edit 2**: What I'm really looking for is the 3D plot corresponding to the following integral function `F(l,theta)`

where `r`

It is a fixed number (say, 10 or whatever). I am particularly in trouble to get rid of the singularities and divergent subsets of the domains of the variable.