Using Rubi, you can investigate a bit further, what steps are required to find an antiderivative
<< Rubi`
int = Steps[Int[r^2 Sin[r^-3 * c], r]]
First, you can show that the solution is indeed one valid antiderivative of your expression:
In[31]:= D[int, r]
Out[31]= r^2 Sin[c/r^3]
Now, you can look at the limits of your integration bounds
In[32]:= Limit[int, r -> 0, Direction -> "FromAbove"]
Out[32]= ConditionalExpression[-(1/6) c (2 Log[c] - Log[c^2]), c \[Element] Reals]
This looks good, but this here not
In[33]:= Limit[int, r -> Infinity]
Out[33]= c \[Infinity]
Therefore, I suspect your version 10.4 result is not correct and the integral does not converge.
