Series of object/strings cannot be converted to Int64Dtype()
**Edited to add information.**

#### Code Sample, a copy-pastable example if possible

```python
a  = pd.Series(['123', '345', '456'])
a.astype(int)            # works
a.astype('Int64')      # doesn't work
```
#### Problem description

Currently, the conversion of object dtypes (containing strings) to Int64 doesn't work, even though it should be able to. It produces a long error (see at the end).

**Important to note:** the above is trying to convert to `Int64` with the capital I. Those are the new nullable-integer arrays that got added to `python`. `pandas` seems to support them, yet I think something inside `astype` wasn't update to reflect that.

In essence, the above should work; there is no reason why it should fail and it's quite simply a bug (in answer to some comments). Moreover, `to_numeric` is not a sufficient replacement here; it doesn't convert to `Int64` when there are missing datatypes, instead it converts to `float` automatically (this is actually a non-trivial problem when dealing with long integer identifiers, such as GAIA target identifiers).

**Traceback:**

<details>

```
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-2-5778d49bfa2e> in <module>()
      2 a  = pd.Series(['123', '345', '456'])
      3 print(a.astype(int))
----> 4 print(a.astype('Int64'))

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/generic.py in astype(self, dtype, copy, errors, **kwargs)
   5880             # else, only a single dtype is given
   5881             new_data = self._data.astype(
-> 5882                 dtype=dtype, copy=copy, errors=errors, **kwargs
   5883             )
   5884             return self._constructor(new_data).__finalize__(self)

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/internals/managers.py in astype(self, dtype, **kwargs)
    579 
    580     def astype(self, dtype, **kwargs):
--> 581         return self.apply("astype", dtype=dtype, **kwargs)
    582 
    583     def convert(self, **kwargs):

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/internals/managers.py in apply(self, f, axes, filter, do_integrity_check, consolidate, **kwargs)
    436                     kwargs[k] = obj.reindex(b_items, axis=axis, copy=align_copy)
    437 
--> 438             applied = getattr(b, f)(**kwargs)
    439             result_blocks = _extend_blocks(applied, result_blocks)
    440 

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/internals/blocks.py in astype(self, dtype, copy, errors, values, **kwargs)
    557 
    558     def astype(self, dtype, copy=False, errors="raise", values=None, **kwargs):
--> 559         return self._astype(dtype, copy=copy, errors=errors, values=values, **kwargs)
    560 
    561     def _astype(self, dtype, copy=False, errors="raise", values=None, **kwargs):

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/internals/blocks.py in _astype(self, dtype, copy, errors, values, **kwargs)
    641                     # _astype_nansafe works fine with 1-d only
    642                     vals1d = values.ravel()
--> 643                     values = astype_nansafe(vals1d, dtype, copy=True, **kwargs)
    644 
    645                 # TODO(extension)

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/dtypes/cast.py in astype_nansafe(arr, dtype, copy, skipna)
    648     # dispatch on extension dtype if needed
    649     if is_extension_array_dtype(dtype):
--> 650         return dtype.construct_array_type()._from_sequence(arr, dtype=dtype, copy=copy)
    651 
    652     if not isinstance(dtype, np.dtype):

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/arrays/integer.py in _from_sequence(cls, scalars, dtype, copy)
    321     @classmethod
    322     def _from_sequence(cls, scalars, dtype=None, copy=False):
--> 323         return integer_array(scalars, dtype=dtype, copy=copy)
    324 
    325     @classmethod

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/arrays/integer.py in integer_array(values, dtype, copy)
    105     TypeError if incompatible types
    106     """
--> 107     values, mask = coerce_to_array(values, dtype=dtype, copy=copy)
    108     return IntegerArray(values, mask)
    109 

/home/sestovic/anaconda3/lib/python3.6/site-packages/pandas/core/arrays/integer.py in coerce_to_array(values, dtype, mask, copy)
    190         ]:
    191             raise TypeError(
--> 192                 "{} cannot be converted to an IntegerDtype".format(values.dtype)
    193             )
    194 

TypeError: object cannot be converted to an IntegerDtype
```

</details>

#### Expected Output

#### Output of ``pd.show_versions()``

<details>

[paste the output of ``pd.show_versions()`` here below this line]
INSTALLED VERSIONS
------------------
commit           : None
python           : 3.6.8.final.0
python-bits      : 64
OS               : Linux
OS-release       : 4.18.16-041816-generic
machine          : x86_64
processor        : x86_64
byteorder        : little
LC_ALL           : None
LANG             : en_GB.UTF-8
LOCALE           : en_GB.UTF-8

pandas           : 0.25.1
numpy            : 1.14.3
pytz             : 2018.4
dateutil         : 2.7.3
pip              : 19.1.1
setuptools       : 39.1.0
Cython           : 0.28.2
pytest           : 3.5.1
hypothesis       : None
sphinx           : 1.7.4
blosc            : None
feather          : None
xlsxwriter       : 1.0.4
lxml.etree       : 4.2.1
html5lib         : 1.0.1
pymysql          : None
psycopg2         : None
jinja2           : 2.10
IPython          : 6.4.0
pandas_datareader: None
bs4              : 4.6.0
bottleneck       : 1.2.1
fastparquet      : None
gcsfs            : None
lxml.etree       : 4.2.1
matplotlib       : 3.1.1
numexpr          : 2.6.5
odfpy            : None
openpyxl         : 2.5.3
pandas_gbq       : None
pyarrow          : None
pytables         : None
s3fs             : None
scipy            : 1.1.0
sqlalchemy       : 1.2.7
tables           : 3.4.3
xarray           : None
xlrd             : 1.1.0
xlwt             : 1.3.0
xlsxwriter       : 1.0.4
</details>
