BUG: is_integer_dtype does not consider Int16Dtype as an integer dtype

[DriesSchaumont]

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Reproducible Example

>>> import pandas as pd
>>> pd.api.types.is_integer_dtype(pd.DataFrame([1, 2], dtype=pd.Int16Dtype()))
False

Issue Description

According to the docs (https://pandas.pydata.org/docs/reference/api/pandas.api.types.is_integer_dtype.html):

The nullable Integer dtypes (e.g. pandas.Int64Dtype) are also considered as integer by this function.

Expected Behavior

Should return True

Installed Versions

commit : 06d2301
python : 3.8.10.final.0
python-bits : 64
OS : Linux
OS-release : 5.4.0-91-generic
Version : #102-Ubuntu SMP Fri Nov 5 16:31:28 UTC 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.4.1
numpy : 1.22.2
pytz : 2021.3
dateutil : 2.8.2
pip : 20.0.2
setuptools : 44.0.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None

[asishm]

Changing the DataFrame to a Series works. Don't think this method supports passing DataFrame as input - the docs mention array-like. The primary reason is probably because dataframes can have multiple dtypes.

[mroeschke]

Correct, is_*_dtypes are only meant to work on scalars and 1D array likes so this behavior is expected

[jreback]

i suppose might be worth adding to the doc string with this as a counter example