diff --git a/pandas/core/algorithms.py b/pandas/core/algorithms.py
index 840e79c6c9ebe..9749297efd004 100644
--- a/pandas/core/algorithms.py
+++ b/pandas/core/algorithms.py
@@ -445,6 +445,8 @@ def isin(comps: AnyArrayLike, values: AnyArrayLike) -> np.ndarray:
     elif isinstance(values, ABCMultiIndex):
         # Avoid raising in extract_array
         values = np.array(values)
+    else:
+        values = extract_array(values, extract_numpy=True)
 
     comps = _ensure_arraylike(comps)
     comps = extract_array(comps, extract_numpy=True)
@@ -459,11 +461,14 @@ def isin(comps: AnyArrayLike, values: AnyArrayLike) -> np.ndarray:
     elif needs_i8_conversion(values.dtype) and not is_object_dtype(comps.dtype):
         # e.g. comps are integers and values are datetime64s
         return np.zeros(comps.shape, dtype=bool)
+        # TODO: not quite right ... Sparse/Categorical
+    elif needs_i8_conversion(values.dtype):
+        return isin(comps, values.astype(object))
 
-    comps, dtype = _ensure_data(comps)
-    values, _ = _ensure_data(values, dtype=dtype)
-
-    f = htable.ismember_object
+    elif is_extension_array_dtype(comps.dtype) or is_extension_array_dtype(
+        values.dtype
+    ):
+        return isin(np.asarray(comps), np.asarray(values))
 
     # GH16012
     # Ensure np.in1d doesn't get object types or it *may* throw an exception
@@ -476,23 +481,15 @@ def isin(comps: AnyArrayLike, values: AnyArrayLike) -> np.ndarray:
             f = lambda c, v: np.logical_or(np.in1d(c, v), np.isnan(c))
         else:
             f = np.in1d
-    elif is_integer_dtype(comps.dtype):
-        try:
-            values = values.astype("int64", copy=False)
-            comps = comps.astype("int64", copy=False)
-            f = htable.ismember_int64
-        except (TypeError, ValueError, OverflowError):
-            values = values.astype(object)
-            comps = comps.astype(object)
-
-    elif is_float_dtype(comps.dtype):
-        try:
-            values = values.astype("float64", copy=False)
-            comps = comps.astype("float64", copy=False)
-            f = htable.ismember_float64
-        except (TypeError, ValueError):
-            values = values.astype(object)
-            comps = comps.astype(object)
+
+    else:
+        common = np.find_common_type([values.dtype, comps.dtype], [])
+        values = values.astype(common, copy=False)
+        comps = comps.astype(common, copy=False)
+        name = common.name
+        if name == "bool":
+            name = "uint8"
+        f = getattr(htable, f"ismember_{name}")
 
     return f(comps, values)
 
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index d836ca7a53249..35411d7e9cfb7 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1044,7 +1044,6 @@ def test_different_nans_as_float64(self):
         expected = np.array([True, True])
         tm.assert_numpy_array_equal(result, expected)
 
-    @pytest.mark.xfail(reason="problem related with issue #34125")
     def test_isin_int_df_string_search(self):
         """Comparing df with int`s (1,2) with a string at isin() ("1")
         -> should not match values because int 1 is not equal str 1"""
@@ -1053,7 +1052,6 @@ def test_isin_int_df_string_search(self):
         expected_false = DataFrame({"values": [False, False]})
         tm.assert_frame_equal(result, expected_false)
 
-    @pytest.mark.xfail(reason="problem related with issue #34125")
     def test_isin_nan_df_string_search(self):
         """Comparing df with nan value (np.nan,2) with a string at isin() ("NaN")
         -> should not match values because np.nan is not equal str NaN"""
@@ -1062,7 +1060,6 @@ def test_isin_nan_df_string_search(self):
         expected_false = DataFrame({"values": [False, False]})
         tm.assert_frame_equal(result, expected_false)
 
-    @pytest.mark.xfail(reason="problem related with issue #34125")
     def test_isin_float_df_string_search(self):
         """Comparing df with floats (1.4245,2.32441) with a string at isin() ("1.4245")
         -> should not match values because float 1.4245 is not equal str 1.4245"""