I have created trigger for after insert now how to do for update with in same trigger

Hi,

Here's how to do it (changes in bold):

CREATE TRIGGER [dbo].[INSERT_IM_ServiceRequest_Hx] ON [dbo].[IM_ServiceRequest] AFTER INSERT, UPDATE
AS

BEGIN

DECLARE @Action AS CHAR(1) = 'I'; -- after insert (by default)
IF EXISTS (SELECT 1 FROM INSERTED) AND EXISTS (SELECT 1 from DELETED)
    SET @Action = 'U'; -- after update
IF (@Action = 'I')
    BEGIN
        INSERT INTO  IM_ServiceRequest_Hx
        SELECT * FROM IM_ServiceRequest
        PRINT 'AFTER INSERT Trigger fired.'
    END
IF (@Action = 'U')
    BEGIN
    -- your code here
    END
END

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Added information:
1. Simplified trigger syntax:

CREATE TRIGGER trigger_name
ON { table | view }
{ FOR | AFTER | INSTEAD OF } { [ INSERT ] [ , ] [ UPDATE ] [ , ] [ DELETE ] }

2. There are 2 special tables in trigger statements: inserted and deleted. Inserted table stores copies of the affected rows after INSERT and UPDATE. Deleted table stores copies of the affected rows after DELETE and UPDATE.

AFTER INSERT: 1 or more records in INSERT table, 0 records in DELETE table.
AFTER UPDATE: 1 or more records in INSERT table, 1 or more records in DELETE table.
AFTER DELETE: 0 records in INSERT table, 1 or more records in DELETE table.

Knowing this, you can determine certain event: AFTER INSERT, UPDATE or DELETE.