please explain direction formula in integration with examples

Dear Krish,

Some of the formulas used in integration are :

1:

1A:

where  is a constant

2:

where  is a constant

3:

4: 

5: 

6:

7:

8:Integration by Substitution

  where  and

9: Integration by Parts

10: 

11: 

12: 

13: 

14:

15:

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