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# Indefinite Integration

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### Indefinite Integration

1. 1. INDEFINITE INTEGRATION
2. 2.
3. 3. STANDARD FORMULA
4. 4.
5. 5.
6. 6.
7. 7. THEOREMS ON INTEGRATION
8. 8. EXAMPLES
9. 9. INTEGRATION BY SUBSTITUTIONSIf we substitute x = (t) in a integral then everywhere x will be replaced in terms of t. dx also gets converted in terms of dt. (t) should be able to take all possible value that x can take.
10. 10. EXAMPLES
11. 11. INTEGRATION BY PART
12. 12. EXAMPLES
13. 13. INTEGRATION OF RATIONAL ALGEBRAICFUNCTIONS BY USING PARTIAL FRACTIONS
14. 14.
15. 15.
16. 16.
17. 17.
18. 18.
19. 19. EXAMPLES
20. 20. Express ax2 + bx + c in the form of perfect square & thenapply the standard results.
21. 21. EXAMPLES
22. 22. Express px + q = A (differential co-efficient of denominator)+ B.
23. 23. EXAMPLES
24. 24. INTEGRATION OF TRIGONOMETRIC FUNCTIONS
25. 25. EXAMPLE
26. 26. Case - IIf m and n are even natural number then converts higherpower into higher angles.Case - IIIf at least m or n is odd natural number then if m is odd putcos x = t and vice-versa.Case - IIIWhen m + n is a negative even integer then put tanx = t.
27. 27. EXAMPLES
28. 28.
29. 29. EXAMPLES
30. 30. INTEGRATION OF TYPE
31. 31. INTEGRATION OF TYPE
32. 32. EXAMPLES
33. 33. INTEGRATION OF TYPE
34. 34.
35. 35.
36. 36.
37. 37.
38. 38. EXAMPLES