INDEFINITE INTEGRATION

STANDARD FORMULA



THEOREMS ON INTEGRATION
EXAMPLES
INTEGRATION BY SUBSTITUTIONSIf we substitute x = (t) in a integral then   everywhere x will be replaced in terms of t.  ...
EXAMPLES
INTEGRATION BY PART
EXAMPLES
INTEGRATION OF RATIONAL ALGEBRAICFUNCTIONS BY USING PARTIAL FRACTIONS
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



EXAMPLES
Express ax2 + bx + c in the form of perfect square & thenapply the standard results.
EXAMPLES
Express px + q = A (differential co-efficient of denominator)+ B.
EXAMPLES
INTEGRATION OF TRIGONOMETRIC FUNCTIONS
EXAMPLE
Case - IIf m and n are even natural number then converts higherpower into higher angles.Case - IIIf at least m or n is odd...
EXAMPLES

EXAMPLES
INTEGRATION OF TYPE
INTEGRATION OF TYPE
EXAMPLES
INTEGRATION OF TYPE




EXAMPLES
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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

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