Integration by applying Partial Fractions PDF

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Summary

Integration by Partial Fractions If the integrand (the expression after the integral sign) is in the form of an algebraic fraction and the integral cannot be evaluated by simple methods, the fraction needs to be expressed in partial fractions before integration takes place....

Description

Partial Fractions

1. Completing the square if table of dz is used

ax2  bx  c

is irreducible. The the

2. If ax2  bx  c is reducible then the fraction is resolved into partial fraction and a table of standard integrals is used. Rules to resolve a fraction into its partial form: 

Factorise the quadratic expression then on top of linear factors write



For linear repeated factor write



If the irreducible quadratic expression is irreducible then write



For a repeated irreducible quadratic factor write

Example

Exercises 3x 2  5x  12 1. dx 2 x2 4





3

4x  6x 2  32x  45 2.  dx x4  16 x2 2x 3  x 2  4 3.  dx 2 x2  4





2

2x  11x  25 dx  x  5 x 2  8 x  25 dx 5.  2 x x  x 1 4. 









2

6. 

x  x  14

 x  2 x2  4

x 1 7.  2 dx x  x  1

dx

A ax  b

B A + ax  b  ax  b  2

Ax  B ax  bx  c 2

Cx  D Ax  B + 2 2 ax  bx  c ax  bx  c  2...