## Integrals

# Integration by Partial Fractions

** TIPS FOR SOLVING INTEGRATING FUNCTIONS**

- Integrals which are in the form

\int \frac{f(x)}{g(x)} dx (Where degree of f(x) < degree of g(x)) **Process :**using the process of partial fractions by the following procedure

\frac{1}{(x+a)(x+b)} = \frac{A}{x+a} + \frac{B}{x+b}

\frac{1}{(x+a)^{2} (x+b)} = \frac{A}{(x+a)} + \frac{B}{(x+a)^{2}} + \frac{C}{(x+b)}

\frac{1}{(x+a)(x^{2}+b)} = \frac{A}{x+a} + \frac{Bx+c}{x^{2}+b}

### View the Topic in this video From 13:35 To 48:50

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S.No |
Form of the rational function |
Form of the partial fraction |

1. |
\frac{px+q}{(x-a)(x-b)},a\neq b | \frac{A}{x-a}+\frac{B}{x-b} |

2. |
\frac{px+q}{(x-a)^2} | \frac{A}{x-a}+\frac{B}{(x-a)^2} |

3. |
\frac{px^2+qx+r}{(x-a)(x-b)(x-c)} | \frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{x-c} |

4. |
\frac{px^2+qx+r}{(x-a)^2(x-b)} | \frac{A}{x-a}+\frac{B}{(x-a)^2}+\frac{C}{x-b} |

5. |
\frac{px^2+qx+r}{(x-a)(x^2+bx+c)} | \frac{A}{x-a}+\frac{Bx+C}{x^2+bx+c} |

where *x ^{2} + bx +c* cannot be factorised further