XII Maths Chapter 7. Integrals | Page 14

Shortcut for Finding Values of A , B and C etc .
Case I . When g ( x ) is expressible as the product of non-repeated line factors .
Trick To find A p put x = a in numerator and denominator after P deleting the factor ( x — ap ). Case II . When g ( x ) is expressible as product of repeated linear factors .
Here , all the constant cannot be calculated by using the method in Case I . However , Bl , B2 , B3 , … , Bn can be found using the same method i . e ., shortcut can be applied only in the case of non-repeated linear factor .
Integration of Irrational Algebraic Function
Irrational function of the form of ( ax + b ) 1 / n and x can be evaluated by substitution ( ax + b ) = t n , thus