2x2 10x 9  x3 dx (x2 9) (x 2) 10. 3 dx Hint: a3 + b3 = (a + b) (a2 a b + b2) – 11. dx 3 a3 - b3 = (a - b) (a2 + a b + b2) 12. 3 dx Summary You have learnt the following from this chapter: i). Splitting a fraction into partial fractions. Type I: (x (x (x a)(x b) a) b)  ax b Type II: A B C (x a)(x b)(x b) (x x a x b b)2     ax b Type III: A Bx  C 2 ( x a px2  qx  r)   Type IV: For improper algebraic fraction, we must divide and consider only the remainder for partial fraction. ii). After partial fractions, integrand is transformed into the form of basic formula which can be integrated. Further Reading 1. Additional pure mathematics By L. Harwood Clarke. Heinemann Educational Books Ltd London. 62 CHAPTER 7
x3  2x2 10x 9 (x2 9) dx 10. (x 2) 3 dx Hint: a3 + b3 = (a + b) (a2 – a b + b2) 11. dx 3 a3 - b3 = (a - b) (a2 + a b + b2) 12. 3 dx Summary You have learnt the following from this chapter: i). Splitting a fraction into partial fractions. Type I: (x a)(x b) (x a) (x b) Type II: ax  b (x a)(x b)(x b)  A x a  B x b  C (x b)2 Type III: ax  b 2  A x a  Bx  C ( px2  qx  r) Type IV: For improper algebraic fraction, we must divide and consider only the remainder for partial fraction. ii). After partial fractions, integrand is transformed into the form of basic formula which can be integrated. Further Reading 1. Additional pure mathematics By L. Harwood Clarke. Heinemann Educational Books Ltd London. 62 CHAPTER 7
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