Ch. 4 Integration - 1

Introduction

standard forms already learnt

∫sin x dx = - cos x + c
∫cos x dx = sin x + c

Ch. 4 Integration - 2

Indefinite integrals

Standard forms

Method of substitution
Linear substitution
Integrating powers of trigonometric functions
Integrating expressions having square roots

Ch. 4 Integration - 4

Integration by partial fractions

Distinct linear factors
(3x-4)/(x-1)(x-2) = 1/(x-1) + 2/(x-2)

disguised linear factors
(x² +15)/(x² -1)(x² +2)

Repeated linear factors
(5x² - 19x - 17)/(x-1)(x-2)²

Non repeated quadratic factors
If the denominator contains a factor ax² + bx + c then the fraction corresponding to it is
(px+ q)/(ax² + bx + c)