Core 3: Integration Skills

Content

1)           Key integration facts

2)          Indefinite integration by substitution

3)          Indefinite Integration by-parts

4)          Key trigonometry facts

5)          Definite integration by by-parts

6)          Definite integration by substitution and some extra facts


 

Key integration facts

Make sure you learn and comfortable with the following facts


 

Integration by substitution

Accustom yourself with the following integral types

This transforms to

 

 

The terms outside the bracket is the same order as the differential of the term inside the bracket.

Let u=

Observe how the  ‘cancels’

 

 

When the power of x is at most 1 both outside and inside the bracket

Let u=3x+2

Rearrange to find x in terms of u.