1. Integration and the Logarithmic Functiondx x 1 x ∫
dx = ∫ =
logex + C
f’(x)
f(x) ∫ = dx
logef(x) + C
Exercise 4.6 (page 146)

2. Integration and the Logarithmic Function
Example 1/3 [ ]
logex 1 2 2 1 x ∫
Area =
dx = 1
= loge2 – loge1
= loge(2÷1)
Exercise 4.6 (page 146)
= loge2 units2

3. Integration and the Logarithmic Function
f’(x)
f(x) = dy dx
Example 2/3 x2
x3 + 7
3x2
x3 + 7 ∫ dx 1 3 ∫
dx =
= loge(x3 + 7) + C 1 3
Exercise 4.6 (page 146)
f’(x)
f(x) ∫ = dx
logef(x) + C

4. Integration and the Logarithmic Function
f’(x)
f(x) = dy dx
Example 3/3
x + 1
x2 + 2x + 4
2(x + 1)
x2 + 2x + 4 ∫ dx 1 2 ∫
dx =
2x + 2
x2 + 2x + 4 ∫ dx 1 2 =
Exercise 4.6 (page 146)
= loge(x2 + 2x + 4) + C 1 2