Exercises for Question Type 5: Integrating rational functions using partial fractions (linear factors)

Question 1

Skill question

Find $\int \frac{1}{x ^{2} - 7 x + 10} d x$ .

[5]

Question 2

Skill question

Compute $\int \frac{2 x - 3}{x ^{2} - 5 x + 6} d x$ .

[4]

Question 3

Skill question

Find $\int \frac{2 x + 1}{x ^{2} + 4 x + 3} d x$ .

[5]

Question 4

Skill question

Evaluate $\int \frac{5 x + 2}{x ^{2} - 9} d x$ .

[5]

Question 5

Skill question

Find $\int \frac{3 x - 2}{x ^{2} + x - 12} d x$ . [6]

[6]

Question 6

Skill question

Evaluate the integral $\int \frac{3 x + 5}{x ^{2} - x - 6} d x$ .

[5]

Question 7

Skill question

Compute $\int \frac{2 x + 3}{x ^{2} + 2 x - 8} d x$ .

[6]

Question 8

Skill question

Evaluate $\int \frac{x + 4}{x ^{2} - 6 x + 5} d x$ .

[5]

Question 9

Skill question

Find $\int \frac{4 x + 7}{x ^{2} - 2 x - 3} d x$ .

[7]

Question 10

Skill question

Evaluate $\int \frac{4 x - 1}{x ^{2} - 4} d x$ .

[6]

Question 11

Skill question

Find $\int \frac{1}{( x - 2 ) ( x + 3 )} d x$ .

[4]

Question 12

Skill question

Evaluate the integral $\int \frac{x}{x ^{2} - 3 x - 28} d x$ .

[6]

IB Mathematics Analysis and Approaches Question Type 5: Integrating Rational Functions Using Partial Fractions Exercises