# Choosing an Integration Method Exercises

### Example 1

For the integral,

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 2

For the integral,

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 3

For the integral,

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 4

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 5

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 6

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 7

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 8

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 9

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 10

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 11

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 12

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 13

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 14

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 15

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 16

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 17

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 18

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 19

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 20

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 21

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.

### Example 22

a. Determine whether the integral should be integrated by substitution, parts, partial fractions, or thinking backwards (no fancy techniques required).

b. If you said 'substitution' for part (a), identify *u*. If you said `parts', identify *u* and *v*'. If you said `thinking backwards', go ahead and find the integral.