# Some Tricks Exercises

### Example 1

Apply the formula for integration by parts with *u* = ln* x* and *v'* = 1 to find

### Example 2

Use integration by parts to find .

### Example 3

Find

by applying the formula for integration by parts with *u* = *x*^{3} and *v'* = *x*^{2}*e*^{x3}.

### Example 4

Find

### Example 5

Use integration by parts to find

taking *u* = sin *x* for the first integration.

### Example 6

Integrate.

### Example 7

Integrate.

### Example 8

Integrate.

### Example 9

Integrate.

### Example 10

Integrate.

### Example 11

Integrate.

### Example 12

Integrate.