### Examples with partial integration

##### Example 1

For the indefinite integral we state

Through partial integration we get

so that

##### Example 2

The indefinite integral can be written as and we state

Through partial integration we get

so that

##### Example 3

The indefinite integral can be written as and we state

Through partial integration we get

so that

##### Example 4

The indefinite integral can be written as and we state

Through partial integration we get

so that

##### Example 5

The indefinite integral can be written as and we state

Through partial integration we get

For the last term we now state

and through further partial integration we get

so that

##### Example 6

The indefinite integral can be written as and we state

Through partial integration we get

so that

##### Example 7

For the indefinite integral we state

Through partial integration we get

so that