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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

 


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