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Examples with partial integration

 

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Example 1a

For the indefinite integral we state

Through partial integration we get

so that

 

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Example 1b

For the same indefinite integral we now state

Through partial integration we get

so that

 

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Additional information

This primitive function has two different solutions. You can write that as

and for the correct values of C_sin and C_cos that provides the Pythagorean identity

 

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