Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts.
If and are inverses of each other on some closed interval, then
(1)
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so
(2)
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where
(3)
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Therefore, if it is possible to find an inverse of , integrate , make the replacement , and subtract the result from to obtain the result for the original integral .
If and are elementary on some closed interval, then is elementary iff is elementary.