 TOPICS  # Inverse Function Integration

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)

so (2)

where (3)

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.

Integration, Integration by Parts

This entry contributed by Bhuvanesh Bhatt

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## References

Key, E. "Disks, Shells, and Integrals of Inverse Functions." Coll. Math. J. 25, 136-138, 1994.Parker, F. D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955.

## Referenced on Wolfram|Alpha

Inverse Function Integration

## Cite this as:

Bhatt, Bhuvanesh. "Inverse Function Integration." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/InverseFunctionIntegration.html