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.

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. Monthly62, 439-440, 1955.