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.

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.