An improper integral is a definite integral that has either or both limits infinite or an integrand
that approaches infinity at one or more points in the
range of integration. Improper integrals cannot be computed using a normal Riemann
integral.

For example, the integral

(1)

is an improper integral. Some such integrals can sometimes be computed by replacing infinite limits with finite values

with one infinitelimit and the other nonzero may also be expressed as finite integrals
over transformed functions. If decreases at least as fast as , then let