Advanced Techniques to compute improper integrals using a CAS
AbstractIn this work we will deal with advance techniques to compute certain types of improper integrals using a CAS. Laplace and Fourier transforms or Residue Theorem in Complex Analysis are some advance techniques which can be used for this matter.
We will introduce the file ImproperIntegrals.mth, developed in DERIVE 6, which deals with such computations. Some CAS use different rules for computing integrations. For example
Rubi system, a rule-based integrator developed by Albert Rich (see http://www.apmaths.uwo.ca/~arich/), is a very powerful system for computing integrals using rules. We will be able to develop new rules schemes for some improper integrals using
ImproperIntegrals.mth. These new rules can extend the types of improper integrals that a CAS can compute.