Integrale improprio svolto con il metodo dei residui

How to solve a definite (improper) integral using the residue method . After having discussed the residue method , we take the opportunity to solve an improper integral for which integrand function is complicated to find a primitive using elementary integration methods . After having demonstrated that the improper integral exists finite (integrability criteria) we will extend the integrand function to a complex function of complex variable and in the Gaussian plane we will determine a generally regular curve in order to apply the residue theorem . Here are some preparatory lessons to better understand this lesson: Integrability criterion in the case of a limited domain, but with an "infinity" point    • Integrali impropri o generalizzati su inte...   Integrability criterion in the case of an unlimited integration domain    • Integrali impropri su intervalli illimitat...   Logarithm in the field of complex numbers and "cut plane"    • Il logaritmo nel campo complesso .   Isolated singular points    • Punti singolari : polo , singolarità fitti...   Residue method    • Integrali con il teorema dei residui .   #salvoromeo #metododeiresidui