Matematické Fórum

Skrytý text:

Step 1. We know that the function



is continuous and bounded. Hence,





Step 2. In the next step we use the itegration by parts to get the identity



In view of the fact that converges and is finite, for the given integral we get a (correct) equation:




Step 3. In the following step it suffices to compute the closed evalutation of the integral on the right hand side of the equation. This is however a known improper integral and the following idetity holds true:



This implies immediately that



Finally, the given integral has the closed evaluation in the form




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Remark. Note that the integral



can be evaluated in a similar manner. We can obtain that