Suppose I have a complicated integral whose exact evaluation seems extremely difficult or may be even impossible, in such a case is there any way to tell if the integration result is finite or not? suppose the problem is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int_{-\infty}^{\infty} f(x;a,b) dx

[/tex]

I think there might be some conditions on the function involved. Actually the function contains some parameters also (a,b) which can be taken to be constants for a particular case. Now I am looking for a condition general enough to handle arbitrary parameters, ie, can I tell if the integral is finite for any arbitrary values of those parameters? If yes, then how or under what condition? Take as an example:

[tex]

\int_{-\infty}^{\infty} e^{-2a \tanh^2(bx)} dx

[/tex]

Is this finite?

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# How to test if a definite integral is finite or not?

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