High School Integration of tan^2 x from - to + infinity

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SUMMARY

The integral ∫tan²(x) from -infinity to +infinity does not converge. This conclusion is supported by the identity 1 + tan²(x) = d/dx(tan(x)), indicating that the integral diverges due to the behavior of the tangent function at its asymptotes. The discussion arose within the context of quantum mechanics, highlighting the importance of understanding the convergence of integrals in advanced physics applications.

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stringsofphysics
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TL;DR
integral from minus to plus infinity of tan^2 x
∫tan^2 x ( -infinity to +infinity)
 
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This integral doesn’t converge. (Hint: ##1+\tan^2x=\frac{d}{dx}\tan x##)

Is there a certain context in which this appeared?

P.S. I assume the last thread was deleted by a mod. If so, this will probably also be deleted. You should provide your own efforts to solve the problem.
 
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Thank you for the reply, it appeared in a part of sum in quantum mechanics.

P.S. I am new to Physics forum. Sorry, not used to its norms
Thanks for inputs!
 
stringsofphysics said:
Thank you for the reply, it appeared in a part of sum in quantum mechanics.

P.S. I am new to Physics forum. Sorry, not used to its norms
Thanks for inputs!
If it's homework, and you would like help, we would like to help you with your homework in order to help you to learn; however, we don't want to just plain do it for you ##-## as @suremarc indicated, you should make and show an attempt ##-## and please use ##\mathrm {\LaTeX}## ##-## if it's not homework, please let us know ##-## your reply that included your saying "it appeared as part of a sum in quantum mechanics" leaves whether it's homework or not as something of a curiosity ##\dots##
 
Last edited:
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@stringsofphysics has been asked to repost in the schoolwork forums and show their work so that we can provide more tutorial help. This thread is closed.
 

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