My question as hinted at in the headline, do you have a recommendations for a book, where explicitly these types of problems are discussed? No sure about $\int_{-\infty}^{\infty} ...dx$.
2026-04-02 12:56:52.1775134612
How to calculate integrals like $\int_{-\infty}^{\infty} e^{-x^2} dx$?
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This integral is very famous and is called the Gaussian integral. There is a wikipedia page dedicated to this integral where you can find multiple proofs that $$ \int_{-\infty}^{+\infty}e^{-x^2}dx=\sqrt{\pi}. $$ As for studying integrals that involve infinite bounds (they are called improper integrals) you can read the great wikipedia page.