Integral of 1/(1 + x^2) from 0 to infinity

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In this problem I work out the Integral of 1/(1 + x^2) from 0 to infinity. This problem appears in an old book called Integral Calculus. It was written by H.B. Phillips and it was published in 1917.

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This cost me like 10 points on an exam cuz I forgot the fact that 1/1+x^2 just equals arctanx. ;c

Suphii
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Appreciate your work man! Thanks for the math information!

RCSmiths
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Dear sorcerer, does calculus by spivak have any prerequisites except for proof writing or does it teach them in the way? Thanks in advance

mathpassion
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Perfect, more videos like that. Thanks!

ANTGPRO
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I m not able to solve maths so fast what should I do?

Sufiarsh
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Why do you suddenly use the word /arctan/ with no definition of such a thing, so that introducing an extra difficulty, a sort of noice, in your communication?

ernestoporrascollantes