Integrals using substitution $x\mapsto x+\frac{1}{x}$

Asked Dec 22 '15 at 17:46

Active Dec 22 '15 at 18:23

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Do you have some links to questions with integrals that require the substitution $x\mapsto x+\frac{1}{x}$ (as a trick)?

I know this trick, but I can't seem to find any integrals to practice it..

edited Dec 22 '15 at 18:23

asked Dec 22 '15 at 17:46

How about $\int \cos (x + \frac{1}{x}) (1-\frac{1}{x^2}) , dx$? :) – MathMajor Dec 22 '15 at 17:48
@MathMajor Haha well I mean integrals which require this substitution as a 'trick'.. :) – Dr. Heinz Doofenshmirtz Dec 22 '15 at 17:49
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I suppose you want exercises that involve multiple substitutions, among which $x \mapsto x + 1/x$? Otherwise, knowing that you need the very substitution you asked for would render them trivial, right? – Lynn Dec 22 '15 at 18:30
Worth mentioning: http://math.stackexchange.com/questions/457231/how-to-prove-int-infty-infty-fxdx-int-infty-infty-f-left/963490 – JMoravitz Dec 22 '15 at 18:35

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