Evaluation of ∫ − ∞ ∞ x 2 ( e 2 x + 1 ) ( x 2 + 1 ) 2 d x

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Evaluation of       ∫          −      ∞              ∞                  x      2              (              e                  2          x                    +      1      )      (              x        2            +      1              )        2              d  x

Amir Beck · Accepted Answer

To elaborate on Quanto&#039;s comment, once you see that identity, your integral is simply       ∫    0    ∞    d  x      /    (  x  +  1      /    x      )    2    =      ∫    0    ∞              d      x              (      x      −      1              /            x              )        2            +      4        =      ∫    0    ∞              d      x                      x        2            +      4        =  π      /    4 by Glasser&#039;s Master theorem.

Evaluation of <msubsup> ∫ <mrow class="MJX-TeXAtom-ORD"> −<

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