Tuesday, January 4, 2022

12 Days of Christmas Integrals: ∫ (a ∙ b) ÷ (a^2 ∙ x^2 + b^2) dx; a,b are constants

 12 Days of Christmas Integrals:  ∫ (a ∙ b) ÷ (a^2 ∙ x^2 + b^2) dx; a, b are constants


On the Eleventh day of Christmas Integrals, the integral featured today is...


∫ (a ∙ b) ÷ (a^2 ∙ x^2 + b^2) dx; a, b are constants


A rather simple integral:


∫ (a ∙ b) ÷ (a^2 ∙ x^2 + b^2) dx


= a ∙ b ∙ ∫ 1÷ (a^2 ∙ x^2 + b^2) dx


= a ∙ b ∙ ∫ 1÷ (b^2 ∙ (a^2/b^2 ∙ x^2 + 1)) dx


= a/b ∙ ∫ 1÷ (a^2/b^2 ∙ x^2 + 1) dx


= ∫ (a/b) ÷ ((a/b)^2 ∙ x^2 + 1) dx


= arctan(a/b ∙ x) + C



Eddie 



All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Retro Review: Texas Instruments BA-Solar

Retro Review: Texas Instruments BA-Solar Finance + Solar + 1980s Quick Facts Model:  BA-Solar Company:  Texas Instruments Years:  1986 - 199...