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Integration of x/(a^2+x^2)^2/3

  1. May 27, 2014 #1
    in this video , the prof had to integrate x/(a^2+x^2)^3/2 , i know we usually do this using substitution , but in the video...he ignored the x and integrate like it was 1/(a^2+x^2)^3/2, how does that work?
    Last edited: May 27, 2014
  2. jcsd
  3. May 27, 2014 #2
    You will probably need to give more information about what he did.
  4. May 27, 2014 #3
    he said integration of x/(a^2+x^2)^3/2= x*(-2)/(a^2+x^2)^1/2*2x
    i really dont know what he did, he differentiated the bottom part then divided by new power and multiplied by differentiation of x^2
  5. May 27, 2014 #4
  6. May 27, 2014 #5
    there was a mistake with the powers in the question and i corrected it
  7. May 27, 2014 #6


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    Look carefully at the integrand x/(a^2+x^2)^(2/3). What is the derivative of (a^2+x^2)? Is it x times some constant perhaps? Can you rewrite the integrand as the product of two expressions, rather than the quotient?

    BTW, your video requires a login to view, so we can't see it.
  8. May 27, 2014 #7

    the power on the brakets is 3/2
  9. May 27, 2014 #8


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    The power on the brackets is immaterial. The principle remains.
  10. May 28, 2014 #9
    i figured out what he did, he differentiated the bottom part...and thats it
  11. May 28, 2014 #10


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    In other words he did exactly the "[itex]u= x^2+ a^2[/itex]" substitution, just not writing it out explicitly.
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