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How to find this integral

  1. Jun 2, 2010 #1
    Hi how to solve this type of integrals

    {t^{k+n}}/{(1+qt)(1+t)^{2k+3}}dt

    here n is natural number if some one know how to solve it with out n also it is okay.
     
  2. jcsd
  3. Jun 4, 2010 #2

    tiny-tim

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    Hi raghavendar24! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    The easiest way is probably to substitute u = 1+t, so that it becomes a sum of terms like 1/(a + bu)ur,

    and then use integration by parts on each term. :smile:
     
  4. Jun 4, 2010 #3
    Hi, thanks for reply,


    yeah if we substitute the transformation 1+u=t,

    the integral tourns out as

    Integrate[(u-1)^{k+n}/(1-q+bq)u^{2k+3},{u,1,2}]

    i am unable to solve it once again just using integral by parts
     
  5. Jun 4, 2010 #4

    tiny-tim

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    oops!

    uhh? :confused: oh-oooh :redface:
    oops! sorry! I meant use partial fractions. :blushing:

    Is that easier? :smile:
     
  6. Jun 8, 2010 #5
    Hie,


    unable to break it through partail fractions, so can i get any alternative idea to solve it
     
  7. Jun 11, 2010 #6
    How to solve the integral


    t^{k+1}/(1+qt)^{2k+2}dt, t from 0 to 1
     
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